ConnectPP 0.6.1
Sean Holden
University of Cambridge, United Kingdom
Solution for SEU140+2
% Formula: antisymmetry_r2_hidden ( axiom ) (definitionally) converted to clauses:
cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% Formula: antisymmetry_r2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(antisymmetry_r2_xboole_0-1, axiom, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
% Formula: commutativity_k2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(commutativity_k2_xboole_0-1, axiom, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
% Formula: commutativity_k3_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(commutativity_k3_xboole_0-1, axiom, ( ( set_intersection2(_u7, _u6) = set_intersection2(_u6, _u7)) )).
% Formula: d10_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d10_xboole_0-1, axiom, ( ( _u9 != _u8) | ~def0(_u8, _u9) )).
cnf(d10_xboole_0-2, axiom, ( ~subset(_u9, _u8) | ~subset(_u8, _u9) | ( _u9 = _u8) )).
cnf(d10_xboole_0-3, axiom, ( def0(_u8, _u9) | subset(_u9, _u8) )).
cnf(d10_xboole_0-4, axiom, ( def0(_u8, _u9) | subset(_u8, _u9) )).
% Formula: d1_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d1_xboole_0-1, axiom, ( ( _u12 != empty_set) | ~in(_u10, _u12) )).
cnf(d1_xboole_0-2, axiom, ( in(skolem1(_u12), _u12) | ( _u12 = empty_set) )).
% Formula: d2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d2_xboole_0-1, axiom, ( ( _u15 != set_union2(_u17, _u16)) | ~def2(_u15, _u16, _u17, _u13) )).
cnf(d2_xboole_0-2, axiom, ( ~def3(_u15, _u16, _u17) | ~def4(_u15, _u16, _u17) | ( _u15 = set_union2(_u17, _u16)) )).
cnf(d2_xboole_0-3, axiom, ( def2(_u15, _u16, _u17, _u13) | ~in(_u13, _u15) | in(_u13, _u17) | in(_u13, _u16) )).
cnf(d2_xboole_0-4, axiom, ( def2(_u15, _u16, _u17, _u13) | ~def1(_u16, _u17, _u13) | in(_u13, _u15) )).
cnf(d2_xboole_0-5, axiom, ( def1(_u16, _u17, _u13) | ~in(_u13, _u17) )).
cnf(d2_xboole_0-6, axiom, ( def1(_u16, _u17, _u13) | ~in(_u13, _u16) )).
cnf(d2_xboole_0-7, axiom, ( def3(_u15, _u16, _u17) | in(skolem2(_u17, _u16, _u15), _u15) )).
cnf(d2_xboole_0-8, axiom, ( def3(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u17) )).
cnf(d2_xboole_0-9, axiom, ( def3(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u16) )).
cnf(d2_xboole_0-10, axiom, ( def4(_u15, _u16, _u17) | in(skolem2(_u17, _u16, _u15), _u17) | in(skolem2(_u17, _u16, _u15), _u16) )).
cnf(d2_xboole_0-11, axiom, ( def4(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u15) )).
% Formula: d3_tarski ( axiom ) (definitionally) converted to clauses:
cnf(d3_tarski-1, axiom, ( ~subset(_u21, _u20) | ~in(_u18, _u21) | in(_u18, _u20) )).
cnf(d3_tarski-2, axiom, ( ~def5(_u21, _u20) | subset(_u21, _u20) )).
cnf(d3_tarski-3, axiom, ( def5(_u21, _u20) | in(skolem3(_u21, _u20), _u21) )).
cnf(d3_tarski-4, axiom, ( def5(_u21, _u20) | ~in(skolem3(_u21, _u20), _u20) )).
% Formula: d3_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d3_xboole_0-1, axiom, ( ( _u24 != set_intersection2(_u26, _u25)) | ~def7(_u22, _u24, _u25, _u26) )).
cnf(d3_xboole_0-2, axiom, ( ~def8(_u24, _u25, _u26) | ~def9(_u24, _u25, _u26) | ( _u24 = set_intersection2(_u26, _u25)) )).
cnf(d3_xboole_0-3, axiom, ( def7(_u22, _u24, _u25, _u26) | ~in(_u22, _u24) | ~def6(_u22, _u25, _u26) )).
cnf(d3_xboole_0-4, axiom, ( def7(_u22, _u24, _u25, _u26) | ~in(_u22, _u26) | ~in(_u22, _u25) | in(_u22, _u24) )).
cnf(d3_xboole_0-5, axiom, ( def6(_u22, _u25, _u26) | in(_u22, _u26) )).
cnf(d3_xboole_0-6, axiom, ( def6(_u22, _u25, _u26) | in(_u22, _u25) )).
cnf(d3_xboole_0-7, axiom, ( def8(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u24) )).
cnf(d3_xboole_0-8, axiom, ( def8(_u24, _u25, _u26) | ~in(skolem4(_u26, _u25, _u24), _u26) | ~in(skolem4(_u26, _u25, _u24), _u25) )).
cnf(d3_xboole_0-9, axiom, ( def9(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u26) )).
cnf(d3_xboole_0-10, axiom, ( def9(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u25) )).
cnf(d3_xboole_0-11, axiom, ( def9(_u24, _u25, _u26) | ~in(skolem4(_u26, _u25, _u24), _u24) )).
% Formula: d4_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d4_xboole_0-1, axiom, ( ( _u29 != set_difference(_u31, _u30)) | ~def11(_u30, _u31, _u27, _u29) )).
cnf(d4_xboole_0-2, axiom, ( ~def12(_u30, _u31, _u29) | ~def13(_u30, _u31, _u29) | ( _u29 = set_difference(_u31, _u30)) )).
cnf(d4_xboole_0-3, axiom, ( def11(_u30, _u31, _u27, _u29) | ~in(_u27, _u29) | ~def10(_u30, _u31, _u27) )).
cnf(d4_xboole_0-4, axiom, ( def11(_u30, _u31, _u27, _u29) | ~in(_u27, _u31) | in(_u27, _u30) | in(_u27, _u29) )).
cnf(d4_xboole_0-5, axiom, ( def10(_u30, _u31, _u27) | in(_u27, _u31) )).
cnf(d4_xboole_0-6, axiom, ( def10(_u30, _u31, _u27) | ~in(_u27, _u30) )).
cnf(d4_xboole_0-7, axiom, ( def12(_u30, _u31, _u29) | in(skolem5(_u31, _u30, _u29), _u29) )).
cnf(d4_xboole_0-8, axiom, ( def12(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u31) | in(skolem5(_u31, _u30, _u29), _u30) )).
cnf(d4_xboole_0-9, axiom, ( def13(_u30, _u31, _u29) | in(skolem5(_u31, _u30, _u29), _u31) )).
cnf(d4_xboole_0-10, axiom, ( def13(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u30) )).
cnf(d4_xboole_0-11, axiom, ( def13(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u29) )).
% Formula: d7_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d7_xboole_0-1, axiom, ( ~disjoint(_u33, _u32) | ( set_intersection2(_u33, _u32) = empty_set) )).
cnf(d7_xboole_0-2, axiom, ( ( set_intersection2(_u33, _u32) != empty_set) | disjoint(_u33, _u32) )).
% Formula: d8_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(d8_xboole_0-1, axiom, ( ~proper_subset(_u35, _u34) | ~def14(_u34, _u35) )).
cnf(d8_xboole_0-2, axiom, ( ~subset(_u35, _u34) | ( _u35 = _u34) | proper_subset(_u35, _u34) )).
cnf(d8_xboole_0-3, axiom, ( def14(_u34, _u35) | subset(_u35, _u34) )).
cnf(d8_xboole_0-4, axiom, ( def14(_u34, _u35) | ( _u35 != _u34) )).
% Formula: dt_k1_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(dt_k1_xboole_0, axiom, $true).
% Formula: dt_k2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(dt_k2_xboole_0, axiom, $true).
% Formula: dt_k3_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(dt_k3_xboole_0, axiom, $true).
% Formula: dt_k4_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(dt_k4_xboole_0, axiom, $true).
% Formula: fc1_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% Formula: fc2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(fc2_xboole_0-1, axiom, ( empty(_u37) | ~empty(set_union2(_u37, _u36)) )).
% Formula: fc3_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(fc3_xboole_0-1, axiom, ( empty(_u39) | ~empty(set_union2(_u38, _u39)) )).
% Formula: idempotence_k2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(idempotence_k2_xboole_0-1, axiom, ( ( set_union2(_u41, _u41) = _u41) )).
% Formula: idempotence_k3_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(idempotence_k3_xboole_0-1, axiom, ( ( set_intersection2(_u43, _u43) = _u43) )).
% Formula: irreflexivity_r2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(irreflexivity_r2_xboole_0-1, axiom, ( ~proper_subset(_u45, _u45) )).
% Formula: l32_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(l32_xboole_1-1, lemma, ( ( set_difference(_u47, _u46) != empty_set) | subset(_u47, _u46) )).
cnf(l32_xboole_1-2, lemma, ( ~subset(_u47, _u46) | ( set_difference(_u47, _u46) = empty_set) )).
% Formula: rc1_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(rc1_xboole_0-1, axiom, ( empty(skolem6) )).
% Formula: rc2_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem7) )).
% Formula: reflexivity_r1_tarski ( axiom ) (definitionally) converted to clauses:
cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u51, _u51) )).
% Formula: symmetry_r1_xboole_0 ( axiom ) (definitionally) converted to clauses:
cnf(symmetry_r1_xboole_0-1, axiom, ( ~disjoint(_u53, _u52) | disjoint(_u52, _u53) )).
% Formula: t12_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t12_xboole_1-1, lemma, ( ~subset(_u55, _u54) | ( set_union2(_u55, _u54) = _u54) )).
% Formula: t17_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t17_xboole_1-1, lemma, ( subset(set_intersection2(_u57, _u56), _u57) )).
% Formula: t19_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t19_xboole_1-1, lemma, ( ~subset(_u60, _u59) | ~subset(_u60, _u58) | subset(_u60, set_intersection2(_u59, _u58)) )).
% Formula: t1_boole ( axiom ) (definitionally) converted to clauses:
cnf(t1_boole-1, axiom, ( ( set_union2(_u61, empty_set) = _u61) )).
% Formula: t1_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t1_xboole_1-1, lemma, ( ~subset(_u64, _u63) | ~subset(_u63, _u62) | subset(_u64, _u62) )).
% Formula: t26_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t26_xboole_1-1, lemma, ( ~subset(_u67, _u66) | subset(set_intersection2(_u67, _u65), set_intersection2(_u66, _u65)) )).
% Formula: t28_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t28_xboole_1-1, lemma, ( ~subset(_u69, _u68) | ( set_intersection2(_u69, _u68) = _u69) )).
% Formula: t2_boole ( axiom ) (definitionally) converted to clauses:
cnf(t2_boole-1, axiom, ( ( set_intersection2(_u70, empty_set) = empty_set) )).
% Formula: t2_tarski ( axiom ) (definitionally) converted to clauses:
cnf(t2_tarski-1, axiom, ( ~def15(_u72, _u73) | ~def16(_u72, _u73) | ( _u73 = _u72) )).
cnf(t2_tarski-2, axiom, ( def15(_u72, _u73) | in(skolem8(_u73, _u72), _u73) )).
cnf(t2_tarski-3, axiom, ( def15(_u72, _u73) | ~in(skolem8(_u73, _u72), _u72) )).
cnf(t2_tarski-4, axiom, ( def16(_u72, _u73) | in(skolem8(_u73, _u72), _u72) )).
cnf(t2_tarski-5, axiom, ( def16(_u72, _u73) | ~in(skolem8(_u73, _u72), _u73) )).
% Formula: t2_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t2_xboole_1-1, lemma, ( subset(empty_set, _u74) )).
% Formula: t33_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t33_xboole_1-1, lemma, ( ~subset(_u77, _u76) | subset(set_difference(_u77, _u75), set_difference(_u76, _u75)) )).
% Formula: t36_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t36_xboole_1-1, lemma, ( subset(set_difference(_u79, _u78), _u79) )).
% Formula: t37_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t37_xboole_1-1, lemma, ( ( set_difference(_u81, _u80) != empty_set) | subset(_u81, _u80) )).
cnf(t37_xboole_1-2, lemma, ( ~subset(_u81, _u80) | ( set_difference(_u81, _u80) = empty_set) )).
% Formula: t39_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t39_xboole_1-1, lemma, ( ( set_union2(_u83, set_difference(_u82, _u83)) = set_union2(_u83, _u82)) )).
% Formula: t3_boole ( axiom ) (definitionally) converted to clauses:
cnf(t3_boole-1, axiom, ( ( set_difference(_u84, empty_set) = _u84) )).
% Formula: t3_xboole_0 ( lemma ) (definitionally) converted to clauses:
cnf(t3_xboole_0-1, lemma, ( disjoint(_u88, _u87) | ~def17(_u87, _u88) )).
cnf(t3_xboole_0-2, lemma, ( ~in(_u86, _u88) | ~in(_u86, _u87) | ~disjoint(_u88, _u87) )).
cnf(t3_xboole_0-3, lemma, ( def17(_u87, _u88) | in(skolem9(_u88, _u87), _u88) )).
cnf(t3_xboole_0-4, lemma, ( def17(_u87, _u88) | in(skolem9(_u88, _u87), _u87) )).
% Formula: t3_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t3_xboole_1-1, lemma, ( ~subset(_u89, empty_set) | ( _u89 = empty_set) )).
% Formula: t40_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t40_xboole_1-1, lemma, ( ( set_difference(set_union2(_u91, _u90), _u90) = set_difference(_u91, _u90)) )).
% Formula: t45_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t45_xboole_1-1, lemma, ( ~subset(_u93, _u92) | ( _u92 = set_union2(_u93, set_difference(_u92, _u93))) )).
% Formula: t48_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t48_xboole_1-1, lemma, ( ( set_difference(_u95, set_difference(_u95, _u94)) = set_intersection2(_u95, _u94)) )).
% Formula: t4_boole ( axiom ) (definitionally) converted to clauses:
cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u96) = empty_set) )).
% Formula: t4_xboole_0 ( lemma ) (definitionally) converted to clauses:
cnf(t4_xboole_0-1, lemma, ( disjoint(_u100, _u99) | in(skolem10(_u100, _u99), set_intersection2(_u100, _u99)) )).
cnf(t4_xboole_0-2, lemma, ( ~in(_u98, set_intersection2(_u100, _u99)) | ~disjoint(_u100, _u99) )).
% Formula: t60_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t60_xboole_1-1, lemma, ( ~subset(_u102, _u101) | ~proper_subset(_u101, _u102) )).
% Formula: t63_xboole_1 ( conjecture ) (definitionally) converted to clauses:
cnf(t63_xboole_1-1, negated_conjecture, ( subset(skolem11, skolem12) )).
cnf(t63_xboole_1-2, negated_conjecture, ( disjoint(skolem12, skolem13) )).
cnf(t63_xboole_1-3, negated_conjecture, ( ~disjoint(skolem11, skolem13) )).
% Formula: t6_boole ( axiom ) (definitionally) converted to clauses:
cnf(t6_boole-1, axiom, ( ~empty(_u106) | ( _u106 = empty_set) )).
% Formula: t7_boole ( axiom ) (definitionally) converted to clauses:
cnf(t7_boole-1, axiom, ( ~in(_u108, _u107) | ~empty(_u107) )).
% Formula: t7_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t7_xboole_1-1, lemma, ( subset(_u110, set_union2(_u110, _u109)) )).
% Formula: t8_boole ( axiom ) (definitionally) converted to clauses:
cnf(t8_boole-1, axiom, ( ~empty(_u112) | ( _u112 = _u111) | ~empty(_u111) )).
% Formula: t8_xboole_1 ( lemma ) (definitionally) converted to clauses:
cnf(t8_xboole_1-1, lemma, ( ~subset(_u115, _u114) | ~subset(_u113, _u114) | subset(set_union2(_u115, _u113), _u114) )).
% Problem matrix:
cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_union2(__eqx_0, __eqx_1) = set_union2(__eqy_0, __eqy_1)) )).
cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_intersection2(__eqx_0, __eqx_1) = set_intersection2(__eqy_0, __eqy_1)) )).
cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem4(__eqx_0, __eqx_1, __eqx_2) = skolem4(__eqy_0, __eqy_1, __eqy_2)) )).
cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem9(__eqx_0, __eqx_1) = skolem9(__eqy_0, __eqy_1)) )).
cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def0(__eqx_0, __eqx_1) | def0(__eqy_0, __eqy_1) )).
cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def1(__eqx_0, __eqx_1, __eqx_2) | def1(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~def2(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | def2(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def3(__eqx_0, __eqx_1, __eqx_2) | def3(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def4(__eqx_0, __eqx_1, __eqx_2) | def4(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def5(__eqx_0, __eqx_1) | def5(__eqy_0, __eqy_1) )).
cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def6(__eqx_0, __eqx_1, __eqx_2) | def6(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~def7(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | def7(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def8(__eqx_0, __eqx_1, __eqx_2) | def8(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def9(__eqx_0, __eqx_1, __eqx_2) | def9(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def10(__eqx_0, __eqx_1, __eqx_2) | def10(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~def11(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | def11(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def12(__eqx_0, __eqx_1, __eqx_2) | def12(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~def13(__eqx_0, __eqx_1, __eqx_2) | def13(__eqy_0, __eqy_1, __eqy_2) )).
cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def14(__eqx_0, __eqx_1) | def14(__eqy_0, __eqy_1) )).
cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def15(__eqx_0, __eqx_1) | def15(__eqy_0, __eqy_1) )).
cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def16(__eqx_0, __eqx_1) | def16(__eqy_0, __eqy_1) )).
cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~def17(__eqx_0, __eqx_1) | def17(__eqy_0, __eqy_1) )).
cnf(matrix-37, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
cnf(matrix-38, plain, ( ~proper_subset(_u3, _u2) | ~proper_subset(_u2, _u3) )).
cnf(matrix-39, plain, ( ( set_union2(_u5, _u4) = set_union2(_u4, _u5)) )).
cnf(matrix-40, plain, ( ( set_intersection2(_u7, _u6) = set_intersection2(_u6, _u7)) )).
cnf(matrix-41, plain, ( ( _u9 != _u8) | ~def0(_u8, _u9) )).
cnf(matrix-42, plain, ( ~subset(_u9, _u8) | ~subset(_u8, _u9) | ( _u9 = _u8) )).
cnf(matrix-43, plain, ( def0(_u8, _u9) | subset(_u9, _u8) )).
cnf(matrix-44, plain, ( def0(_u8, _u9) | subset(_u8, _u9) )).
cnf(matrix-45, plain, ( ( _u12 != empty_set) | ~in(_u10, _u12) )).
cnf(matrix-46, plain, ( in(skolem1(_u12), _u12) | ( _u12 = empty_set) )).
cnf(matrix-47, plain, ( ( _u15 != set_union2(_u17, _u16)) | ~def2(_u15, _u16, _u17, _u13) )).
cnf(matrix-48, plain, ( ~def3(_u15, _u16, _u17) | ~def4(_u15, _u16, _u17) | ( _u15 = set_union2(_u17, _u16)) )).
cnf(matrix-49, plain, ( def2(_u15, _u16, _u17, _u13) | ~in(_u13, _u15) | in(_u13, _u17) | in(_u13, _u16) )).
cnf(matrix-50, plain, ( def2(_u15, _u16, _u17, _u13) | ~def1(_u16, _u17, _u13) | in(_u13, _u15) )).
cnf(matrix-51, plain, ( def1(_u16, _u17, _u13) | ~in(_u13, _u17) )).
cnf(matrix-52, plain, ( def1(_u16, _u17, _u13) | ~in(_u13, _u16) )).
cnf(matrix-53, plain, ( def3(_u15, _u16, _u17) | in(skolem2(_u17, _u16, _u15), _u15) )).
cnf(matrix-54, plain, ( def3(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u17) )).
cnf(matrix-55, plain, ( def3(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u16) )).
cnf(matrix-56, plain, ( def4(_u15, _u16, _u17) | in(skolem2(_u17, _u16, _u15), _u17) | in(skolem2(_u17, _u16, _u15), _u16) )).
cnf(matrix-57, plain, ( def4(_u15, _u16, _u17) | ~in(skolem2(_u17, _u16, _u15), _u15) )).
cnf(matrix-58, plain, ( ~subset(_u21, _u20) | ~in(_u18, _u21) | in(_u18, _u20) )).
cnf(matrix-59, plain, ( ~def5(_u21, _u20) | subset(_u21, _u20) )).
cnf(matrix-60, plain, ( def5(_u21, _u20) | in(skolem3(_u21, _u20), _u21) )).
cnf(matrix-61, plain, ( def5(_u21, _u20) | ~in(skolem3(_u21, _u20), _u20) )).
cnf(matrix-62, plain, ( ( _u24 != set_intersection2(_u26, _u25)) | ~def7(_u22, _u24, _u25, _u26) )).
cnf(matrix-63, plain, ( ~def8(_u24, _u25, _u26) | ~def9(_u24, _u25, _u26) | ( _u24 = set_intersection2(_u26, _u25)) )).
cnf(matrix-64, plain, ( def7(_u22, _u24, _u25, _u26) | ~in(_u22, _u24) | ~def6(_u22, _u25, _u26) )).
cnf(matrix-65, plain, ( def7(_u22, _u24, _u25, _u26) | ~in(_u22, _u26) | ~in(_u22, _u25) | in(_u22, _u24) )).
cnf(matrix-66, plain, ( def6(_u22, _u25, _u26) | in(_u22, _u26) )).
cnf(matrix-67, plain, ( def6(_u22, _u25, _u26) | in(_u22, _u25) )).
cnf(matrix-68, plain, ( def8(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u24) )).
cnf(matrix-69, plain, ( def8(_u24, _u25, _u26) | ~in(skolem4(_u26, _u25, _u24), _u26) | ~in(skolem4(_u26, _u25, _u24), _u25) )).
cnf(matrix-70, plain, ( def9(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u26) )).
cnf(matrix-71, plain, ( def9(_u24, _u25, _u26) | in(skolem4(_u26, _u25, _u24), _u25) )).
cnf(matrix-72, plain, ( def9(_u24, _u25, _u26) | ~in(skolem4(_u26, _u25, _u24), _u24) )).
cnf(matrix-73, plain, ( ( _u29 != set_difference(_u31, _u30)) | ~def11(_u30, _u31, _u27, _u29) )).
cnf(matrix-74, plain, ( ~def12(_u30, _u31, _u29) | ~def13(_u30, _u31, _u29) | ( _u29 = set_difference(_u31, _u30)) )).
cnf(matrix-75, plain, ( def11(_u30, _u31, _u27, _u29) | ~in(_u27, _u29) | ~def10(_u30, _u31, _u27) )).
cnf(matrix-76, plain, ( def11(_u30, _u31, _u27, _u29) | ~in(_u27, _u31) | in(_u27, _u30) | in(_u27, _u29) )).
cnf(matrix-77, plain, ( def10(_u30, _u31, _u27) | in(_u27, _u31) )).
cnf(matrix-78, plain, ( def10(_u30, _u31, _u27) | ~in(_u27, _u30) )).
cnf(matrix-79, plain, ( def12(_u30, _u31, _u29) | in(skolem5(_u31, _u30, _u29), _u29) )).
cnf(matrix-80, plain, ( def12(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u31) | in(skolem5(_u31, _u30, _u29), _u30) )).
cnf(matrix-81, plain, ( def13(_u30, _u31, _u29) | in(skolem5(_u31, _u30, _u29), _u31) )).
cnf(matrix-82, plain, ( def13(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u30) )).
cnf(matrix-83, plain, ( def13(_u30, _u31, _u29) | ~in(skolem5(_u31, _u30, _u29), _u29) )).
cnf(matrix-84, plain, ( ~disjoint(_u33, _u32) | ( set_intersection2(_u33, _u32) = empty_set) )).
cnf(matrix-85, plain, ( ( set_intersection2(_u33, _u32) != empty_set) | disjoint(_u33, _u32) )).
cnf(matrix-86, plain, ( ~proper_subset(_u35, _u34) | ~def14(_u34, _u35) )).
cnf(matrix-87, plain, ( ~subset(_u35, _u34) | ( _u35 = _u34) | proper_subset(_u35, _u34) )).
cnf(matrix-88, plain, ( def14(_u34, _u35) | subset(_u35, _u34) )).
cnf(matrix-89, plain, ( def14(_u34, _u35) | ( _u35 != _u34) )).
cnf(matrix-90, plain, ( empty(empty_set) )).
cnf(matrix-91, plain, ( empty(_u37) | ~empty(set_union2(_u37, _u36)) )).
cnf(matrix-92, plain, ( empty(_u39) | ~empty(set_union2(_u38, _u39)) )).
cnf(matrix-93, plain, ( ( set_union2(_u41, _u41) = _u41) )).
cnf(matrix-94, plain, ( ( set_intersection2(_u43, _u43) = _u43) )).
cnf(matrix-95, plain, ( ~proper_subset(_u45, _u45) )).
cnf(matrix-96, plain, ( ( set_difference(_u47, _u46) != empty_set) | subset(_u47, _u46) )).
cnf(matrix-97, plain, ( ~subset(_u47, _u46) | ( set_difference(_u47, _u46) = empty_set) )).
cnf(matrix-98, plain, ( empty(skolem6) )).
cnf(matrix-99, plain, ( ~empty(skolem7) )).
cnf(matrix-100, plain, ( subset(_u51, _u51) )).
cnf(matrix-101, plain, ( ~disjoint(_u53, _u52) | disjoint(_u52, _u53) )).
cnf(matrix-102, plain, ( ~subset(_u55, _u54) | ( set_union2(_u55, _u54) = _u54) )).
cnf(matrix-103, plain, ( subset(set_intersection2(_u57, _u56), _u57) )).
cnf(matrix-104, plain, ( ~subset(_u60, _u59) | ~subset(_u60, _u58) | subset(_u60, set_intersection2(_u59, _u58)) )).
cnf(matrix-105, plain, ( ( set_union2(_u61, empty_set) = _u61) )).
cnf(matrix-106, plain, ( ~subset(_u64, _u63) | ~subset(_u63, _u62) | subset(_u64, _u62) )).
cnf(matrix-107, plain, ( ~subset(_u67, _u66) | subset(set_intersection2(_u67, _u65), set_intersection2(_u66, _u65)) )).
cnf(matrix-108, plain, ( ~subset(_u69, _u68) | ( set_intersection2(_u69, _u68) = _u69) )).
cnf(matrix-109, plain, ( ( set_intersection2(_u70, empty_set) = empty_set) )).
cnf(matrix-110, plain, ( ~def15(_u72, _u73) | ~def16(_u72, _u73) | ( _u73 = _u72) )).
cnf(matrix-111, plain, ( def15(_u72, _u73) | in(skolem8(_u73, _u72), _u73) )).
cnf(matrix-112, plain, ( def15(_u72, _u73) | ~in(skolem8(_u73, _u72), _u72) )).
cnf(matrix-113, plain, ( def16(_u72, _u73) | in(skolem8(_u73, _u72), _u72) )).
cnf(matrix-114, plain, ( def16(_u72, _u73) | ~in(skolem8(_u73, _u72), _u73) )).
cnf(matrix-115, plain, ( subset(empty_set, _u74) )).
cnf(matrix-116, plain, ( ~subset(_u77, _u76) | subset(set_difference(_u77, _u75), set_difference(_u76, _u75)) )).
cnf(matrix-117, plain, ( subset(set_difference(_u79, _u78), _u79) )).
cnf(matrix-118, plain, ( ( set_difference(_u81, _u80) != empty_set) | subset(_u81, _u80) )).
cnf(matrix-119, plain, ( ~subset(_u81, _u80) | ( set_difference(_u81, _u80) = empty_set) )).
cnf(matrix-120, plain, ( ( set_union2(_u83, set_difference(_u82, _u83)) = set_union2(_u83, _u82)) )).
cnf(matrix-121, plain, ( ( set_difference(_u84, empty_set) = _u84) )).
cnf(matrix-122, plain, ( disjoint(_u88, _u87) | ~def17(_u87, _u88) )).
cnf(matrix-123, plain, ( ~in(_u86, _u88) | ~in(_u86, _u87) | ~disjoint(_u88, _u87) )).
cnf(matrix-124, plain, ( def17(_u87, _u88) | in(skolem9(_u88, _u87), _u88) )).
cnf(matrix-125, plain, ( def17(_u87, _u88) | in(skolem9(_u88, _u87), _u87) )).
cnf(matrix-126, plain, ( ~subset(_u89, empty_set) | ( _u89 = empty_set) )).
cnf(matrix-127, plain, ( ( set_difference(set_union2(_u91, _u90), _u90) = set_difference(_u91, _u90)) )).
cnf(matrix-128, plain, ( ~subset(_u93, _u92) | ( _u92 = set_union2(_u93, set_difference(_u92, _u93))) )).
cnf(matrix-129, plain, ( ( set_difference(_u95, set_difference(_u95, _u94)) = set_intersection2(_u95, _u94)) )).
cnf(matrix-130, plain, ( ( set_difference(empty_set, _u96) = empty_set) )).
cnf(matrix-131, plain, ( disjoint(_u100, _u99) | in(skolem10(_u100, _u99), set_intersection2(_u100, _u99)) )).
cnf(matrix-132, plain, ( ~in(_u98, set_intersection2(_u100, _u99)) | ~disjoint(_u100, _u99) )).
cnf(matrix-133, plain, ( ~subset(_u102, _u101) | ~proper_subset(_u101, _u102) )).
cnf(matrix-134, plain, ( subset(skolem11, skolem12) )).
cnf(matrix-135, plain, ( disjoint(skolem12, skolem13) )).
cnf(matrix-136, plain, ( ~disjoint(skolem11, skolem13) )).
cnf(matrix-137, plain, ( ~empty(_u106) | ( _u106 = empty_set) )).
cnf(matrix-138, plain, ( ~in(_u108, _u107) | ~empty(_u107) )).
cnf(matrix-139, plain, ( subset(_u110, set_union2(_u110, _u109)) )).
cnf(matrix-140, plain, ( ~empty(_u112) | ( _u112 = _u111) | ~empty(_u111) )).
cnf(matrix-141, plain, ( ~subset(_u115, _u114) | ~subset(_u113, _u114) | subset(set_union2(_u115, _u113), _u114) )).
% Proof stack:
cnf(proof-stack, plain,
proof_stack(
start(134),
left_branch(0, 107, 0, 2),
left_branch(0, 58, 0, 3),
left_branch(0, 132, 0, 4),
left_branch(0, 135, 0, 5),
right_branch(5),
right_branch(4),
left_branch(0, 131, 1, 5),
left_branch(0, 136, 0, 6),
right_branch(6),
right_branch(5),
right_branch(3),
right_branch(2)
)).
CSE_E 1.7
Peiyao Liu
Xihua University, China
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_0_41 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture c_0_15 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture t63_xboole_1 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(t6_boole, axiom, ![X1]:(empty(X1)=>X1=empty_set), file('../problem_tptp_2024/SEU140+2.p', t6_boole)).
fof(rc1_xboole_0, axiom, ?[X1]:empty(X1), file('../problem_tptp_2024/SEU140+2.p', rc1_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('../problem_tptp_2024/SEU140+2.p', d3_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('../problem_tptp_2024/SEU140+2.p', t48_xboole_1)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('../problem_tptp_2024/SEU140+2.p', l32_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('../problem_tptp_2024/SEU140+2.p', t63_xboole_1)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('../problem_tptp_2024/SEU140+2.p', t3_xboole_0)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('../problem_tptp_2024/SEU140+2.p', t3_boole)).
fof(c_0_8, plain, ![X237]:(~empty(X237)|X237=empty_set), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])).
fof(c_0_9, plain, empty(esk6_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])])).
fof(c_0_10, plain, ![X145, X146, X147, X148, X149, X150, X151, X152]:((((in(X148,X145)|~in(X148,X147)|X147!=set_intersection2(X145,X146))&(in(X148,X146)|~in(X148,X147)|X147!=set_intersection2(X145,X146)))&(~in(X149,X145)|~in(X149,X146)|in(X149,X147)|X147!=set_intersection2(X145,X146)))&((~in(esk4_3(X150,X151,X152),X152)|(~in(esk4_3(X150,X151,X152),X150)|~in(esk4_3(X150,X151,X152),X151))|X152=set_intersection2(X150,X151))&((in(esk4_3(X150,X151,X152),X150)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))&(in(esk4_3(X150,X151,X152),X151)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_11, lemma, ![X223, X224]:set_difference(X223,set_difference(X223,X224))=set_intersection2(X223,X224), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_12, lemma, ![X174, X175]:((set_difference(X174,X175)!=empty_set|subset(X174,X175))&(~subset(X174,X175)|set_difference(X174,X175)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_13, plain, (X1=empty_set|~empty(X1)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_14, plain, (empty(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
fof(c_0_15, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
fof(c_0_16, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t3_xboole_0])).
cnf(c_0_17, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_18, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_19, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_20, plain, (empty_set=esk6_0), inference(spm,[status(thm)],[c_0_13, c_0_14])).
fof(c_0_21, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])).
fof(c_0_22, plain, ![X211]:set_difference(X211,empty_set)=X211, inference(variable_rename,[status(thm)],[t3_boole])).
fof(c_0_23, lemma, ![X212, X213, X215, X216, X217]:(((in(esk9_2(X212,X213),X212)|disjoint(X212,X213))&(in(esk9_2(X212,X213),X213)|disjoint(X212,X213)))&(~in(X217,X215)|~in(X217,X216)|~disjoint(X215,X216))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])])).
cnf(c_0_24, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_17, c_0_18])).
cnf(c_0_25, lemma, (set_difference(X1,X2)=esk6_0|~subset(X1,X2)), inference(rw,[status(thm)],[c_0_19, c_0_20])).
cnf(c_0_26, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_27, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_28, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_29, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_30, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_31, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_32, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_24])).
cnf(c_0_33, negated_conjecture, (set_difference(esk11_0,esk12_0)=esk6_0), inference(spm,[status(thm)],[c_0_25, c_0_26])).
cnf(c_0_34, plain, (set_difference(X1,esk6_0)=X1), inference(rw,[status(thm)],[c_0_27, c_0_20])).
cnf(c_0_35, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_36, negated_conjecture, (~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_28, c_0_29])).
cnf(c_0_37, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
cnf(c_0_38, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_34])).
cnf(c_0_39, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_35])).
cnf(c_0_40, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_36, c_0_37])).
cnf(c_0_41, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40]), ['proof']).
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_0_16 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture prove_inverse_is_self_cancelling is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% WARNING: Took the negated conjecture prove_inverse_is_self_cancelling as the proved formula
% CPUTIME: 0.05
% SUCCESS: Verified
% SZS status Verified
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('../problem_tptp_2024/Axioms/BOO001-0.ax', associativity)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('../problem_tptp_2024/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('../problem_tptp_2024/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('../problem_tptp_2024/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('../problem_tptp_2024/Axioms/BOO001-0.ax', left_inverse)).
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('../problem_tptp_2024/BOO001-1.p', prove_inverse_is_self_cancelling)).
cnf(c_0_6, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity).
cnf(c_0_7, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1).
cnf(c_0_8, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse).
cnf(c_0_10, plain, (multiply(X1,X2,multiply(inverse(X2),X3,X2))=multiply(X1,X3,X2)), inference(spm,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_11, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2).
cnf(c_0_12, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse).
cnf(c_0_13, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_9])).
cnf(c_0_14, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling).
cnf(c_0_15, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_12, c_0_13])).
cnf(c_0_16, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), ['proof']).
CSI_Enigma 1.0.6
Guoyan Zeng
Southwest Jiaotong University, China
Solution for SEU140+2
cnf(i_0_154, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2)))), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_154)).
cnf(i_0_86, negated_conjecture, (disjoint(esk12_0,esk13_0)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_86)).
cnf(i_0_110, plain, (X1=empty_set|in(esk1_1(X1),X1)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_110)).
cnf(i_0_140, plain, (X1!=set_difference(X2,X3)|~in(X4,X3)|~in(X4,X1)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_140)).
cnf(i_0_103, negated_conjecture, (~disjoint(esk11_0,esk13_0)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_103)).
cnf(i_0_129, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_129)).
cnf(i_0_116, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_116)).
cnf(i_0_148, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_148)).
cnf(i_0_114, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_114)).
cnf(i_0_85, negated_conjecture, (subset(esk11_0,esk12_0)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_85)).
cnf(i_0_125, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_125)).
cnf(i_0_96, lemma, (subset(set_difference(X1,X2),X1)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_96)).
cnf(i_0_90, plain, (set_difference(X1,empty_set)=X1), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_90)).
cnf(i_0_130, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-7utvw75k/input.p', i_0_130)).
cnf(c_0_169, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2)))), i_0_154).
cnf(c_0_170, negated_conjecture, (disjoint(esk12_0,esk13_0)), i_0_86).
cnf(c_0_171, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_169, c_0_170])).
cnf(c_0_172, plain, (X1=empty_set|in(esk1_1(X1),X1)), i_0_110).
cnf(c_0_173, plain, (X1!=set_difference(X2,X3)|~in(X4,X3)|~in(X4,X1)), i_0_140).
cnf(c_0_174, negated_conjecture, (~disjoint(esk11_0,esk13_0)), i_0_103).
cnf(c_0_175, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), i_0_129).
cnf(c_0_176, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), i_0_116).
cnf(c_0_177, plain, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_171, c_0_172])).
cnf(c_0_178, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), i_0_148).
cnf(c_0_179, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), i_0_114).
cnf(c_0_180, negated_conjecture, (subset(esk11_0,esk12_0)), i_0_85).
cnf(c_0_181, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_173])).
cnf(c_0_182, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_174, c_0_175])).
cnf(c_0_183, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2)), i_0_125).
cnf(c_0_184, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_176, c_0_177])).
cnf(c_0_185, lemma, (subset(set_difference(X1,X2),X1)), i_0_96).
cnf(c_0_186, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_178])).
cnf(c_0_187, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_179, c_0_180])).
cnf(c_0_188, plain, (set_difference(X1,empty_set)=X1), i_0_90).
cnf(c_0_189, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), i_0_130).
cnf(c_0_190, plain, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_181, c_0_182])).
cnf(c_0_191, plain, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183, c_0_184]), c_0_185])])).
cnf(c_0_192, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186, c_0_187]), c_0_188])).
cnf(c_0_193, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_174, c_0_189])).
cnf(c_0_194, plain, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_190, c_0_191])).
cnf(c_0_195, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_193]), c_0_194]), ['proof']).
Solution for BOO001-1
cnf(i_0_11, plain, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_11)).
cnf(i_0_7, plain, (multiply(X1,X2,X2)=X2), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_7)).
cnf(i_0_9, plain, (multiply(X1,X2,inverse(X2))=X1), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_9)).
cnf(i_0_8, plain, (multiply(X1,X1,X2)=X1), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_8)).
cnf(i_0_10, plain, (multiply(inverse(X1),X1,X2)=X2), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_10)).
cnf(i_0_12, negated_conjecture, (inverse(inverse(a))!=a), file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.out2Eni-okic8kel/lgb.p', i_0_12)).
cnf(c_0_19, plain, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), i_0_11).
cnf(c_0_20, plain, (multiply(X1,X2,X2)=X2), i_0_7).
cnf(c_0_21, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_19, c_0_20])).
cnf(c_0_22, plain, (multiply(X1,X2,inverse(X2))=X1), i_0_9).
cnf(c_0_23, plain, (multiply(X1,X2,X3)=multiply(X1,X3,multiply(inverse(X3),X2,X3))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
cnf(c_0_24, plain, (multiply(X1,X1,X2)=X1), i_0_8).
cnf(c_0_25, plain, (multiply(inverse(X1),X1,X2)=X2), i_0_10).
cnf(c_0_26, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_22])).
cnf(c_0_27, negated_conjecture, (inverse(inverse(a))!=a), i_0_12).
cnf(c_0_28, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_25, c_0_26])).
cnf(c_0_29, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])]), ['proof']).
Drodi 4.1.0
Oscar Contreras
Amateur Programmer, Spain
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f2762 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f52 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f51 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(f5,axiom,(
(! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f8,axiom,(
(! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f9,axiom,(
(! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f34,lemma,(
(! [A,B] :( subset(A,B)=> set_intersection2(A,B) = A ) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f43,lemma,(
(! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] :~ ( in(C,A)& in(C,B) ) ))& ~ ( (? [C] :( in(C,A)& in(C,B) ))& disjoint(A,B) ) ) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f51,conjecture,(
(! [A,B,C] :( ( subset(A,B)& disjoint(B,C) )=> disjoint(A,C) ) )),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/SEU140+2.p')).
fof(f52,negated_conjecture,(
~((! [A,B,C] :( ( subset(A,B)& disjoint(B,C) )=> disjoint(A,C) ) ))),
inference(negated_conjecture,[status(cth)],[f51])).
fof(f64,plain,(
![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
inference(NNF_transformation,[status(esa)],[f5])).
fof(f65,plain,(
(![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
inference(miniscoping,[status(esa)],[f64])).
fof(f66,plain,(
![X0,X1]: (~X0=X1|subset(X0,X1))),
inference(cnf_transformation,[status(thm)],[f65])).
fof(f83,plain,(
![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
inference(pre_NNF_transformation,[status(esa)],[f8])).
fof(f84,plain,(
![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
inference(NNF_transformation,[status(esa)],[f83])).
fof(f85,plain,(
(![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
inference(miniscoping,[status(esa)],[f84])).
fof(f86,plain,(
(![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK2_skl(B,A),A)&~in(sK2_skl(B,A),B))))),
inference(skolemization,[status(esa),new_symbols(skolem,[sK2_skl])],[f85])).
fof(f87,plain,(
![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
inference(cnf_transformation,[status(thm)],[f86])).
fof(f90,plain,(
![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
inference(NNF_transformation,[status(esa)],[f9])).
fof(f91,plain,(
(![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
inference(miniscoping,[status(esa)],[f90])).
fof(f92,plain,(
(![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|((~in(sK3_skl(C,B,A),C)|(~in(sK3_skl(C,B,A),A)|~in(sK3_skl(C,B,A),B)))&(in(sK3_skl(C,B,A),C)|(in(sK3_skl(C,B,A),A)&in(sK3_skl(C,B,A),B))))))),
inference(skolemization,[status(esa),new_symbols(skolem,[sK3_skl])],[f91])).
fof(f94,plain,(
![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
inference(cnf_transformation,[status(thm)],[f92])).
fof(f154,plain,(
![A,B]: (~subset(A,B)|set_intersection2(A,B)=A)),
inference(pre_NNF_transformation,[status(esa)],[f34])).
fof(f155,plain,(
![X0,X1]: (~subset(X0,X1)|set_intersection2(X0,X1)=X0)),
inference(cnf_transformation,[status(thm)],[f154])).
fof(f173,plain,(
![A,B]: ((disjoint(A,B)|(?[C]: (in(C,A)&in(C,B))))&((![C]: (~in(C,A)|~in(C,B)))|~disjoint(A,B)))),
inference(pre_NNF_transformation,[status(esa)],[f43])).
fof(f174,plain,(
(![A,B]: (disjoint(A,B)|(?[C]: (in(C,A)&in(C,B)))))&(![A,B]: ((![C]: (~in(C,A)|~in(C,B)))|~disjoint(A,B)))),
inference(miniscoping,[status(esa)],[f173])).
fof(f175,plain,(
(![A,B]: (disjoint(A,B)|(in(sK8_skl(B,A),A)&in(sK8_skl(B,A),B))))&(![A,B]: ((![C]: (~in(C,A)|~in(C,B)))|~disjoint(A,B)))),
inference(skolemization,[status(esa),new_symbols(skolem,[sK8_skl])],[f174])).
fof(f176,plain,(
![X0,X1]: (disjoint(X0,X1)|in(sK8_skl(X1,X0),X0))),
inference(cnf_transformation,[status(thm)],[f175])).
fof(f177,plain,(
![X0,X1]: (disjoint(X0,X1)|in(sK8_skl(X1,X0),X1))),
inference(cnf_transformation,[status(thm)],[f175])).
fof(f178,plain,(
![X0,X1,X2]: (~in(X0,X1)|~in(X0,X2)|~disjoint(X1,X2))),
inference(cnf_transformation,[status(thm)],[f175])).
fof(f193,plain,(
(?[A,B,C]: ((subset(A,B)&disjoint(B,C))&~disjoint(A,C)))),
inference(pre_NNF_transformation,[status(esa)],[f52])).
fof(f194,plain,(
?[A,C]: ((?[B]: (subset(A,B)&disjoint(B,C)))&~disjoint(A,C))),
inference(miniscoping,[status(esa)],[f193])).
fof(f195,plain,(
((subset(sK10_skl,sK12_skl)&disjoint(sK12_skl,sK11_skl))&~disjoint(sK10_skl,sK11_skl))),
inference(skolemization,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl])],[f194])).
fof(f196,plain,(
subset(sK10_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f195])).
fof(f197,plain,(
disjoint(sK12_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f195])).
fof(f198,plain,(
~disjoint(sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f195])).
fof(f210,plain,(
![X0]: (subset(X0,X0))),
inference(destructive_equality_resolution,[status(thm)],[f66])).
fof(f217,plain,(
![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
inference(destructive_equality_resolution,[status(thm)],[f94])).
fof(f241,plain,(
![X0,X1,X2,X3]: (~in(X0,X1)|~disjoint(X1,X2)|~subset(X3,X2)|~in(X0,X3))),
inference(resolution,[status(thm)],[f178,f87])).
fof(f392,plain,(
![X0,X1]: (~in(X0,sK12_skl)|~subset(X1,sK11_skl)|~in(X0,X1))),
inference(resolution,[status(thm)],[f241,f197])).
fof(f470,plain,(
![X0]: (~in(X0,sK12_skl)|~in(X0,sK11_skl))),
inference(resolution,[status(thm)],[f392,f210])).
fof(f1283,plain,(
set_intersection2(sK10_skl,sK12_skl)=sK10_skl),
inference(resolution,[status(thm)],[f155,f196])).
fof(f1338,plain,(
![X0]: (~in(X0,sK10_skl)|in(X0,sK12_skl))),
inference(paramodulation,[status(thm)],[f1283,f217])).
fof(f1729,plain,(
in(sK8_skl(sK11_skl,sK10_skl),sK10_skl)),
inference(resolution,[status(thm)],[f176,f198])).
fof(f1741,plain,(
in(sK8_skl(sK11_skl,sK10_skl),sK11_skl)),
inference(resolution,[status(thm)],[f177,f198])).
fof(f1764,plain,(
in(sK8_skl(sK11_skl,sK10_skl),sK12_skl)),
inference(resolution,[status(thm)],[f1729,f1338])).
fof(f2747,plain,(
~in(sK8_skl(sK11_skl,sK10_skl),sK11_skl)),
inference(resolution,[status(thm)],[f1764,f470])).
fof(f2762,plain,(
$false),
inference(forward_subsumption_resolution,[status(thm)],[f2747,f1741])).
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f202 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f6 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% WARNING: Took the negated conjecture f6 as the proved formula
% CPUTIME: 0.05
% SUCCESS: Verified
% SZS status Verified
fof(f1,axiom,(
(![V,W,X,Y,Z]: (multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) ))),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f2,axiom,(
(![Y,X]: (multiply(Y,X,X) = X ))),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f3,axiom,(
(![X,Y]: (multiply(X,X,Y) = X ))),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f4,axiom,(
(![Y,X]: (multiply(inverse(Y),Y,X) = X ))),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f5,axiom,(
(![X,Y]: (multiply(X,Y,inverse(Y)) = X ))),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f6,negated_conjecture,(
inverse(inverse(a)) != a ),
file('/run/media/oscar/Elements/temp/TPTP-v8.1.2/Problems/BOO001-1.p')).
fof(f7,plain,(
![X0,X1,X2,X3,X4]: (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4))=multiply(X0,X1,multiply(X2,X3,X4)))),
inference(cnf_transformation,[status(thm)],[f1])).
fof(f8,plain,(
![X0,X1]: (multiply(X0,X1,X1)=X1)),
inference(cnf_transformation,[status(thm)],[f2])).
fof(f9,plain,(
![X0,X1]: (multiply(X0,X0,X1)=X0)),
inference(cnf_transformation,[status(thm)],[f3])).
fof(f10,plain,(
![X0,X1]: (multiply(inverse(X0),X0,X1)=X1)),
inference(cnf_transformation,[status(thm)],[f4])).
fof(f11,plain,(
![X0,X1]: (multiply(X0,X1,inverse(X1))=X0)),
inference(cnf_transformation,[status(thm)],[f5])).
fof(f12,plain,(
~inverse(inverse(a))=a),
inference(cnf_transformation,[status(thm)],[f6])).
fof(f25,plain,(
![X0,X1,X2,X3]: (multiply(X0,X1,multiply(X0,X2,X3))=multiply(X0,X2,multiply(inverse(X2),X1,X3)))),
inference(paramodulation,[status(thm)],[f11,f7])).
fof(f60,plain,(
![X0,X1,X2]: (multiply(X0,inverse(X1),multiply(X0,X1,X2))=multiply(X0,X1,inverse(X1)))),
inference(paramodulation,[status(thm)],[f9,f25])).
fof(f76,plain,(
![X0,X1,X2]: (multiply(X0,inverse(X1),multiply(X0,X1,X2))=X0)),
inference(forward_demodulation,[status(thm)],[f11,f60])).
fof(f156,plain,(
![X0,X1]: (multiply(X0,inverse(X1),X1)=X0)),
inference(paramodulation,[status(thm)],[f8,f76])).
fof(f175,plain,(
![X0]: (X0=inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f10,f156])).
fof(f193,plain,(
~a=a),
inference(backward_demodulation,[status(thm)],[f175,f12])).
fof(f202,plain,(
$false),
inference(trivial_equality_resolution,[status(thm)],[f193])).
E 3.3.0
Stephan Schulz
DHBW Stuttgart, Germany
Solution for SET014^4
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_0_10 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture c_0_3 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture thm as the proved formula
% CPUTIME: 0.05
% SUCCESS: Verified
% SZS status Verified
thf(thm, conjecture, ![X22:$i > $o, X23:$i > $o, X24:$i > $o]:(((subset @ X22 @ X24)&(subset @ X23 @ X24))=>(subset @ (union @ X22 @ X23) @ X24)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SET014^4.p', thm)).
thf(union, axiom, ((union)=(^[X5:$i > $o, X6:$i > $o, X4:$i]:(((X5 @ X4)|(X6 @ X4))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/SET008^0.ax', union)).
thf(subset, axiom, ((subset)=(^[X16:$i > $o, X17:$i > $o]:(![X4:$i]:(((X16 @ X4)=>(X17 @ X4)))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/SET008^0.ax', subset)).
thf(c_0_3, negated_conjecture, ~(![X22:$i > $o, X23:$i > $o, X24:$i > $o]:((![X29:$i]:((X22 @ X29)=>(X24 @ X29))&![X30:$i]:((X23 @ X30)=>(X24 @ X30)))=>![X32:$i]:(((X22 @ X32)|(X23 @ X32))=>(X24 @ X32)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]), union]), subset])).
thf(c_0_4, negated_conjecture, ![X37:$i, X38:$i]:(((~(epred1_0 @ X37)|(epred3_0 @ X37))&(~(epred2_0 @ X38)|(epred3_0 @ X38)))&(((epred1_0 @ esk1_0)|(epred2_0 @ esk1_0))&~(epred3_0 @ esk1_0))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])).
thf(c_0_5, negated_conjecture, ![X1:$i]:((epred3_0 @ X1)|~(epred2_0 @ X1)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_6, negated_conjecture, ((epred1_0 @ esk1_0)|(epred2_0 @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_7, negated_conjecture, ~(epred3_0 @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_8, negated_conjecture, ![X1:$i]:((epred3_0 @ X1)|~(epred1_0 @ X1)), inference(split_conjunct,[status(thm)],[c_0_4])).
thf(c_0_9, negated_conjecture, (epred1_0 @ esk1_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5, c_0_6]), c_0_7])).
thf(c_0_10, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_9]), c_0_7]), ['proof']).
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_0_56 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture c_0_14 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture t63_xboole_1 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t4_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d1_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d3_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d10_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t36_xboole_1)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_boole)).
fof(c_0_11, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~in(X3,set_intersection2(X1,X2))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t4_xboole_0])).
fof(c_0_12, lemma, ![X226, X227, X229, X230, X231]:((disjoint(X226,X227)|in(esk10_2(X226,X227),set_intersection2(X226,X227)))&(~in(X231,set_intersection2(X229,X230))|~disjoint(X229,X230))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])).
fof(c_0_13, lemma, ![X223, X224]:set_difference(X223,set_difference(X223,X224))=set_intersection2(X223,X224), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_14, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
cnf(c_0_15, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_16, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_17, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])).
fof(c_0_18, plain, ![X1]:(X1=empty_set<=>![X2]:~in(X2,X1)), inference(fof_simplification,[status(thm)],[d1_xboole_0])).
fof(c_0_19, plain, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~in(X4,X2)))), inference(fof_simplification,[status(thm)],[d4_xboole_0])).
fof(c_0_20, lemma, ![X1, X2]:(~((~disjoint(X1,X2)&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), inference(fof_simplification,[status(thm)],[t3_xboole_0])).
cnf(c_0_21, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_15, c_0_16])).
cnf(c_0_22, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_23, plain, ![X126, X127, X128]:((X126!=empty_set|~in(X127,X126))&(in(esk1_1(X128),X128)|X128=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])).
fof(c_0_24, plain, ![X145, X146, X147, X148, X149, X150, X151, X152]:((((in(X148,X145)|~in(X148,X147)|X147!=set_intersection2(X145,X146))&(in(X148,X146)|~in(X148,X147)|X147!=set_intersection2(X145,X146)))&(~in(X149,X145)|~in(X149,X146)|in(X149,X147)|X147!=set_intersection2(X145,X146)))&((~in(esk4_3(X150,X151,X152),X152)|(~in(esk4_3(X150,X151,X152),X150)|~in(esk4_3(X150,X151,X152),X151))|X152=set_intersection2(X150,X151))&((in(esk4_3(X150,X151,X152),X150)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))&(in(esk4_3(X150,X151,X152),X151)|in(esk4_3(X150,X151,X152),X152)|X152=set_intersection2(X150,X151))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_25, plain, ![X154, X155, X156, X157, X158, X159, X160, X161]:((((in(X157,X154)|~in(X157,X156)|X156!=set_difference(X154,X155))&(~in(X157,X155)|~in(X157,X156)|X156!=set_difference(X154,X155)))&(~in(X158,X154)|in(X158,X155)|in(X158,X156)|X156!=set_difference(X154,X155)))&((~in(esk5_3(X159,X160,X161),X161)|(~in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X160))|X161=set_difference(X159,X160))&((in(esk5_3(X159,X160,X161),X159)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))&(~in(esk5_3(X159,X160,X161),X160)|in(esk5_3(X159,X160,X161),X161)|X161=set_difference(X159,X160))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])).
fof(c_0_26, lemma, ![X212, X213, X215, X216, X217]:(((in(esk9_2(X212,X213),X212)|disjoint(X212,X213))&(in(esk9_2(X212,X213),X213)|disjoint(X212,X213)))&(~in(X217,X215)|~in(X217,X216)|~disjoint(X215,X216))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])])])).
fof(c_0_27, lemma, ![X174, X175]:((set_difference(X174,X175)!=empty_set|subset(X174,X175))&(~subset(X174,X175)|set_difference(X174,X175)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_28, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
cnf(c_0_29, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_30, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_31, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_32, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_33, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
fof(c_0_34, plain, ![X124, X125]:(((subset(X124,X125)|X124!=X125)&(subset(X125,X124)|X124!=X125))&(~subset(X124,X125)|~subset(X125,X124)|X124=X125)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_35, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_36, negated_conjecture, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_28, c_0_29])).
fof(c_0_37, lemma, ![X205, X206]:subset(set_difference(X205,X206),X205), inference(variable_rename,[status(thm)],[t36_xboole_1])).
cnf(c_0_38, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_30, c_0_16])).
cnf(c_0_39, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_40, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_41, plain, ![X211]:set_difference(X211,empty_set)=X211, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_42, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_31])).
cnf(c_0_43, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
cnf(c_0_44, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_34])).
cnf(c_0_45, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_35, c_0_36])).
cnf(c_0_46, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_47, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_38])).
cnf(c_0_48, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_49, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_50, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_51, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
cnf(c_0_52, lemma, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])])).
cnf(c_0_53, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])).
cnf(c_0_54, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_32, c_0_50])).
cnf(c_0_55, lemma, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_51, c_0_52])).
cnf(c_0_56, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), ['proof']).
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_0_16 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture prove_inverse_is_self_cancelling is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% WARNING: Took the negated conjecture prove_inverse_is_self_cancelling as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', associativity)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', left_inverse)).
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/BOO001-1.p', prove_inverse_is_self_cancelling)).
cnf(c_0_6, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity).
cnf(c_0_7, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1).
cnf(c_0_8, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse).
cnf(c_0_10, plain, (multiply(X1,X2,X3)=multiply(X1,X3,multiply(inverse(X3),X2,X3))), inference(spm,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_11, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2).
cnf(c_0_12, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse).
cnf(c_0_13, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_9])).
cnf(c_0_14, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling).
cnf(c_0_15, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_12, c_0_13])).
cnf(c_0_16, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), ['proof']).
iProver 3.9.3
Konstantin Korovin
University of Manchester, United Kingdom
Solution for DAT013_1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_1785 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f4 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f3 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(type_def_5, type, array: $tType).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: $int).
tff(func_def_10, type, sK3: $int).
tff(f3,conjecture,(
! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
file('/shareddata/TPTP-v9.0.0/Problems/DAT/DAT013_1.p',co1)).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
inference(negated_conjecture,[status(cth)],[f3])).
tff(f5,plain,(
~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
inference(theory_normalization,[],[f4])).
tff(f12,plain,(
( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
introduced(theory_axiom_146,[])).
tff(f13,plain,(
( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
introduced(theory_axiom_147,[])).
tff(f19,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
inference(ennf_transformation,[],[f5])).
tff(f20,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
inference(flattening,[],[f19])).
tff(f21,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
inference(rectify,[],[f20])).
tff(f22,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
introduced(choice_axiom,[])).
tff(f23,plain,(
? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
introduced(choice_axiom,[])).
tff(f24,plain,(
(~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
tff(f27,plain,(
( ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
inference(cnf_transformation,[],[f24])).
tff(f28,plain,(
~$less(sK3,$sum(sK1,3))),
inference(cnf_transformation,[],[f24])).
tff(f29,plain,(
~$less(sK2,sK3)),
inference(cnf_transformation,[],[f24])).
tff(f30,plain,(
~$less(0,read(sK0,sK3))),
inference(cnf_transformation,[],[f24])).
tcf(c_53,plain,![X0_int:$int,X1_int:$int]:
(X0_int = X1_int|$less(X0_int,X1_int)|$less(X1_int,X0_int)),
inference(cnf_transformation,[],[f13])).
tcf(c_54,plain,![X0_int:$int,X1_int:$int,X2_int:$int]:
(~$less(X0_int,X1_int)|~$less(X1_int,X2_int)|$less(X0_int,X2_int)),
inference(cnf_transformation,[],[f12])).
tcf(c_63,plain,
(~$less(0,read(sK0,sK3))),
inference(cnf_transformation,[],[f30])).
tcf(c_64,plain, (~$less(sK2,sK3)),inference(cnf_transformation,[],[f29])).
tcf(c_65,plain,
(~$less(sK3,$sum(sK1,3))),
inference(cnf_transformation,[],[f28])).
tcf(c_66,plain,![X0_int:$int]:
($less(0,read(sK0,X0_int))|$less(X0_int,sK1)|$less(sK2,X0_int)),
inference(cnf_transformation,[],[f27])).
tcf(c_547,plain,
($less(sK2,sK3)|$less(sK3,sK1)),
inference(superposition,[status(thm)],[c_66,c_63])).
tcf(c_548,plain,
($less(sK3,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_547,c_64])).
tcf(c_728,plain,![X0_int:$int]:
(~$less(sK1,X0_int)|$less(sK3,X0_int)),
inference(superposition,[status(thm)],[c_548,c_54])).
tcf(c_947,plain,![X0_int:$int]:
(X0_int = sK1|$less(X0_int,sK1)|$less(sK3,X0_int)),
inference(superposition,[status(thm)],[c_53,c_728])).
tcf(c_1522,plain,
($sum(sK1,3) = sK1|$less($sum(sK1,3),sK1)),
inference(superposition,[status(thm)],[c_947,c_65])).
tcf(c_1785,plain,
($false),
inference(smt_theory_normalisation,[status(thm)],[c_1522])).
Solution for DAT335_2
%------ Positive definition of '$ki_accessible'
fof(lit_def,axiom,
(! [X0_'$ki_world',X1_'$ki_world'] :
( '$ki_accessible'(X0_'$ki_world',X1_'$ki_world') <=>
(
(
( X1_'$ki_world'=X0_'$ki_world' )
)
)
)
)
).
%------ Positive definition of teach
fof(lit_def,axiom,
(! [X0_'$ki_world',X0,X1] :
( teach(X0_'$ki_world',X0,X1) <=>
(
(
( X0=sue & X1=psych )
&
( X0_'$ki_world'!='$ki_local_world' )
)
|
(
( X0=sue & X1=cs )
)
|
(
( X0=mary & X1=psych )
&
( X0_'$ki_world'!='$ki_local_world' )
)
|
(
( X0=mary & X1=cs )
)
|
(
( X0=sK1(X0_'$ki_world') & X1=cs )
)
|
(
( X0=john & X1=math )
)
|
(
( X0_'$ki_world'='$ki_local_world' & X0=sue & X1=psych )
)
|
(
( X0_'$ki_world'='$ki_local_world' & X0=mary & X1=psych )
)
)
)
)
).
%------ Positive definition of '$ki_exists_in_world_$i'
fof(lit_def,axiom,
(! [X0_'$ki_world',X0] :
( '$ki_exists_in_world_$i'(X0_'$ki_world',X0) <=>
$true
)
)
).
Solution for SWW469_10
%------ Positive definition of equality_sorted
fof(lit_def,axiom,
(! [X0_$tType,X0_state,X1_state] :
( equality_sorted(X0_$tType,X0_state,X1_state) <=>
(
(
( X0_$tType=state )
&
( X0_state!=sK0 | X1_state!=sK1 )
&
( X0_state!=sK1 )
&
( X1_state!=sK1 )
)
|
(
( X0_$tType=state & X0_state=sK1 & X1_state=sK1 )
)
|
(
( X0_$tType=state & X1_state=X0_state )
&
( X0_state!=sK1 )
)
)
)
)
).
%------ Positive definition of hoare_1310879719gleton
fof(lit_def,axiom,
( hoare_1310879719gleton <=>
$true
)
).
%------ Positive definition of induct_false
fof(lit_def,axiom,
( induct_false <=>
$false
)
).
%------ Positive definition of induct_true
fof(lit_def,axiom,
( induct_true <=>
$true
)
).
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_8041 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f52 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f51 as the proved formula
% CPUTIME: 0.07
% SUCCESS: Verified
% SZS status Verified
fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('/shareddata/TPTP-v9.0.0/Problems/SEU/SEU140+2.p',d3_tarski)).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('/shareddata/TPTP-v9.0.0/Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('/shareddata/TPTP-v9.0.0/Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[status(cth)],[f51])).
fof(f62,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f67,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
inference(ennf_transformation,[],[f8])).
fof(f82,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f62])).
fof(f87,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f88,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f87])).
fof(f105,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
inference(nnf_transformation,[],[f67])).
fof(f106,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(rectify,[],[f105])).
fof(f107,plain,(
! [X0,X1] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f108,plain,(
! [X0,X1] : ((subset(X0,X1) | (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f106,f107])).
fof(f129,plain,(
! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f130,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f133,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
introduced(choice_axiom,[])).
fof(f134,plain,(
~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f150,plain,(
( ! [X3,X0,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f108])).
fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f199,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f130])).
fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).
fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).
tcf(c_66,plain,![X0:$i,X1:$i,X2:$i]:
(~in(X0,X1)|~subset(X1,X2)|in(X0,X2)),
inference(cnf_transformation,[],[f150])).
tcf(c_111,plain,![X0:$i,X1:$i,X2:$i]:
(~in(X0,X1)|~in(X0,X2)|~disjoint(X2,X1)),
inference(cnf_transformation,[],[f199])).
tcf(c_112,plain,![X0:$i,X1:$i]:
(in(sK8(X0,X1),X1)|disjoint(X0,X1)),
inference(cnf_transformation,[],[f198])).
tcf(c_113,plain,![X0:$i,X1:$i]:
(in(sK8(X0,X1),X0)|disjoint(X0,X1)),
inference(cnf_transformation,[],[f197])).
tcf(c_121,plain,
(~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f210])).
tcf(c_122,plain,
(disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f209])).
tcf(c_123,plain,
(subset(sK10,sK11)),
inference(cnf_transformation,[],[f208])).
tcf(c_3342,plain,
(in(sK8(sK10,sK12),sK12)|disjoint(sK10,sK12)),
inference(instantiation,[status(thm)],[c_112])).
tcf(c_3343,plain,
(in(sK8(sK10,sK12),sK10)|disjoint(sK10,sK12)),
inference(instantiation,[status(thm)],[c_113])).
tcf(c_3627,plain,![X0:$i]:
(~in(sK8(sK10,sK12),X0)|~in(sK8(sK10,sK12),sK12)|~disjoint(X0,sK12)),
inference(instantiation,[status(thm)],[c_111])).
tcf(c_3703,plain,![X0:$i]:
(~in(sK8(sK10,sK12),sK10)|~subset(sK10,X0)|in(sK8(sK10,sK12),X0)),
inference(instantiation,[status(thm)],[c_66])).
tcf(c_7507,plain,
(~in(sK8(sK10,sK12),sK12)|~in(sK8(sK10,sK12),sK11)|~disjoint(sK11,sK12)),
inference(instantiation,[status(thm)],[c_3627])).
tcf(c_8040,plain,
(~in(sK8(sK10,sK12),sK10)|~subset(sK10,sK11)|in(sK8(sK10,sK12),sK11)),
inference(instantiation,[status(thm)],[c_3703])).
tcf(c_8041,plain,
($false),
inference(prop_impl_just,
[status(thm)],
[c_8040,c_7507,c_3343,c_3342,c_121,c_122,c_123])).
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root c_310 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the derivation root c_310 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(f1,axiom,(
( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
file('/shareddata/TPTP-v9.0.0/Problems/BOO/BOO001-1.p',associativity)).
fof(f2,axiom,(
( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
file('/shareddata/TPTP-v9.0.0/Problems/BOO/BOO001-1.p',ternary_multiply_1)).
fof(f5,axiom,(
( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
file('/shareddata/TPTP-v9.0.0/Problems/BOO/BOO001-1.p',right_inverse)).
fof(f6,axiom,(
a != inverse(inverse(a))),
file('/shareddata/TPTP-v9.0.0/Problems/BOO/BOO001-1.p',prove_inverse_is_self_cancelling)).
tcf(c_55,plain,![X0:$i,X1:$i,X2:$i,X3:$i,X4:$i]:
(multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))),
inference(cnf_transformation,[],[f1])).
tcf(c_56,plain,![X0:$i,X1:$i]:
(multiply(X0,X1,X1) = X1),
inference(cnf_transformation,[],[f2])).
tcf(c_59,plain,![X0:$i,X1:$i]:
(multiply(X0,X1,inverse(X1)) = X0),
inference(cnf_transformation,[],[f5])).
tcf(c_60,plain,
(inverse(inverse(a)) != a),
inference(cnf_transformation,[],[f6])).
tcf(c_121,plain,![X0:$i,X1:$i,X2:$i,X3:$i]:
(multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))),
inference(superposition,[status(thm)],[c_56,c_55])).
tcf(c_156,plain,![X0:$i,X1:$i,X2:$i]:
(multiply(X0,X1,multiply(X2,X0,X1)) = multiply(X2,X0,X1)),
inference(superposition,[status(thm)],[c_56,c_121])).
tcf(c_279,plain,![X0:$i,X1:$i]:
(multiply(X0,inverse(X0),X1) = X1),
inference(superposition,[status(thm)],[c_59,c_156])).
tcf(c_304,plain,![X0:$i]:
(inverse(inverse(X0)) = X0),
inference(superposition,[status(thm)],[c_279,c_59])).
tcf(c_310,plain,
($false),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_304])).
Vampire 4.9
Michael Rawson
TU Wien, Austria
Solution for SET014^4
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f114 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f16 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f15 as the proved formula
% CPUTIME: 0.07
% SUCCESS: Verified
% SZS status Verified
thf(func_def_0, type, in: $i > ($i > $o) > $o).
thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
thf(func_def_3, type, emptyset: $i > $o).
thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
thf(func_def_5, type, singleton: $i > $i > $o).
thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_10, type, complement: ($i > $o) > $i > $o).
thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
thf(func_def_28, type, sK0: $i > $o).
thf(func_def_29, type, sK1: $i > $o).
thf(func_def_30, type, sK2: $i > $o).
thf(f114,plain,(
$false),
inference(avatar_sat_refutation,[status(thm)],[f92,f102,f113])).
thf(f113,plain,(
~spl3_1),
inference(avatar_contradiction_clause,[status(thm)],[f112])).
thf(f112,plain,(
$false | ~spl3_1),
inference(trivial_inequality_removal,[status(thm)],[f108])).
thf(f108,plain,(
($false = $true) | ~spl3_1),
inference(superposition,[status(thm)],[f106,f73])).
thf(f73,plain,(
((sK0 @ sK4) = $false)),
inference(binary_proxy_clausification,[status(thm)],[f72])).
thf(f72,plain,(
($false = (((sK1 @ sK4) | (sK2 @ sK4)) => (sK0 @ sK4)))),
inference(beta_eta_normalization,[status(thm)],[f71])).
thf(f71,plain,(
(((^[Y0 : $i]: (((sK1 @ Y0) | (sK2 @ Y0)) => (sK0 @ Y0))) @ sK4) = $false)),
inference(sigma_clausification,[status(thm)],[f70])).
thf(f70,plain,(
((!! @ $i @ (^[Y0 : $i]: (((sK1 @ Y0) | (sK2 @ Y0)) => (sK0 @ Y0)))) != $true)),
inference(beta_eta_normalization,[status(thm)],[f68])).
thf(f68,plain,(
(((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ sK1 @ sK2) @ sK0) != $true)),
inference(definition_unfolding,[status(thm)],[f54,f51,f61])).
thf(f61,plain,(
(union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
inference(cnf_transformation,[status(thm)],[f30])).
thf(f30,plain,(
(union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
inference(fool_elimination,[status(thm)],[f29])).
thf(f29,plain,(
((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = union)),
inference(rectify,[status(thm)],[f6])).
thf(f6,axiom,(
((^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : ((X2 @ X3) | (X0 @ X3))) = union)),
file('/tmp/tmp.slMwWcQSPA/Vampire_2879376.p',union)).
thf(f51,plain,(
(subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
inference(cnf_transformation,[status(thm)],[f19])).
thf(f19,plain,(
(subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
inference(fool_elimination,[status(thm)],[f18])).
thf(f18,plain,(
((^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) => (X1 @ X2)))) = subset)),
inference(rectify,[status(thm)],[f12])).
thf(f12,axiom,(
((^[X0 : $i > $o, X2 : $i > $o] : (! [X3 : $i] : ((X0 @ X3) => (X2 @ X3)))) = subset)),
file('/tmp/tmp.slMwWcQSPA/Vampire_2879376.p',subset)).
thf(f54,plain,(
((subset @ (union @ sK1 @ sK2) @ sK0) != $true)),
inference(cnf_transformation,[status(thm)],[f48])).
thf(f48,plain,(
((subset @ sK1 @ sK0) = $true) & ((subset @ (union @ sK1 @ sK2) @ sK0) != $true) & ((subset @ sK2 @ sK0) = $true)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f46,f47])).
thf(f47,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((subset @ X1 @ X0) = $true) & ((subset @ (union @ X1 @ X2) @ X0) != $true) & ((subset @ X2 @ X0) = $true)) => (((subset @ sK1 @ sK0) = $true) & ((subset @ (union @ sK1 @ sK2) @ sK0) != $true) & ((subset @ sK2 @ sK0) = $true))),
introduced(definition,[],[choice_axiom])).
thf(f46,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((subset @ X1 @ X0) = $true) & ((subset @ (union @ X1 @ X2) @ X0) != $true) & ((subset @ X2 @ X0) = $true))),
inference(flattening,[status(thm)],[f45])).
thf(f45,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((subset @ (union @ X1 @ X2) @ X0) != $true) & (((subset @ X2 @ X0) = $true) & ((subset @ X1 @ X0) = $true)))),
inference(ennf_transformation,[status(thm)],[f43])).
thf(f43,plain,(
~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((((subset @ X2 @ X0) = $true) & ((subset @ X1 @ X0) = $true)) => ((subset @ (union @ X1 @ X2) @ X0) = $true))),
inference(fool_elimination,[status(thm)],[f42])).
thf(f42,plain,(
~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((subset @ X2 @ X0) & (subset @ X1 @ X0)) => (subset @ (union @ X1 @ X2) @ X0))),
inference(rectify,[status(thm)],[f16])).
thf(f16,negated_conjecture,(
~! [X4 : $i > $o,X0 : $i > $o,X2 : $i > $o] : (((subset @ X2 @ X4) & (subset @ X0 @ X4)) => (subset @ (union @ X0 @ X2) @ X4))),
inference(negated_conjecture,[status(cth)],[f15])).
thf(f15,conjecture,(
! [X4 : $i > $o,X0 : $i > $o,X2 : $i > $o] : (((subset @ X2 @ X4) & (subset @ X0 @ X4)) => (subset @ (union @ X0 @ X2) @ X4))),
file('/tmp/tmp.slMwWcQSPA/Vampire_2879376.p',thm)).
thf(f106,plain,(
((sK0 @ sK4) = $true) | ~spl3_1),
inference(trivial_inequality_removal,[status(thm)],[f104])).
thf(f104,plain,(
($false = $true) | ((sK0 @ sK4) = $true) | ~spl3_1),
inference(superposition,[status(thm)],[f79,f87])).
thf(f87,plain,(
((sK1 @ sK4) = $true) | ~spl3_1),
inference(avatar_component_clause,[status(thm)],[f85])).
thf(f85,definition,(
spl3_1 <=> ((sK1 @ sK4) = $true)),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
thf(f79,plain,(
( ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK0 @ X1) = $true)) )),
inference(binary_proxy_clausification,[status(thm)],[f78])).
thf(f78,plain,(
( ! [X1 : $i] : ((((sK1 @ X1) => (sK0 @ X1)) = $true)) )),
inference(beta_eta_normalization,[status(thm)],[f77])).
thf(f77,plain,(
( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ Y0) => (sK0 @ Y0))) @ X1) = $true)) )),
inference(pi_clausification,[status(thm)],[f76])).
thf(f76,plain,(
((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK0 @ Y0)))) = $true)),
inference(beta_eta_normalization,[status(thm)],[f67])).
thf(f67,plain,(
(((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ sK1 @ sK0) = $true)),
inference(definition_unfolding,[status(thm)],[f55,f51])).
thf(f55,plain,(
((subset @ sK1 @ sK0) = $true)),
inference(cnf_transformation,[status(thm)],[f48])).
thf(f102,plain,(
~spl3_2),
inference(avatar_contradiction_clause,[status(thm)],[f101])).
thf(f101,plain,(
$false | ~spl3_2),
inference(trivial_inequality_removal,[status(thm)],[f98])).
thf(f98,plain,(
($false = $true) | ~spl3_2),
inference(superposition,[status(thm)],[f73,f96])).
thf(f96,plain,(
((sK0 @ sK4) = $true) | ~spl3_2),
inference(trivial_inequality_removal,[status(thm)],[f93])).
thf(f93,plain,(
((sK0 @ sK4) = $true) | ($false = $true) | ~spl3_2),
inference(superposition,[status(thm)],[f83,f91])).
thf(f91,plain,(
((sK2 @ sK4) = $true) | ~spl3_2),
inference(avatar_component_clause,[status(thm)],[f89])).
thf(f89,definition,(
spl3_2 <=> ((sK2 @ sK4) = $true)),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
thf(f83,plain,(
( ! [X1 : $i] : (((sK2 @ X1) = $false) | ((sK0 @ X1) = $true)) )),
inference(binary_proxy_clausification,[status(thm)],[f82])).
thf(f82,plain,(
( ! [X1 : $i] : ((((sK2 @ X1) => (sK0 @ X1)) = $true)) )),
inference(beta_eta_normalization,[status(thm)],[f81])).
thf(f81,plain,(
( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ Y0) => (sK0 @ Y0))) @ X1) = $true)) )),
inference(pi_clausification,[status(thm)],[f80])).
thf(f80,plain,(
((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK0 @ Y0)))) = $true)),
inference(beta_eta_normalization,[status(thm)],[f69])).
thf(f69,plain,(
(((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ sK2 @ sK0) = $true)),
inference(definition_unfolding,[status(thm)],[f53,f51])).
thf(f53,plain,(
((subset @ sK2 @ sK0) = $true)),
inference(cnf_transformation,[status(thm)],[f48])).
thf(f92,plain,(
spl3_1 | spl3_2),
inference(avatar_split_clause,[status(thm)],[f75,f89,f85])).
thf(f75,plain,(
((sK2 @ sK4) = $true) | ((sK1 @ sK4) = $true)),
inference(binary_proxy_clausification,[status(thm)],[f74])).
thf(f74,plain,(
(((sK1 @ sK4) | (sK2 @ sK4)) = $true)),
inference(binary_proxy_clausification,[status(thm)],[f72])).
Solution for DAT013_1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f277 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% FAILURE: Negated conjecture f4 is not a leaf or CTH from a conjecture
% CPUTIME: 0.06
% FAILURE: Not verified
% SZS status NotVerified
tff(type_def_5, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_7, type, sK0: $int).
tff(func_def_8, type, sK1: $int).
tff(func_def_9, type, sK2: array).
tff(func_def_10, type, sK3: $int).
tff(f277,plain,(
$false),
inference(avatar_sat_refutation,[],[f77,f192,f276])).
tff(f276,plain,(
~spl4_6),
inference(avatar_contradiction_clause,[],[f275])).
tff(f275,plain,(
$false | ~spl4_6),
inference(subsumption_resolution,[],[f273,f11])).
tff(f11,plain,(
( ! [X0 : $int] : (~$less(X0,X0)) )),
introduced(theory_axiom_150,[])).
tff(f273,plain,(
$less(sK0,sK0) | ~spl4_6),
inference(resolution,[],[f257,f48])).
tff(f48,plain,(
( ! [X0 : $int] : (~$less(X0,sK3) | $less(X0,sK0)) )),
inference(resolution,[],[f47,f12])).
tff(f12,plain,(
( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
introduced(theory_axiom_151,[])).
tff(f47,plain,(
$less(sK3,sK0)),
inference(subsumption_resolution,[],[f45,f28])).
tff(f28,plain,(
~$less(sK1,sK3)),
inference(cnf_transformation,[],[f25])).
tff(f25,plain,(
! [X3 : $int] : ($less(sK1,X3) | $less(0,read(sK2,X3)) | $less(X3,sK0)) & (~$less(0,read(sK2,sK3)) & ~$less(sK3,$sum(sK0,3)) & ~$less(sK1,sK3))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f22,f24,f23])).
tff(f23,plain,(
? [X0 : $int,X1 : $int,X2 : array] : (! [X3 : $int] : ($less(X1,X3) | $less(0,read(X2,X3)) | $less(X3,X0)) & ? [X4 : $int] : (~$less(0,read(X2,X4)) & ~$less(X4,$sum(X0,3)) & ~$less(X1,X4))) => (! [X3 : $int] : ($less(sK1,X3) | $les
s(0,read(sK2,X3)) | $less(X3,sK0)) & ? [X4 : $int] : (~$less(0,read(sK2,X4)) & ~$less(X4,$sum(sK0,3)) & ~$less(sK1,X4)))),
introduced(choice_axiom,[])).
tff(f24,plain,(
? [X4 : $int] : (~$less(0,read(sK2,X4)) & ~$less(X4,$sum(sK0,3)) & ~$less(sK1,X4)) => (~$less(0,read(sK2,sK3)) & ~$less(sK3,$sum(sK0,3)) & ~$less(sK1,sK3))),
introduced(choice_axiom,[])).
tff(f22,plain,(
? [X0 : $int,X1 : $int,X2 : array] : (! [X3 : $int] : ($less(X1,X3) | $less(0,read(X2,X3)) | $less(X3,X0)) & ? [X4 : $int] : (~$less(0,read(X2,X4)) & ~$less(X4,$sum(X0,3)) & ~$less(X1,X4)))),
inference(rectify,[],[f21])).
tff(f21,plain,(
? [X2 : $int,X1 : $int,X0 : array] : (! [X3 : $int] : ($less(X1,X3) | $less(0,read(X0,X3)) | $less(X3,X2)) & ? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X4,$sum(X2,3)) & ~$less(X1,X4)))),
inference(flattening,[],[f20])).
tff(f20,plain,(
? [X1 : $int,X2 : $int,X0 : array] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X1,X4) & ~$less(X4,$sum(X2,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X3,X2) | $less(X1,X3))))),
inference(ennf_transformation,[],[f18])).
tff(f18,plain,(
~! [X1 : $int,X2 : $int,X0 : array] : (! [X3 : $int] : ((~$less(X3,X2) & ~$less(X1,X3)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X1,X4) & ~$less(X4,$sum(X2,3))) => $less(0,read(X0,X4))))),
inference(rectify,[],[f5])).
tff(f5,plain,(
~! [X0 : array,X2 : $int,X1 : $int] : (! [X3 : $int] : ((~$less(X3,X1) & ~$less(X2,X3)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
~! [X0 : array,X2 : $int,X1 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
tff(f3,conjecture,(
! [X0 : array,X2 : $int,X1 : $int] : (! [X3 : $int] : (($lesseq(X1,X3) & $lesseq(X3,X2)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
file('Problems/DAT/DAT013_1.p',unknown)).
tff(f45,plain,(
$less(sK3,sK0) | $less(sK1,sK3)),
inference(resolution,[],[f31,f30])).
tff(f30,plain,(
~$less(0,read(sK2,sK3))),
inference(cnf_transformation,[],[f25])).
tff(f31,plain,(
( ! [X3 : $int] : ($less(0,read(sK2,X3)) | $less(X3,sK0) | $less(sK1,X3)) )),
inference(cnf_transformation,[],[f25])).
tff(f257,plain,(
$less(sK0,sK3) | ~spl4_6),
inference(evaluation,[],[f253])).
tff(f253,plain,(
~$less(0,3) | $less(sK0,sK3) | ~spl4_6),
inference(superposition,[],[f208,f8])).
tff(f8,plain,(
( ! [X0 : $int] : ($sum(X0,0) = X0) )),
introduced(theory_axiom_145,[])).
tff(f208,plain,(
( ! [X0 : $int] : ($less($sum(sK0,X0),sK3) | ~$less(X0,3)) ) | ~spl4_6),
inference(superposition,[],[f200,f6])).
tff(f6,plain,(
( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
introduced(theory_axiom_143,[])).
tff(f200,plain,(
( ! [X0 : $int] : ($less($sum(X0,sK0),sK3) | ~$less(X0,3)) ) | ~spl4_6),
inference(resolution,[],[f198,f14])).
tff(f14,plain,(
( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
introduced(theory_axiom_153,[])).
tff(f198,plain,(
( ! [X0 : $int] : (~$less(X0,$sum(3,sK0)) | $less(X0,sK3)) ) | ~spl4_6),
inference(resolution,[],[f76,f12])).
tff(f76,plain,(
$less($sum(3,sK0),sK3) | ~spl4_6),
inference(avatar_component_clause,[],[f75])).
tff(f75,plain,(
spl4_6 <=> $less($sum(3,sK0),sK3)),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])])).
tff(f192,plain,(
~spl4_5),
inference(avatar_contradiction_clause,[],[f191])).
tff(f191,plain,(
$false | ~spl4_5),
inference(subsumption_resolution,[],[f189,f11])).
tff(f189,plain,(
$less(sK0,sK0) | ~spl4_5),
inference(resolution,[],[f172,f48])).
tff(f172,plain,(
$less(sK0,sK3) | ~spl4_5),
inference(evaluation,[],[f168])).
tff(f168,plain,(
$less(sK0,sK3) | ~$less(0,3) | ~spl4_5),
inference(superposition,[],[f107,f8])).
tff(f107,plain,(
( ! [X0 : $int] : ($less($sum(sK0,X0),sK3) | ~$less(X0,3)) ) | ~spl4_5),
inference(superposition,[],[f81,f6])).
tff(f81,plain,(
( ! [X0 : $int] : ($less($sum(X0,sK0),sK3) | ~$less(X0,3)) ) | ~spl4_5),
inference(superposition,[],[f14,f73])).
tff(f73,plain,(
sK3 = $sum(3,sK0) | ~spl4_5),
inference(avatar_component_clause,[],[f72])).
tff(f72,plain,(
spl4_5 <=> sK3 = $sum(3,sK0)),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])])).
tff(f77,plain,(
spl4_5 | spl4_6),
inference(avatar_split_clause,[],[f37,f75,f72])).
tff(f37,plain,(
$less($sum(3,sK0),sK3) | sK3 = $sum(3,sK0)),
inference(resolution,[],[f34,f13])).
tff(f13,plain,(
( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
introduced(theory_axiom_152,[])).
tff(f34,plain,(
~$less(sK3,$sum(3,sK0))),
inference(forward_demodulation,[],[f29,f6])).
tff(f29,plain,(
~$less(sK3,$sum(sK0,3))),
inference(cnf_transformation,[],[f25])).
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f277 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% FAILURE: Negated conjecture f4 is not a leaf or CTH from a conjecture
% CPUTIME: 0.06
% FAILURE: Not verified
% SZS status NotVerified
fof(f1031,plain,(
$false),
inference(resolution,[],[f995,f351])).
fof(f351,plain,(
in(sK3(sK0,sK2),set_difference(sK0,set_difference(sK0,sK2)))),
inference(resolution,[],[f201,f128])).
fof(f128,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f90])).
fof(f90,plain,(
~disjoint(sK0,sK2) & disjoint(sK1,sK2) & subset(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f66,f89])).
fof(f89,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK0,sK2) & disjoint(sK1,sK2) & subset(sK0,sK1))),
introduced(choice_axiom,[])).
fof(f66,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f65])).
fof(f65,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f201,plain,(
( ! [X0,X1] : (disjoint(X0,X1) | in(sK3(X0,X1),set_difference(X0,set_difference(X0,X1)))) )),
inference(definition_unfolding,[],[f137,f135])).
fof(f135,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f137,plain,(
( ! [X0,X1] : (in(sK3(X0,X1),set_intersection2(X0,X1)) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f92])).
fof(f92,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : ~in(X2,set_intersection2(X0,X1))) & (in(sK3(X0,X1),set_intersection2(X0,X1)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f68,f91])).
fof(f91,plain,(
! [X0,X1] : (? [X3] : in(X3,set_intersection2(X0,X1)) => in(sK3(X0,X1),set_intersection2(X0,X1)))),
introduced(choice_axiom,[])).
fof(f68,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : ~in(X2,set_intersection2(X0,X1))) & (? [X3] : in(X3,set_intersection2(X0,X1)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f58])).
fof(f58,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : in(X2,set_intersection2(X0,X1))) & ~(! [X3] : ~in(X3,set_intersection2(X0,X1)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f49])).
fof(f49,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : in(X2,set_intersection2(X0,X1))) & ~(! [X2] : ~in(X2,set_intersection2(X0,X1)) & ~disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f995,plain,(
( ! [X0] : (~in(sK3(sK0,sK2),set_difference(sK0,X0))) )),
inference(resolution,[],[f963,f226])).
fof(f226,plain,(
( ! [X0,X1,X4] : (in(X4,X0) | ~in(X4,set_difference(X0,X1))) )),
inference(equality_resolution,[],[f182])).
fof(f182,plain,(
( ! [X2,X0,X1,X4] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f114])).
fof(f114,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK7(X0,X1,X2),X1) | ~in(sK7(X0,X1,X2),X0) | ~in(sK7(X0,X1,X2),X2)) & ((~in(sK7(X0,X1,X2),X1) & in(sK7(X0,X1,X2),X0)) | in(sK7(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f112,f113])).
fof(f113,plain,(
! [X0,X1,X2] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK7(X0,X1,X2),X1) | ~in(sK7(X0,X1,X2),X0) | ~in(sK7(X0,X1,X2),X2)) & ((~in(sK7(X0,X1,X2),X1) & in(sK7(X0,X1,X2),X0)) | in(sK7(X0,X1,X2),X2))))),
introduced(choice_axiom,[])).
fof(f112,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(rectify,[],[f111])).
fof(f111,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(flattening,[],[f110])).
fof(f110,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(nnf_transformation,[],[f10])).
fof(f10,axiom,(
! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f963,plain,(
~in(sK3(sK0,sK2),sK0)),
inference(resolution,[],[f548,f126])).
fof(f126,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f90])).
fof(f548,plain,(
( ! [X0] : (~subset(X0,sK1) | ~in(sK3(sK0,sK2),X0)) )),
inference(resolution,[],[f291,f390])).
fof(f390,plain,(
in(sK3(sK0,sK2),sK2)),
inference(resolution,[],[f351,f222])).
fof(f222,plain,(
( ! [X0,X1,X4] : (~in(X4,set_difference(X0,set_difference(X0,X1))) | in(X4,X1)) )),
inference(equality_resolution,[],[f214])).
fof(f214,plain,(
( ! [X2,X0,X1,X4] : (in(X4,X1) | ~in(X4,X2) | set_difference(X0,set_difference(X0,X1)) != X2) )),
inference(definition_unfolding,[],[f177,f135])).
fof(f177,plain,(
( ! [X2,X0,X1,X4] : (in(X4,X1) | ~in(X4,X2) | set_intersection2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f109])).
fof(f109,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) = X2 | ((~in(sK6(X0,X1,X2),X1) | ~in(sK6(X0,X1,X2),X0) | ~in(sK6(X0,X1,X2),X2)) & ((in(sK6(X0,X1,X2),X1) & in(sK6(X0,X1,X2),X0)) | in(sK6(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | ~in(X4,X1) | ~in(X4,X0)) & ((in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_intersection2(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f107,f108])).
fof(f108,plain,(
! [X0,X1,X2] : (? [X3] : ((~in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((~in(sK6(X0,X1,X2),X1) | ~in(sK6(X0,X1,X2),X0) | ~in(sK6(X0,X1,X2),X2)) & ((in(sK6(X0,X1,X2),X1) & in(sK6(X0,X1,X2),X0)) | in(sK6(X0,X1,X2),X2))))),
introduced(choice_axiom,[])).
fof(f107,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) = X2 | ? [X3] : ((~in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | ~in(X4,X1) | ~in(X4,X0)) & ((in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_intersection2(X0,X1) != X2))),
inference(rectify,[],[f106])).
fof(f106,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) = X2 | ? [X3] : ((~in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | ~in(X3,X1) | ~in(X3,X0)) & ((in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_intersection2(X0,X1) != X2))),
inference(flattening,[],[f105])).
fof(f105,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) = X2 | ? [X3] : (((~in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (~in(X3,X1) | ~in(X3,X0))) & ((in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_intersection2(X0,X1) != X2))),
inference(nnf_transformation,[],[f9])).
fof(f9,axiom,(
! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X1) & in(X3,X0))))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f291,plain,(
( ! [X0,X1] : (~in(X0,sK2) | ~in(X0,X1) | ~subset(X1,sK1)) )),
inference(resolution,[],[f278,f188])).
fof(f188,plain,(
( ! [X3,X0,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
! [X0,X1] : ((subset(X0,X1) | (~in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f116,f117])).
fof(f117,plain,(
! [X0,X1] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f116,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(rectify,[],[f115])).
fof(f115,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
inference(nnf_transformation,[],[f83])).
fof(f83,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
inference(ennf_transformation,[],[f8])).
fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f278,plain,(
( ! [X0] : (~in(X0,sK1) | ~in(X0,sK2)) )),
inference(resolution,[],[f141,f127])).
fof(f127,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f90])).
fof(f141,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f94])).
fof(f94,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK4(X0,X1),X1) & in(sK4(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f69,f93])).
fof(f93,plain,(
! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK4(X0,X1),X1) & in(sK4(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f69,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f59])).
fof(f59,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',unknown)).
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f87 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the derivation root f87 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(f87,plain,(
$false),
inference(trivial_inequality_removal,[],[f85])).
fof(f85,plain,(
a != a),
inference(backward_demodulation,[],[f6,f79])).
fof(f79,plain,(
( ! [X0] : (inverse(inverse(X0)) = X0) )),
inference(superposition,[],[f71,f5])).
fof(f5,axiom,(
( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f71,plain,(
( ! [X0,X1] : (multiply(X1,inverse(X1),X0) = X0) )),
inference(superposition,[],[f24,f5])).
fof(f24,plain,(
( ! [X2,X0,X1] : (multiply(X2,X0,X1) = multiply(X0,X1,multiply(X2,X0,X1))) )),
inference(superposition,[],[f7,f2])).
fof(f2,axiom,(
( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f7,plain,(
( ! [X2,X3,X0,X1] : (multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))) )),
inference(superposition,[],[f1,f2])).
fof(f1,axiom,(
( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f6,axiom,(
a != inverse(inverse(a))),
file('Problems/BOO/BOO001-1.p',unknown)).
Vampire 5.0
Michael Rawson
University of Southampton, United Kongdom
Notes regarding saturations
Vampire can testify (counter)-satisfiability of a given problem by finitely saturating the
corresponding preprocessed clause set (using a complete version of a calculus). It then reports
SZS Status Satisfiable.
As supporting evidence, Vampire prints two artefacts:
The saturated clause set itself between SZS output start Saturation and SZS output
end Saturation, and a section of "Definitions and Model Updates".
Among the preprocessing steps used by Vampire in order to transform an arbitrary first-order
problem into the CNF on which saturation starts are some steps (we call them
interferences) which only preserve model existence, but not all models, or which modify
the signature.
Each of these steps comes with a model-theoretic argument of the form: "If you give me a model
of the post-step F, this is what you must do to get a model of pre-step F".
The "Definitions and Model Updates" section lists these transformations in the order in which
they should be applied to the model of the final CNF (that just got saturated) in order to arrive
at a model of the original input problem.
These transformations are implemented in Vampire already to work on finite models found by its
finite model finder, but since the model represented by finite saturations is only implicit, we do
our best to at least report what transformations have been recorded and should be played back.
Here is an explanation for the transformations implemented (so far):
- Eliminated symbols are defined in terms of their original definitions. E.g. for predicates:
for all inputs,
define r(X0,X1) := p(X0,b)
or for functions (constants):
for all inputs,
define a := aa
- Partially eliminated definitions (e.g., when Vampire turns
![X:ta] : (~qq(X) <=> ~(q(X) & (?[X:ta] : q(X))))
into
![X:ta] : (~qq(X) <= ~(q(X) & (?[X:ta] : q(X))))
because all the remaining occurrences of qq are positive.) may require conditional atom flips:
for all groundings,
whenever ? [X1 : ta] : q(X1) & q(X0) is true, set qq(X0) to true
Here "for all groundings" suggests a Herbrand model, but the meaning is the same as "for
all inputs".
- We also have globally flip the polarity of every occurrence of a predicate, e.g.,
'$ki_accessible', which means: "negate the whole truth table for the corresponding
predicate" and complements the optional random_polarities preprocessing step ("As part of
preprocessing, randomly (though consistently) flip polarities of non-equality predicates in
the whole CNF.").
- To complement blocked clause elimination
(https://easychair.org/publications/paper/Bl2v/open)
we may introduce a more complicated version of a conditional flip. E.g.,
for all groundings, until fixed point,
whenever teach(X1,X0,cs) | ~'$ki_accessible'('$ki_local_world',X1) | ~teach('$ki_local_world',X0,psych) | ~'$ki_exists_in_world_$i'('$ki_local_world',X0) is false, set teach(X1,X0,cs) to true
The "until fixed point" bit is necessary and explained in Lemma 4 of the BCE paper.
In a nutshell, this means: if you go over your groundings and flip something, you have to
then restart and go from the beginning again.
In the finite model building version of this (which actually does the changes as described)
we use a do-while loop
(https://github.com/vprover/vampire/blob/0dce69acaa3452831bf8f851485da9266aa02b57/FMB/FiniteModelMultiSorted.cpp#L1093)
Solution for SET014^4
thf(func_def_0, type, in: $i > ($i > $o) > $o).
thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
thf(func_def_3, type, emptyset: $i > $o).
thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
thf(func_def_5, type, singleton: $i > $i > $o).
thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
thf(func_def_10, type, complement: ($i > $o) > $i > $o).
thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
thf(func_def_28, type, sK0: $i > $o).
thf(func_def_29, type, sK1: $i > $o).
thf(func_def_30, type, sK2: $i > $o).
thf(f113,plain,(
$false),
inference(avatar_sat_refutation,[],[f92,f106,f112])).
thf(f112,plain,(
~spl3_1),
inference(avatar_contradiction_clause,[],[f111])).
thf(f111,plain,(
$false | ~spl3_1),
inference(trivial_inequality_removal,[],[f107])).
thf(f107,plain,(
($true = $false) | ~spl3_1),
inference(superposition,[],[f87,f96])).
thf(f96,plain,(
($false = (sK2 @ sK4))),
inference(trivial_inequality_removal,[],[f94])).
thf(f94,plain,(
($true = $false) | ($false = (sK2 @ sK4))),
inference(superposition,[],[f79,f73])).
thf(f73,plain,(
((sK1 @ sK4) = $false)),
inference(binary_proxy_clausification,[],[f72])).
thf(f72,plain,(
((((sK2 @ sK4) | (sK0 @ sK4)) => (sK1 @ sK4)) = $false)),
inference(beta_eta_normalization,[],[f71])).
thf(f71,plain,(
($false = ((^[Y0 : $i]: (((sK2 @ Y0) | (sK0 @ Y0)) => (sK1 @ Y0))) @ sK4))),
inference(sigma_clausification,[],[f70])).
thf(f70,plain,(
($true != (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0) | (sK0 @ Y0)) => (sK1 @ Y0)))))),
inference(beta_eta_normalization,[],[f67])).
thf(f67,plain,(
($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ sK2 @ sK0) @ sK1))),
inference(definition_unfolding,[],[f59,f52,f60])).
thf(f60,plain,(
(union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
inference(cnf_transformation,[],[f28])).
thf(f28,plain,(
(union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
inference(fool_elimination,[],[f27])).
thf(f27,plain,(
((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = union)),
inference(rectify,[],[f6])).
thf(f6,axiom,(
((^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : ((X2 @ X3) | (X0 @ X3))) = union)),
file('Problems/SET/SET014^4.p',union)).
thf(f52,plain,(
(subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
inference(cnf_transformation,[],[f36])).
thf(f36,plain,(
(subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
inference(fool_elimination,[],[f35])).
thf(f35,plain,(
(subset = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))))),
inference(rectify,[],[f12])).
thf(f12,axiom,(
(subset = (^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))))),
file('Problems/SET/SET014^4.p',subset)).
thf(f59,plain,(
((subset @ (union @ sK2 @ sK0) @ sK1) != $true)),
inference(cnf_transformation,[],[f48])).
thf(f48,plain,(
((subset @ (union @ sK2 @ sK0) @ sK1) != $true) & ($true = (subset @ sK0 @ sK1)) & ($true = (subset @ sK2 @ sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f46,f47])).
thf(f47,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != (subset @ (union @ X2 @ X0) @ X1)) & ($true = (subset @ X0 @ X1)) & ($true = (subset @ X2 @ X1))) => (((subset @ (union @ sK2 @ sK0) @ sK1) != $true) & ($true = (subset @ sK0
@ sK1)) & ($true = (subset @ sK2 @ sK1)))),
introduced(choice_axiom,[])).
thf(f46,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != (subset @ (union @ X2 @ X0) @ X1)) & ($true = (subset @ X0 @ X1)) & ($true = (subset @ X2 @ X1)))),
inference(flattening,[],[f45])).
thf(f45,plain,(
? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (($true != (subset @ (union @ X2 @ X0) @ X1)) & (($true = (subset @ X2 @ X1)) & ($true = (subset @ X0 @ X1))))),
inference(ennf_transformation,[],[f30])).
thf(f30,plain,(
~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : ((($true = (subset @ X2 @ X1)) & ($true = (subset @ X0 @ X1))) => ($true = (subset @ (union @ X2 @ X0) @ X1)))),
inference(fool_elimination,[],[f29])).
thf(f29,plain,(
~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $o] : (((subset @ X2 @ X1) & (subset @ X0 @ X1)) => (subset @ (union @ X2 @ X0) @ X1))),
inference(rectify,[],[f16])).
thf(f16,negated_conjecture,(
~! [X2 : $i > $o,X4 : $i > $o,X0 : $i > $o] : (((subset @ X0 @ X4) & (subset @ X2 @ X4)) => (subset @ (union @ X0 @ X2) @ X4))),
inference(negated_conjecture,[],[f15])).
thf(f15,conjecture,(
! [X2 : $i > $o,X4 : $i > $o,X0 : $i > $o] : (((subset @ X0 @ X4) & (subset @ X2 @ X4)) => (subset @ (union @ X0 @ X2) @ X4))),
file('Problems/SET/SET014^4.p',thm)).
thf(f79,plain,(
( ! [X1 : $i] : (($true = (sK1 @ X1)) | ((sK2 @ X1) = $false)) )),
inference(binary_proxy_clausification,[],[f78])).
thf(f78,plain,(
( ! [X1 : $i] : (($true = ((sK2 @ X1) => (sK1 @ X1)))) )),
inference(beta_eta_normalization,[],[f77])).
thf(f77,plain,(
( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ Y0) => (sK1 @ Y0))) @ X1))) )),
inference(pi_clausification,[],[f76])).
thf(f76,plain,(
($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK1 @ Y0)))))),
inference(beta_eta_normalization,[],[f69])).
thf(f69,plain,(
($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ sK2 @ sK1))),
inference(definition_unfolding,[],[f57,f52])).
thf(f57,plain,(
($true = (subset @ sK2 @ sK1))),
inference(cnf_transformation,[],[f48])).
thf(f87,plain,(
($true = (sK2 @ sK4)) | ~spl3_1),
inference(avatar_component_clause,[],[f85])).
thf(f85,plain,(
spl3_1 <=> ($true = (sK2 @ sK4))),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
thf(f106,plain,(
~spl3_2),
inference(avatar_contradiction_clause,[],[f105])).
thf(f105,plain,(
$false | ~spl3_2),
inference(trivial_inequality_removal,[],[f101])).
thf(f101,plain,(
($true = $false) | ~spl3_2),
inference(superposition,[],[f100,f91])).
thf(f91,plain,(
($true = (sK0 @ sK4)) | ~spl3_2),
inference(avatar_component_clause,[],[f89])).
thf(f89,plain,(
spl3_2 <=> ($true = (sK0 @ sK4))),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
thf(f100,plain,(
((sK0 @ sK4) = $false)),
inference(trivial_inequality_removal,[],[f97])).
thf(f97,plain,(
($true = $false) | ((sK0 @ sK4) = $false)),
inference(superposition,[],[f83,f73])).
thf(f83,plain,(
( ! [X1 : $i] : (($true = (sK1 @ X1)) | ($false = (sK0 @ X1))) )),
inference(binary_proxy_clausification,[],[f82])).
thf(f82,plain,(
( ! [X1 : $i] : (($true = ((sK0 @ X1) => (sK1 @ X1)))) )),
inference(beta_eta_normalization,[],[f81])).
thf(f81,plain,(
( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK1 @ Y0))) @ X1))) )),
inference(pi_clausification,[],[f80])).
thf(f80,plain,(
($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK1 @ Y0)))))),
inference(beta_eta_normalization,[],[f68])).
thf(f68,plain,(
($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ sK0 @ sK1))),
inference(definition_unfolding,[],[f58,f52])).
thf(f58,plain,(
($true = (subset @ sK0 @ sK1))),
inference(cnf_transformation,[],[f48])).
thf(f92,plain,(
spl3_1 | spl3_2),
inference(avatar_split_clause,[],[f75,f89,f85])).
thf(f75,plain,(
($true = (sK2 @ sK4)) | ($true = (sK0 @ sK4))),
inference(binary_proxy_clausification,[],[f74])).
thf(f74,plain,(
($true = ((sK2 @ sK4) | (sK0 @ sK4)))),
inference(binary_proxy_clausification,[],[f72])).
Solution for DAT013_1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f43 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f4 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f3 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
tff(type_def_5, type, array: $tType).
tff(func_def_0, type, read: (array * $int) > $int).
tff(func_def_1, type, write: (array * $int * $int) > array).
tff(func_def_5, type, sK0: array).
tff(func_def_6, type, sK1: $int).
tff(func_def_7, type, sK2: $int).
tff(func_def_8, type, sK3: $int).
tff(func_def_9, type, -1: $int > $int).
tff(f43,plain,(
$false),
inference(avatar_sat_refutation,[],[f35,f38,f42])).
tff(f42,plain,(
~spl4_1),
inference(avatar_contradiction_clause,[],[f41])).
tff(f41,plain,(
$false | ~spl4_1),
inference(alasca_normalization,[],[f40])).
tff(f40,plain,(
$greater($sum($sum($uminus(sK3),$sum(-2,sK3)),-1),0) | ~spl4_1),
inference(alasca_fourier_motzkin,[],[f30,f20])).
tff(f20,plain,(
$greater($sum(-1(sK1),$sum(sK3,-2)),0)),
inference(alasca_normalization,[],[f16])).
tff(f16,plain,(
~$less(sK3,$sum(sK1,3))),
inference(cnf_transformation,[],[f12])).
tff(f12,plain,(
(~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
tff(f10,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1))) => (? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~
$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) & ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)))),
introduced(definition,[],[choice_axiom])).
tff(f11,plain,(
? [X3 : $int] : (~$less(0,read(sK0,X3)) & ~$less(sK2,X3) & ~$less(X3,$sum(sK1,3))) => (~$less(0,read(sK0,sK3)) & ~$less(sK2,sK3) & ~$less(sK3,$sum(sK1,3)))),
introduced(definition,[],[choice_axiom])).
tff(f9,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X3 : $int] : (~$less(0,read(X0,X3)) & ~$less(X2,X3) & ~$less(X3,$sum(X1,3))) & ! [X4 : $int] : ($less(0,read(X0,X4)) | $less(X2,X4) | $less(X4,X1)))),
inference(rectify,[],[f8])).
tff(f8,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & ~$less(X2,X4) & ~$less(X4,$sum(X1,3))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | $less(X2,X3) | $less(X3,X1)))),
inference(flattening,[],[f7])).
tff(f7,plain,(
? [X0 : array,X1 : $int,X2 : $int] : (? [X4 : $int] : (~$less(0,read(X0,X4)) & (~$less(X2,X4) & ~$less(X4,$sum(X1,3)))) & ! [X3 : $int] : ($less(0,read(X0,X3)) | ($less(X2,X3) | $less(X3,X1))))),
inference(ennf_transformation,[],[f5])).
tff(f5,plain,(
~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : ((~$less(X2,X3) & ~$less(X3,X1)) => $less(0,read(X0,X3))) => ! [X4 : $int] : ((~$less(X2,X4) & ~$less(X4,$sum(X1,3))) => $less(0,read(X0,X4))))),
inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
inference(negated_conjecture,[status(cth)],[f3])).
tff(f3,conjecture,(
! [X0 : array,X1 : $int,X2 : $int] : (! [X3 : $int] : (($lesseq(X3,X2) & $lesseq(X1,X3)) => $greater(read(X0,X3),0)) => ! [X4 : $int] : (($lesseq(X4,X2) & $lesseq($sum(X1,3),X4)) => $greater(read(X0,X4),0)))),
file('Problems/DAT/DAT013_1.p',unknown)).
tff(f30,plain,(
$greater($sum(sK1,-1(sK3)),0) | ~spl4_1),
inference(avatar_component_clause,[],[f28])).
tff(f28,definition,(
spl4_1 <=> $greater($sum(sK1,-1(sK3)),0)),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
tff(f38,plain,(
~spl4_2),
inference(avatar_contradiction_clause,[],[f37])).
tff(f37,plain,(
$false | ~spl4_2),
inference(alasca_normalization,[],[f36])).
tff(f36,plain,(
$greater($sum($sum($sum(1,$uminus(sK3)),sK3),-1),0) | ~spl4_2),
inference(alasca_fourier_motzkin,[],[f21,f34])).
tff(f34,plain,(
$greater($sum(-1(sK2),sK3),0) | ~spl4_2),
inference(avatar_component_clause,[],[f32])).
tff(f32,definition,(
spl4_2 <=> $greater($sum(-1(sK2),sK3),0)),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
tff(f21,plain,(
$greater($sum(sK2,$sum(-1(sK3),1)),0)),
inference(alasca_normalization,[],[f17])).
tff(f17,plain,(
~$less(sK2,sK3)),
inference(cnf_transformation,[],[f12])).
tff(f35,plain,(
spl4_1 | spl4_2),
inference(avatar_split_clause,[],[f26,f32,f28])).
tff(f26,plain,(
$greater($sum(-1(sK2),sK3),0) | $greater($sum(sK1,-1(sK3)),0)),
inference(alasca_normalization,[],[f25])).
tff(f25,plain,(
$greater($sum(sK3,-1(sK2)),0) | $greater($sum(-1(sK3),sK1),0) | $greater($sum(1,-1),0)),
inference(alasca_fourier_motzkin,[],[f19,f22])).
tff(f22,plain,(
$greater($sum(1,-1(read(sK0,sK3))),0)),
inference(alasca_normalization,[],[f18])).
tff(f18,plain,(
~$less(0,read(sK0,sK3))),
inference(cnf_transformation,[],[f12])).
tff(f19,plain,(
( ! [X4 : $int] : ($greater(read(sK0,X4),0) | $greater($sum(X4,-1(sK2)),0) | $greater($sum(-1(X4),sK1),0)) )),
inference(alasca_normalization,[],[f15])).
tff(f15,plain,(
( ! [X4 : $int] : ($less(0,read(sK0,X4)) | $less(sK2,X4) | $less(X4,sK1)) )),
inference(cnf_transformation,[],[f12])).
Saturation for DAT335_2
% (3727607)# SZS output start Saturation.
cnf(u30,negated_conjecture,
'$ki_accessible'('$ki_local_world',X1) | teach(X1,X0,cs) | ~teach('$ki_local_world',X0,psych) | ~'$ki_exists_in_world_$i'('$ki_local_world',X0)).
cnf(u25,axiom,
teach(X0,sue,psych) | '$ki_accessible'('$ki_local_world',X0)).
cnf(u24,axiom,
~'$ki_accessible'(X0,X0)).
cnf(u27,axiom,
teach(X0,sK1(X0),cs) | '$ki_accessible'('$ki_local_world',X0)).
cnf(u16,axiom,
'$ki_exists_in_world_$i'(X0,X1)).
cnf(u26,axiom,
teach(X0,mary,psych) | '$ki_accessible'('$ki_local_world',X0)).
cnf(u29,axiom,
teach(X0,john,math) | '$ki_accessible'('$ki_local_world',X0)).
cnf(u31,negated_conjecture,
teach('$ki_local_world',X0,cs) | ~teach('$ki_local_world',X0,psych) | ~'$ki_exists_in_world_$i'('$ki_local_world',X0)).
% (3727607)# SZS output end Saturation.
% (3727607)# SZS output start Definitions and Model Updates.
globally flip the polarity of every occurrence of predicate "'$ki_accessible'"
% (3727607)# SZS output end Definitions and Model Updates.
Finite Model for DAT335_2
tff('declare_$i1',type,'fmb_$i_1':$i).
tff('finite_domain_$i',axiom,
! [X:$i] : (
X = 'fmb_$i_1'
) ).
tff('declare_$ki_world',type,'$ki_world':$tType).
tff('declare_$ki_world1',type,'fmb_$ki_world_1':'$ki_world').
tff('finite_domain_$ki_world',axiom,
! [X:'$ki_world'] : (
X = 'fmb_$ki_world_1'
) ).
tff('declare_$ki_local_world',type,'$ki_local_world':'$ki_world').
tff('$ki_local_world_definition',axiom,'$ki_local_world' = 'fmb_$ki_world_1').
tff(declare_cs,type,cs:$i).
tff(cs_definition,axiom,cs = 'fmb_$i_1').
tff(declare_sue,type,sue:$i).
tff(sue_definition,axiom,sue = 'fmb_$i_1').
tff(declare_mary,type,mary:$i).
tff(mary_definition,axiom,mary = 'fmb_$i_1').
tff(declare_john,type,john:$i).
tff(john_definition,axiom,john = 'fmb_$i_1').
tff(declare_math,type,math:$i).
tff(math_definition,axiom,math = 'fmb_$i_1').
tff(declare_psych,type,psych:$i).
tff(psych_definition,axiom,psych = 'fmb_$i_1').
tff('declare_$ki_accessible',type,'$ki_accessible': ('$ki_world' * '$ki_world') > $o).
tff('predicate_$ki_accessible',axiom,
'$ki_accessible'('fmb_$ki_world_1','fmb_$ki_world_1')
).
tff(declare_teach,type,teach: ('$ki_world' * $i * $i) > $o).
tff(predicate_teach,axiom,
teach('fmb_$ki_world_1','fmb_$i_1','fmb_$i_1')
).
tff('declare_$ki_exists_in_world_$i',type,'$ki_exists_in_world_$i': ('$ki_world' * $i) > $o).
tff('predicate_$ki_exists_in_world_$i',axiom,
'$ki_exists_in_world_$i'('fmb_$ki_world_1','fmb_$i_1')
).
Saturation for SWW469_10
% # SZS output start Saturation.
cnf(u15,hypothesis,
sK0 != sK1).
cnf(u14,hypothesis,
hoare_1310879719gleton).
% # SZS output end Saturation.
% # SZS output start Definitions and Model Updates.
for all inputs,
define induct_false := $false
for all inputs,
define induct_true := $true
for all groundings,
whenever ? [X0 : state,X1 : state] : X0 != X1 is true, set hoare_1310879719gleton to true
% # SZS output end Definitions and Model Updates.
Finite Model for SWW469_10
tff('declare_$i1',type,'fmb_$i_1':$i).
tff('finite_domain_$i',axiom,
! [X:$i] : (
X = 'fmb_$i_1'
) ).
tff(declare_state,type,state:$tType).
tff(declare_state1,type,fmb_state_1:state).
tff(declare_state2,type,fmb_state_2:state).
tff(finite_domain_state,axiom,
! [X:state] : (
X = fmb_state_1 | X = fmb_state_2
) ).
tff(distinct_domain_state,axiom,
fmb_state_1 != fmb_state_2
).
tff(declare_induct_false,type,induct_false: $o).
tff(induct_false_definition,axiom,~induct_false).
tff(declare_induct_true,type,induct_true: $o).
tff(induct_true_definition,axiom,induct_true).
tff(declare_hoare_1310879719gleton,type,hoare_1310879719gleton: $o).
tff(hoare_1310879719gleton_definition,axiom,hoare_1310879719gleton).
Solution for SEU140+2
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f1401 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f52 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% NOTICE: Took the conjecture f51 as the proved formula
% CPUTIME: 0.07
% SUCCESS: Verified
% SZS status Verified
fof(f1401,plain,(
$false),
inference(subsumption_resolution,[],[f1400,f210])).
fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f134,plain,(
~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f133,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
introduced(definition,[],[choice_axiom])).
fof(f88,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f87])).
fof(f87,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[status(cth)],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f1400,plain,(
disjoint(sK10,sK12)),
inference(resolution,[],[f1383,f179])).
fof(f179,plain,(
( ! [X0,X1] : (~disjoint(X0,X1) | disjoint(X1,X0)) )),
inference(cnf_transformation,[],[f72])).
fof(f72,plain,(
! [X0,X1] : (disjoint(X1,X0) | ~disjoint(X0,X1))),
inference(ennf_transformation,[],[f27])).
fof(f27,axiom,(
! [X0,X1] : (disjoint(X0,X1) => disjoint(X1,X0))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f1383,plain,(
disjoint(sK12,sK10)),
inference(duplicate_literal_removal,[],[f1380])).
fof(f1380,plain,(
disjoint(sK12,sK10) | disjoint(sK12,sK10)),
inference(resolution,[],[f510,f402])).
fof(f402,plain,(
( ! [X0] : (in(sK8(X0,sK10),sK11) | disjoint(X0,sK10)) )),
inference(resolution,[],[f389,f198])).
fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f130,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f129,plain,(
! [X0,X1] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(definition,[],[choice_axiom])).
fof(f82,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f62])).
fof(f62,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f389,plain,(
( ! [X0] : (~in(X0,sK10) | in(X0,sK11)) )),
inference(superposition,[],[f237,f320])).
fof(f320,plain,(
sK11 = set_union2(sK10,sK11)),
inference(resolution,[],[f180,f208])).
fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).
fof(f180,plain,(
( ! [X0,X1] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
inference(cnf_transformation,[],[f73])).
fof(f73,plain,(
! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
inference(ennf_transformation,[],[f28])).
fof(f28,axiom,(
! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f237,plain,(
( ! [X0,X1,X4] : (in(X4,set_union2(X0,X1)) | ~in(X4,X0)) )),
inference(equality_resolution,[],[f145])).
fof(f145,plain,(
( ! [X2,X0,X1,X4] : (in(X4,X2) | ~in(X4,X0) | set_union2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f104])).
fof(f104,plain,(
! [X0,X1,X2] : ((set_union2(X0,X1) = X2 | (((~in(sK1(X0,X1,X2),X1) & ~in(sK1(X0,X1,X2),X0)) | ~in(sK1(X0,X1,X2),X2)) & (in(sK1(X0,X1,X2),X1) | in(sK1(X0,X1,X2),X0) | in(sK1(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | (~in(X4,X1) & ~in(X4,X0))) & (in(X4,X1) | in(X4,X0) | ~in(X4,X2))) | set_union2(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f102,f103])).
fof(f103,plain,(
! [X0,X1,X2] : (? [X3] : (((~in(X3,X1) & ~in(X3,X0)) | ~in(X3,X2)) & (in(X3,X1) | in(X3,X0) | in(X3,X2))) => (((~in(sK1(X0,X1,X2),X1) & ~in(sK1(X0,X1,X2),X0)) | ~in(sK1(X0,X1,X2),X2)) & (in(sK1(X0,X1,X2),X1) | in(sK1(X0,X1,X2),X0) | in(sK1(X0,X1,X2),X2))))),
introduced(definition,[],[choice_axiom])).
fof(f102,plain,(
! [X0,X1,X2] : ((set_union2(X0,X1) = X2 | ? [X3] : (((~in(X3,X1) & ~in(X3,X0)) | ~in(X3,X2)) & (in(X3,X1) | in(X3,X0) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | (~in(X4,X1) & ~in(X4,X0))) & (in(X4,X1) | in(X4,X0) | ~in(X4,X2))) | set_union2(X0,X1) != X2))),
inference(rectify,[],[f101])).
fof(f101,plain,(
! [X0,X1,X2] : ((set_union2(X0,X1) = X2 | ? [X3] : (((~in(X3,X1) & ~in(X3,X0)) | ~in(X3,X2)) & (in(X3,X1) | in(X3,X0) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (~in(X3,X1) & ~in(X3,X0))) & (in(X3,X1) | in(X3,X0) | ~in(X3,X2))) | set_union2(X0,X1) != X2))),
inference(flattening,[],[f100])).
fof(f100,plain,(
! [X0,X1,X2] : ((set_union2(X0,X1) = X2 | ? [X3] : (((~in(X3,X1) & ~in(X3,X0)) | ~in(X3,X2)) & ((in(X3,X1) | in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (~in(X3,X1) & ~in(X3,X0))) & ((in(X3,X1) | in(X3,X0)) | ~in(X3,X2))) | set_union2(X0,X1) != X2))),
inference(nnf_transformation,[],[f7])).
fof(f7,axiom,(
! [X0,X1,X2] : (set_union2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X1) | in(X3,X0))))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f510,plain,(
( ! [X0] : (~in(sK8(sK12,X0),sK11) | disjoint(sK12,X0)) )),
inference(resolution,[],[f454,f197])).
fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f454,plain,(
( ! [X0] : (~in(X0,sK12) | ~in(X0,sK11)) )),
inference(resolution,[],[f199,f271])).
fof(f271,plain,(
disjoint(sK12,sK11)),
inference(resolution,[],[f179,f209])).
fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f199,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f130])).
% SZS output end Proof for SEU140+2
Solution for BOO001-1
% SUCCESS: Derivation has unique formula names
% SUCCESS: All derived formulae have parents and inference information
% WARNING: Took the first false root f295 as the single derivation root
% SUCCESS: Derivation is acyclic
% SUCCESS: Derivation looks like a refutation
% SUCCESS: Negated conjecture f6 is a leaf or CTH from a conjecture
% SUCCESS: Assumptions are propagated
% SUCCESS: Assumptions are discharged
% WARNING: Took the negated conjecture f6 as the proved formula
% CPUTIME: 0.06
% SUCCESS: Verified
% SZS status Verified
fof(f295,plain,(
$false),
inference(trivial_inequality_removal,[],[f289])).
fof(f289,plain,(
a != a),
inference(superposition,[],[f6,f224])).
fof(f224,plain,(
( ! [X0] : (inverse(inverse(X0)) = X0) )),
inference(superposition,[],[f5,f158])).
fof(f158,plain,(
( ! [X0,X1] : (multiply(X1,inverse(X1),X0) = X0) )),
inference(forward_demodulation,[],[f146,f25])).
fof(f25,plain,(
( ! [X2,X0] : (multiply(X0,X2,X0) = X0) )),
inference(forward_demodulation,[],[f22,f3])).
fof(f3,axiom,(
( ! [X2,X3] : (multiply(X2,X2,X3) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f22,plain,(
( ! [X2,X3,X0,X1] : (multiply(X0,X0,multiply(X1,X2,X3)) = multiply(X0,X2,X0)) )),
inference(forward_demodulation,[],[f13,f3])).
fof(f13,plain,(
( ! [X2,X3,X0,X1] : (multiply(X0,X0,multiply(X1,X2,X3)) = multiply(multiply(X0,X0,X1),X2,X0)) )),
inference(superposition,[],[f1,f3])).
fof(f1,axiom,(
( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f146,plain,(
( ! [X0,X1] : (multiply(X1,inverse(X1),multiply(X0,X1,X0)) = X0) )),
inference(superposition,[],[f7,f119])).
fof(f119,plain,(
( ! [X3,X0,X1] : (multiply(X3,X1,multiply(X0,inverse(X1),X3)) = X3) )),
inference(forward_demodulation,[],[f118,f88])).
fof(f88,plain,(
( ! [X2,X3,X0,X1,X4] : (multiply(X0,X1,multiply(X2,X3,X0)) = multiply(X0,X1,multiply(X2,X3,multiply(X4,X0,inverse(X1))))) )),
inference(forward_demodulation,[],[f86,f28])).
fof(f28,plain,(
( ! [X2,X3,X0,X1] : (multiply(multiply(X0,X1,X2),X3,X0) = multiply(X0,X1,multiply(X2,X3,X0))) )),
inference(superposition,[],[f1,f25])).
fof(f86,plain,(
( ! [X2,X3,X0,X1,X4] : (multiply(multiply(X0,X1,X2),X3,X0) = multiply(X0,X1,multiply(X2,X3,multiply(X4,X0,inverse(X1))))) )),
inference(superposition,[],[f1,f70])).
fof(f70,plain,(
( ! [X2,X0,X1] : (multiply(X0,X2,multiply(X1,X0,inverse(X2))) = X0) )),
inference(forward_demodulation,[],[f38,f2])).
fof(f2,axiom,(
( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f38,plain,(
( ! [X2,X0,X1] : (multiply(X1,X0,X0) = multiply(X0,X2,multiply(X1,X0,inverse(X2)))) )),
inference(superposition,[],[f7,f5])).
fof(f118,plain,(
( ! [X2,X3,X0,X1] : (multiply(X3,X1,multiply(X0,inverse(X1),multiply(X2,X3,inverse(X1)))) = X3) )),
inference(superposition,[],[f70,f12])).
fof(f12,plain,(
( ! [X2,X3,X0,X1] : (multiply(X1,X0,multiply(X2,X3,X0)) = multiply(multiply(X1,X0,X2),X3,X0)) )),
inference(superposition,[],[f1,f2])).
fof(f7,plain,(
( ! [X2,X3,X0,X1] : (multiply(X1,X0,multiply(X0,X2,X3)) = multiply(X0,X2,multiply(X1,X0,X3))) )),
inference(superposition,[],[f1,f2])).
fof(f5,axiom,(
( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f6,negated_conjecture,(
a != inverse(inverse(a))),
file('Problems/BOO/BOO001-1.p',unknown)).