TSTP Solution File: SEU107+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Mar 6 09:20:14 EST 2024
% Result : Theorem 21.98s 22.15s
% Output : Proof 21.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Mar 3 10:32:18 EST 2024
% 0.13/0.34 % CPUTime :
% 21.98/22.15 % SZS status Theorem for theBenchmark
% 21.98/22.15 % SZS output start Proof for theBenchmark
% 21.98/22.15
% 21.98/22.15 % Formula: antisymmetry_r2_hidden ( axiom ) converted to clauses:
% 21.98/22.15 cnf(antisymmetry_r2_hidden-1, axiom, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 21.98/22.15
% 21.98/22.15 % Formula: cc1_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(cc1_finset_1-1, axiom, ( ~empty(_u2) | finite(_u2) )).
% 21.98/22.15
% 21.98/22.15 % Formula: cc1_finsub_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(cc1_finsub_1-1, axiom, ( ~preboolean(_u3) | cup_closed(_u3) )).
% 21.98/22.15 cnf(cc1_finsub_1-2, axiom, ( ~preboolean(_u3) | diff_closed(_u3) )).
% 21.98/22.15
% 21.98/22.15 % Formula: cc2_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(cc2_finset_1-1, axiom, ( ~finite(_u5) | ~element(_u4, powerset(_u5)) | finite(_u4) )).
% 21.98/22.15
% 21.98/22.15 % Formula: cc2_finsub_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(cc2_finsub_1-1, axiom, ( ~cup_closed(_u6) | ~diff_closed(_u6) | preboolean(_u6) )).
% 21.98/22.15
% 21.98/22.15 % Formula: dt_k2_finsub_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(dt_k2_finsub_1-1, axiom, ( empty(_u9) | ~preboolean(_u9) | ~element(_u8, _u9) | ~element(_u7, _u9) | element(prebool_difference(_u9, _u8, _u7), _u9) )).
% 21.98/22.15
% 21.98/22.15 % Formula: existence_m1_subset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(existence_m1_subset_1-1, axiom, ( element(skolem1(_u11), _u11) )).
% 21.98/22.15
% 21.98/22.15 % Formula: fc12_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(fc12_finset_1-1, axiom, ( ~finite(_u13) | finite(set_difference(_u13, _u12)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: fc1_subset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(fc1_subset_1-1, axiom, ( ~empty(powerset(_u14)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: fc1_xboole_0 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(fc1_xboole_0-1, axiom, ( empty(empty_set) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc1_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc1_finset_1-1, axiom, ( ~empty(skolem2) )).
% 21.98/22.15 cnf(rc1_finset_1-2, axiom, ( finite(skolem2) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc1_finsub_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc1_finsub_1-1, axiom, ( ~empty(skolem3) )).
% 21.98/22.15 cnf(rc1_finsub_1-2, axiom, ( cup_closed(skolem3) )).
% 21.98/22.15 cnf(rc1_finsub_1-3, axiom, ( cap_closed(skolem3) )).
% 21.98/22.15 cnf(rc1_finsub_1-4, axiom, ( diff_closed(skolem3) )).
% 21.98/22.15 cnf(rc1_finsub_1-5, axiom, ( preboolean(skolem3) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc1_subset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc1_subset_1-1, axiom, ( empty(_u18) | element(skolem4(_u18), powerset(_u18)) )).
% 21.98/22.15 cnf(rc1_subset_1-2, axiom, ( empty(_u18) | ~empty(skolem4(_u18)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc1_xboole_0 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc1_xboole_0-1, axiom, ( empty(skolem5) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc2_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc2_finset_1-1, axiom, ( element(skolem6(_u21), powerset(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-2, axiom, ( empty(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-3, axiom, ( relation(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-4, axiom, ( function(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-5, axiom, ( one_to_one(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-6, axiom, ( epsilon_transitive(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-7, axiom, ( epsilon_connected(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-8, axiom, ( ordinal(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-9, axiom, ( natural(skolem6(_u21)) )).
% 21.98/22.15 cnf(rc2_finset_1-10, axiom, ( finite(skolem6(_u21)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc2_subset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc2_subset_1-1, axiom, ( element(skolem7(_u23), powerset(_u23)) )).
% 21.98/22.15 cnf(rc2_subset_1-2, axiom, ( empty(skolem7(_u23)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc2_xboole_0 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc2_xboole_0-1, axiom, ( ~empty(skolem8) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc3_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc3_finset_1-1, axiom, ( empty(_u26) | element(skolem9(_u26), powerset(_u26)) )).
% 21.98/22.15 cnf(rc3_finset_1-2, axiom, ( empty(_u26) | ~empty(skolem9(_u26)) )).
% 21.98/22.15 cnf(rc3_finset_1-3, axiom, ( empty(_u26) | finite(skolem9(_u26)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: rc4_finset_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(rc4_finset_1-1, axiom, ( empty(_u28) | element(skolem10(_u28), powerset(_u28)) )).
% 21.98/22.15 cnf(rc4_finset_1-2, axiom, ( empty(_u28) | ~empty(skolem10(_u28)) )).
% 21.98/22.15 cnf(rc4_finset_1-3, axiom, ( empty(_u28) | finite(skolem10(_u28)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: redefinition_k2_finsub_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(redefinition_k2_finsub_1-1, axiom, ( empty(_u31) | ~preboolean(_u31) | ~element(_u30, _u31) | ~element(_u29, _u31) | ( prebool_difference(_u31, _u30, _u29) = set_difference(_u30, _u29)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: reflexivity_r1_tarski ( axiom ) converted to clauses:
% 21.98/22.15 cnf(reflexivity_r1_tarski-1, axiom, ( subset(_u33, _u33) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t18_finsub_1 ( conjecture ) converted to clauses:
% 21.98/22.15 cnf(t18_finsub_1-1, negated_conjecture, ( ~empty(skolem11) )).
% 21.98/22.15 cnf(t18_finsub_1-2, negated_conjecture, ( preboolean(skolem11) )).
% 21.98/22.15 cnf(t18_finsub_1-3, negated_conjecture, ( ~in(empty_set, skolem11) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t1_subset ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t1_subset-1, axiom, ( ~in(_u36, _u35) | element(_u36, _u35) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t2_subset ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t2_subset-1, axiom, ( ~element(_u38, _u37) | empty(_u37) | in(_u38, _u37) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t37_xboole_1 ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t37_xboole_1-1, axiom, ( ( set_difference(_u43, _u41) != empty_set) | subset(_u43, _u41) )).
% 21.98/22.15 cnf(t37_xboole_1-2, axiom, ( ~subset(_u44, _u42) | ( set_difference(_u44, _u42) = empty_set) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t3_boole ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t3_boole-1, axiom, ( ( set_difference(_u45, empty_set) = _u45) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t3_subset ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t3_subset-1, axiom, ( ~element(_u50, powerset(_u48)) | subset(_u50, _u48) )).
% 21.98/22.15 cnf(t3_subset-2, axiom, ( ~subset(_u51, _u49) | element(_u51, powerset(_u49)) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t4_boole ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t4_boole-1, axiom, ( ( set_difference(empty_set, _u52) = empty_set) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t4_subset ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t4_subset-1, axiom, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t5_subset ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t5_subset-1, axiom, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t6_boole ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t6_boole-1, axiom, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t7_boole ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t7_boole-1, axiom, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 21.98/22.15
% 21.98/22.15 % Formula: t8_boole ( axiom ) converted to clauses:
% 21.98/22.15 cnf(t8_boole-1, axiom, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 21.98/22.15
% 21.98/22.15 % Problem matrix:
% 21.98/22.15 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 21.98/22.15 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 21.98/22.15 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 21.98/22.15 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( prebool_difference(__eqx_0, __eqx_1, __eqx_2) = prebool_difference(__eqy_0, __eqy_1, __eqy_2)) )).
% 21.98/22.15 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( set_difference(__eqx_0, __eqx_1) = set_difference(__eqy_0, __eqy_1)) )).
% 21.98/22.15 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 21.98/22.15 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~in(__eqx_0, __eqx_1) | in(__eqy_0, __eqy_1) )).
% 21.98/22.15 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 21.98/22.15 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~finite(__eqx_0) | finite(__eqy_0) )).
% 21.98/22.15 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~preboolean(__eqx_0) | preboolean(__eqy_0) )).
% 21.98/22.15 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~cup_closed(__eqx_0) | cup_closed(__eqy_0) )).
% 21.98/22.15 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~diff_closed(__eqx_0) | diff_closed(__eqy_0) )).
% 21.98/22.15 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~element(__eqx_0, __eqx_1) | element(__eqy_0, __eqy_1) )).
% 21.98/22.15 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~cap_closed(__eqx_0) | cap_closed(__eqy_0) )).
% 21.98/22.15 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 21.98/22.15 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 21.98/22.15 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 21.98/22.15 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_transitive(__eqx_0) | epsilon_transitive(__eqy_0) )).
% 21.98/22.15 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~epsilon_connected(__eqx_0) | epsilon_connected(__eqy_0) )).
% 21.98/22.15 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~ordinal(__eqx_0) | ordinal(__eqy_0) )).
% 21.98/22.15 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ~natural(__eqx_0) | natural(__eqy_0) )).
% 21.98/22.15 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 21.98/22.15 cnf(matrix-28, plain, ( ~in(_u1, _u0) | ~in(_u0, _u1) )).
% 21.98/22.15 cnf(matrix-29, plain, ( ~empty(_u2) | finite(_u2) )).
% 21.98/22.15 cnf(matrix-30, plain, ( ~preboolean(_u3) | cup_closed(_u3) )).
% 21.98/22.15 cnf(matrix-31, plain, ( ~preboolean(_u3) | diff_closed(_u3) )).
% 21.98/22.15 cnf(matrix-32, plain, ( ~finite(_u5) | ~element(_u4, powerset(_u5)) | finite(_u4) )).
% 21.98/22.15 cnf(matrix-33, plain, ( ~cup_closed(_u6) | ~diff_closed(_u6) | preboolean(_u6) )).
% 21.98/22.15 cnf(matrix-34, plain, ( empty(_u9) | ~preboolean(_u9) | ~element(_u8, _u9) | ~element(_u7, _u9) | element(prebool_difference(_u9, _u8, _u7), _u9) )).
% 21.98/22.15 cnf(matrix-35, plain, ( element(skolem1(_u11), _u11) )).
% 21.98/22.15 cnf(matrix-36, plain, ( ~finite(_u13) | finite(set_difference(_u13, _u12)) )).
% 21.98/22.15 cnf(matrix-37, plain, ( ~empty(powerset(_u14)) )).
% 21.98/22.15 cnf(matrix-38, plain, ( empty(empty_set) )).
% 21.98/22.15 cnf(matrix-39, plain, ( ~empty(skolem2) )).
% 21.98/22.15 cnf(matrix-40, plain, ( finite(skolem2) )).
% 21.98/22.15 cnf(matrix-41, plain, ( ~empty(skolem3) )).
% 21.98/22.15 cnf(matrix-42, plain, ( cup_closed(skolem3) )).
% 21.98/22.15 cnf(matrix-43, plain, ( cap_closed(skolem3) )).
% 21.98/22.15 cnf(matrix-44, plain, ( diff_closed(skolem3) )).
% 21.98/22.15 cnf(matrix-45, plain, ( preboolean(skolem3) )).
% 21.98/22.15 cnf(matrix-46, plain, ( empty(_u18) | element(skolem4(_u18), powerset(_u18)) )).
% 21.98/22.15 cnf(matrix-47, plain, ( empty(_u18) | ~empty(skolem4(_u18)) )).
% 21.98/22.15 cnf(matrix-48, plain, ( empty(skolem5) )).
% 21.98/22.15 cnf(matrix-49, plain, ( element(skolem6(_u21), powerset(_u21)) )).
% 21.98/22.15 cnf(matrix-50, plain, ( empty(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-51, plain, ( relation(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-52, plain, ( function(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-53, plain, ( one_to_one(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-54, plain, ( epsilon_transitive(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-55, plain, ( epsilon_connected(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-56, plain, ( ordinal(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-57, plain, ( natural(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-58, plain, ( finite(skolem6(_u21)) )).
% 21.98/22.15 cnf(matrix-59, plain, ( element(skolem7(_u23), powerset(_u23)) )).
% 21.98/22.15 cnf(matrix-60, plain, ( empty(skolem7(_u23)) )).
% 21.98/22.15 cnf(matrix-61, plain, ( ~empty(skolem8) )).
% 21.98/22.15 cnf(matrix-62, plain, ( empty(_u26) | element(skolem9(_u26), powerset(_u26)) )).
% 21.98/22.15 cnf(matrix-63, plain, ( empty(_u26) | ~empty(skolem9(_u26)) )).
% 21.98/22.15 cnf(matrix-64, plain, ( empty(_u26) | finite(skolem9(_u26)) )).
% 21.98/22.15 cnf(matrix-65, plain, ( empty(_u28) | element(skolem10(_u28), powerset(_u28)) )).
% 21.98/22.15 cnf(matrix-66, plain, ( empty(_u28) | ~empty(skolem10(_u28)) )).
% 21.98/22.15 cnf(matrix-67, plain, ( empty(_u28) | finite(skolem10(_u28)) )).
% 21.98/22.15 cnf(matrix-68, plain, ( empty(_u31) | ~preboolean(_u31) | ~element(_u30, _u31) | ~element(_u29, _u31) | ( prebool_difference(_u31, _u30, _u29) = set_difference(_u30, _u29)) )).
% 21.98/22.15 cnf(matrix-69, plain, ( subset(_u33, _u33) )).
% 21.98/22.15 cnf(matrix-70, plain, ( ~empty(skolem11) )).
% 21.98/22.15 cnf(matrix-71, plain, ( preboolean(skolem11) )).
% 21.98/22.15 cnf(matrix-72, plain, ( ~in(empty_set, skolem11) )).
% 21.98/22.15 cnf(matrix-73, plain, ( ~in(_u36, _u35) | element(_u36, _u35) )).
% 21.98/22.15 cnf(matrix-74, plain, ( ~element(_u38, _u37) | empty(_u37) | in(_u38, _u37) )).
% 21.98/22.15 cnf(matrix-75, plain, ( ( set_difference(_u43, _u41) != empty_set) | subset(_u43, _u41) )).
% 21.98/22.15 cnf(matrix-76, plain, ( ~subset(_u44, _u42) | ( set_difference(_u44, _u42) = empty_set) )).
% 21.98/22.15 cnf(matrix-77, plain, ( ( set_difference(_u45, empty_set) = _u45) )).
% 21.98/22.15 cnf(matrix-78, plain, ( ~element(_u50, powerset(_u48)) | subset(_u50, _u48) )).
% 21.98/22.15 cnf(matrix-79, plain, ( ~subset(_u51, _u49) | element(_u51, powerset(_u49)) )).
% 21.98/22.15 cnf(matrix-80, plain, ( ( set_difference(empty_set, _u52) = empty_set) )).
% 21.98/22.15 cnf(matrix-81, plain, ( ~in(_u55, _u54) | ~element(_u54, powerset(_u53)) | element(_u55, _u53) )).
% 21.98/22.15 cnf(matrix-82, plain, ( ~in(_u58, _u57) | ~element(_u57, powerset(_u56)) | ~empty(_u56) )).
% 21.98/22.15 cnf(matrix-83, plain, ( ~empty(_u59) | ( _u59 = empty_set) )).
% 21.98/22.15 cnf(matrix-84, plain, ( ~in(_u61, _u60) | ~empty(_u60) )).
% 21.98/22.15 cnf(matrix-85, plain, ( ~empty(_u63) | ( _u63 = _u62) | ~empty(_u62) )).
% 21.98/22.15
% 21.98/22.15 % Proof stack:
% 21.98/22.15 cnf(proof-stack, plain,
% 21.98/22.15 proof_stack(
% 21.98/22.15 start(70),
% 21.98/22.15 left_branch(0, 34, 0, 2),
% 21.98/22.15 left_branch(0, 18, 2, 3),
% 21.98/22.15 left_branch(0, 68, 4, 4),
% 21.98/22.15 reduction(0, 0),
% 21.98/22.15 left_branch(0, 35, 0, 6),
% 21.98/22.15 right_branch(6),
% 21.98/22.15 left_branch(0, 35, 0, 7),
% 21.98/22.15 right_branch(7),
% 21.98/22.15 left_branch(0, 71, 0, 8),
% 21.98/22.15 right_branch(8),
% 21.98/22.15 right_branch(4),
% 21.98/22.15 left_branch(0, 18, 2, 5),
% 21.98/22.15 left_branch(0, 76, 1, 6),
% 21.98/22.15 left_branch(0, 69, 0, 7),
% 21.98/22.15 right_branch(7),
% 21.98/22.15 right_branch(6),
% 21.98/22.15 left_branch(0, 74, 0, 7),
% 21.98/22.15 left_branch(0, 72, 0, 8),
% 21.98/22.15 right_branch(8),
% 21.98/22.15 reduction(0, 0),
% 21.98/22.15 right_branch(7),
% 21.98/22.15 left_branch(0, 77, 0, 8),
% 21.98/22.15 right_branch(8),
% 21.98/22.15 right_branch(5),
% 21.98/22.15 left_branch(0, 2, 2, 6),
% 21.98/22.15 left_branch(0, 1, 1, 7),
% 21.98/22.15 left_branch(0, 77, 0, 8),
% 21.98/22.15 right_branch(8),
% 21.98/22.15 right_branch(7),
% 21.98/22.15 left_branch(0, 5, 2, 8),
% 21.98/22.15 left_branch(0, 0, 0, 9),
% 21.98/22.15 right_branch(9),
% 21.98/22.15 left_branch(0, 0, 0, 10),
% 21.98/22.15 right_branch(10),
% 21.98/22.15 right_branch(8),
% 21.98/22.15 right_branch(6),
% 21.98/22.15 right_branch(3),
% 21.98/22.15 left_branch(0, 35, 0, 4),
% 21.98/22.15 right_branch(4),
% 21.98/22.15 lemmata(0, 1),
% 21.98/22.15 left_branch(0, 71, 0, 6),
% 21.98/22.15 right_branch(6),
% 21.98/22.15 right_branch(2)
% 21.98/22.15 )).
% 21.98/22.15 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------