TSTP Solution File: SET639+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET639+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n020.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 : Mon Mar 25 14:32:10 EDT 2024
% Result : Theorem 1.23s 1.46s
% Output : Proof 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET639+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Mar 20 21:20:43 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.23/1.46 % SZS status Theorem for theBenchmark
% 1.23/1.46 % SZS output start Proof for theBenchmark
% 1.23/1.46
% 1.23/1.46 % Formula: subset_intersection ( axiom ) converted to clauses:
% 1.23/1.46 cnf(subset_intersection-1, axiom, ( ~subset(_u1, _u0) | ( intersection(_u1, _u0) = _u1) )).
% 1.23/1.46
% 1.23/1.46 % Formula: empty_set_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(empty_set_defn-1, axiom, ( ~member(_u2, empty_set) )).
% 1.23/1.46
% 1.23/1.46 % Formula: intersection_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(intersection_defn-1, axiom, ( ~member(_u6, intersection(_u10, _u8)) | member(_u6, _u10) )).
% 1.23/1.46 cnf(intersection_defn-2, axiom, ( ~member(_u6, intersection(_u10, _u8)) | member(_u6, _u8) )).
% 1.23/1.46 cnf(intersection_defn-3, axiom, ( ~member(_u7, _u11) | ~member(_u7, _u9) | member(_u7, intersection(_u11, _u9)) )).
% 1.23/1.46
% 1.23/1.46 % Formula: subset_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(subset_defn-1, axiom, ( ~subset(_u18, _u16) | ~member(_u12, _u18) | member(_u12, _u16) )).
% 1.23/1.46 cnf(subset_defn-2, axiom, ( subset(_u19, _u17) | member(skolem1(_u19, _u17), _u19) )).
% 1.23/1.46 cnf(subset_defn-3, axiom, ( subset(_u19, _u17) | ~member(skolem1(_u19, _u17), _u17) )).
% 1.23/1.46
% 1.23/1.46 % Formula: equal_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(equal_defn-1, axiom, ( ( _u24 != _u22) | subset(_u24, _u22) )).
% 1.23/1.46 cnf(equal_defn-2, axiom, ( ( _u24 != _u22) | subset(_u22, _u24) )).
% 1.23/1.46 cnf(equal_defn-3, axiom, ( ~subset(_u25, _u23) | ~subset(_u23, _u25) | ( _u25 = _u23) )).
% 1.23/1.46
% 1.23/1.46 % Formula: commutativity_of_intersection ( axiom ) converted to clauses:
% 1.23/1.46 cnf(commutativity_of_intersection-1, axiom, ( ( intersection(_u27, _u26) = intersection(_u26, _u27)) )).
% 1.23/1.46
% 1.23/1.46 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 1.23/1.46 cnf(reflexivity_of_subset-1, axiom, ( subset(_u28, _u28) )).
% 1.23/1.46
% 1.23/1.46 % Formula: empty_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(empty_defn-1, axiom, ( ~empty(_u32) | ~member(_u29, _u32) )).
% 1.23/1.46 cnf(empty_defn-2, axiom, ( member(skolem2(_u33), _u33) | empty(_u33) )).
% 1.23/1.46
% 1.23/1.46 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 1.23/1.46 cnf(equal_member_defn-1, axiom, ( ( _u44 != _u42) | ~member(_u38, _u44) | member(_u38, _u42) )).
% 1.23/1.46 cnf(equal_member_defn-2, axiom, ( ( _u44 != _u42) | ~member(_u39, _u42) | member(_u39, _u44) )).
% 1.23/1.46 cnf(equal_member_defn-3, axiom, ( ( _u45 = _u43) | member(skolem3(_u45, _u43), _u45) | member(skolem4(_u45, _u43), _u43) )).
% 1.23/1.46 cnf(equal_member_defn-4, axiom, ( ( _u45 = _u43) | member(skolem3(_u45, _u43), _u45) | ~member(skolem4(_u45, _u43), _u45) )).
% 1.23/1.46 cnf(equal_member_defn-5, axiom, ( ( _u45 = _u43) | ~member(skolem3(_u45, _u43), _u43) | member(skolem4(_u45, _u43), _u43) )).
% 1.23/1.46 cnf(equal_member_defn-6, axiom, ( ( _u45 = _u43) | ~member(skolem3(_u45, _u43), _u43) | ~member(skolem4(_u45, _u43), _u45) )).
% 1.23/1.46
% 1.23/1.46 % Formula: prove_th121 ( conjecture ) (definitionally) converted to clauses:
% 1.23/1.46 cnf(prove_th121-1, negated_conjecture, ( subset(skolem5, skolem6) )).
% 1.23/1.46 cnf(prove_th121-2, negated_conjecture, ( ( intersection(skolem6, skolem5) = empty_set) )).
% 1.23/1.46 cnf(prove_th121-3, negated_conjecture, ( ( skolem5 != empty_set) )).
% 1.23/1.46
% 1.23/1.46 % Problem matrix:
% 1.23/1.46 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 1.23/1.46 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 1.23/1.46 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 1.23/1.46 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 1.23/1.46 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 1.23/1.46 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem2(__eqx_0) = skolem2(__eqy_0)) )).
% 1.23/1.46 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 1.23/1.46 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 1.23/1.46 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 1.23/1.46 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 1.23/1.46 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ~empty(__eqx_0) | empty(__eqy_0) )).
% 1.23/1.46 cnf(matrix-11, plain, ( ~subset(_u1, _u0) | ( intersection(_u1, _u0) = _u1) )).
% 1.23/1.46 cnf(matrix-12, plain, ( ~member(_u2, empty_set) )).
% 1.23/1.46 cnf(matrix-13, plain, ( ~member(_u6, intersection(_u10, _u8)) | member(_u6, _u10) )).
% 1.23/1.46 cnf(matrix-14, plain, ( ~member(_u6, intersection(_u10, _u8)) | member(_u6, _u8) )).
% 1.23/1.46 cnf(matrix-15, plain, ( ~member(_u7, _u11) | ~member(_u7, _u9) | member(_u7, intersection(_u11, _u9)) )).
% 1.23/1.46 cnf(matrix-16, plain, ( ~subset(_u18, _u16) | ~member(_u12, _u18) | member(_u12, _u16) )).
% 1.23/1.46 cnf(matrix-17, plain, ( subset(_u19, _u17) | member(skolem1(_u19, _u17), _u19) )).
% 1.23/1.46 cnf(matrix-18, plain, ( subset(_u19, _u17) | ~member(skolem1(_u19, _u17), _u17) )).
% 1.23/1.46 cnf(matrix-19, plain, ( ( _u24 != _u22) | subset(_u24, _u22) )).
% 1.23/1.46 cnf(matrix-20, plain, ( ( _u24 != _u22) | subset(_u22, _u24) )).
% 1.23/1.46 cnf(matrix-21, plain, ( ~subset(_u25, _u23) | ~subset(_u23, _u25) | ( _u25 = _u23) )).
% 1.23/1.46 cnf(matrix-22, plain, ( ( intersection(_u27, _u26) = intersection(_u26, _u27)) )).
% 1.23/1.46 cnf(matrix-23, plain, ( subset(_u28, _u28) )).
% 1.23/1.46 cnf(matrix-24, plain, ( ~empty(_u32) | ~member(_u29, _u32) )).
% 1.23/1.46 cnf(matrix-25, plain, ( member(skolem2(_u33), _u33) | empty(_u33) )).
% 1.23/1.46 cnf(matrix-26, plain, ( ( _u44 != _u42) | ~member(_u38, _u44) | member(_u38, _u42) )).
% 1.23/1.46 cnf(matrix-27, plain, ( ( _u44 != _u42) | ~member(_u39, _u42) | member(_u39, _u44) )).
% 1.23/1.46 cnf(matrix-28, plain, ( ( _u45 = _u43) | member(skolem3(_u45, _u43), _u45) | member(skolem4(_u45, _u43), _u43) )).
% 1.23/1.46 cnf(matrix-29, plain, ( ( _u45 = _u43) | member(skolem3(_u45, _u43), _u45) | ~member(skolem4(_u45, _u43), _u45) )).
% 1.23/1.46 cnf(matrix-30, plain, ( ( _u45 = _u43) | ~member(skolem3(_u45, _u43), _u43) | member(skolem4(_u45, _u43), _u43) )).
% 1.23/1.46 cnf(matrix-31, plain, ( ( _u45 = _u43) | ~member(skolem3(_u45, _u43), _u43) | ~member(skolem4(_u45, _u43), _u45) )).
% 1.23/1.46 cnf(matrix-32, plain, ( subset(skolem5, skolem6) )).
% 1.23/1.46 cnf(matrix-33, plain, ( ( intersection(skolem6, skolem5) = empty_set) )).
% 1.23/1.46 cnf(matrix-34, plain, ( ( skolem5 != empty_set) )).
% 1.23/1.46
% 1.23/1.46 % Proof stack:
% 1.23/1.46 cnf(proof-stack, plain,
% 1.23/1.46 proof_stack(
% 1.23/1.46 start(12),
% 1.23/1.46 left_branch(0, 28, 2, 2),
% 1.23/1.46 left_branch(0, 34, 0, 3),
% 1.23/1.46 right_branch(3),
% 1.23/1.46 left_branch(0, 16, 1, 4),
% 1.23/1.46 left_branch(0, 32, 0, 5),
% 1.23/1.46 right_branch(5),
% 1.23/1.46 left_branch(0, 15, 0, 6),
% 1.23/1.46 left_branch(0, 26, 1, 7),
% 1.23/1.46 left_branch(0, 33, 0, 8),
% 1.23/1.46 right_branch(8),
% 1.23/1.46 left_branch(0, 12, 0, 9),
% 1.23/1.46 right_branch(9),
% 1.23/1.46 right_branch(7),
% 1.23/1.46 reduction(0, 1),
% 1.23/1.46 right_branch(6),
% 1.23/1.46 right_branch(4),
% 1.23/1.46 right_branch(2)
% 1.23/1.46 )).
% 1.23/1.46 % SZS output end Proof for theBenchmark
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