%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET012-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 : Tue May 5 05:06:48 PM UTC 2026
% Result : Unsatisfiable 2.10s 1.98s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 11 unt; 7 nHn; 32 RR)
% Number of literals : 74 ( 0 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
cnf(set_equal_sets_are_subsets2,axiom,
( subset(X2,X1)
| ~ equal_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
cnf(symmetry_for_set_equal,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
cnf(complement_of_a_is_b,hypothesis,
equal_sets(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',not_member_of_set_and_complement) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
cnf(member_of_set_or_complement,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_set_or_complement) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
cnf(transitivity_for_set_equal,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',transitivity_for_set_equal) ).
cnf(complement_of_b_is_c,hypothesis,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
cnf(subsets_are_set_equal_sets,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
cnf(prove_a_equals_c,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
cnf(c_0_12,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_13,axiom,
( subset(X2,X1)
| ~ equal_sets(X1,X2) ),
set_equal_sets_are_subsets2 ).
cnf(c_0_14,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
symmetry_for_set_equal ).
cnf(c_0_15,hypothesis,
equal_sets(complement(a),b),
complement_of_a_is_b ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ equal_sets(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,hypothesis,
equal_sets(b,complement(a)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
not_member_of_set_and_complement ).
cnf(c_0_19,hypothesis,
( member(X1,complement(a))
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_21,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
member_of_set_or_complement ).
cnf(c_0_22,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_23,hypothesis,
( member(X1,b)
| ~ member(X1,complement(a)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,hypothesis,
( ~ member(X1,a)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( subset(X1,complement(X2))
| member(member_of_1_not_of_2(X1,complement(X2)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( subset(complement(X1),X2)
| ~ member(member_of_1_not_of_2(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,hypothesis,
( member(X1,a)
| member(X1,b) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,hypothesis,
( subset(X1,complement(b))
| ~ member(member_of_1_not_of_2(X1,complement(b)),a) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,hypothesis,
( subset(complement(b),X1)
| member(member_of_1_not_of_2(complement(b),X1),a) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
transitivity_for_set_equal ).
cnf(c_0_31,hypothesis,
equal_sets(complement(b),c),
complement_of_b_is_c ).
cnf(c_0_32,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_33,hypothesis,
subset(a,complement(b)),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_34,hypothesis,
subset(complement(b),a),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_35,hypothesis,
( equal_sets(X1,c)
| ~ equal_sets(X1,complement(b)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,hypothesis,
equal_sets(a,complement(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
~ equal_sets(a,c),
prove_a_equals_c ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET012-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:03:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.10/1.98 % Version : CSE_E---1.7
% 2.10/1.98 % Problem : theBenchmark.p
% 2.10/1.98 % SZS status Unsatisfiable for theBenchmark.p
% 2.10/1.98 % SZS output start CNFRefutation
% See solution above
% 2.10/1.99 % Total time : 1.368s
%------------------------------------------------------------------------------