%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET012-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 1.41s 1.79s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 6 unt; 6 nHn; 12 RR)
% Number of literals : 38 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',not_member_of_set_and_complement) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
cnf(member_of_set_or_complement,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set_or_complement) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
cnf(subsets_are_set_equal_sets,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
cnf(prove_involution,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_involution) ).
cnf(c_0_6,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
not_member_of_set_and_complement ).
cnf(c_0_7,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_8,plain,
( subset(complement(X1),X2)
| ~ member(member_of_1_not_of_2(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
member_of_set_or_complement ).
cnf(c_0_10,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_11,plain,
( subset(complement(complement(X1)),X2)
| member(member_of_1_not_of_2(complement(complement(X1)),X2),X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( subset(X1,complement(X2))
| member(member_of_1_not_of_2(X1,complement(X2)),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_14,plain,
subset(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,complement(complement(X2)))
| ~ member(member_of_1_not_of_2(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_16,plain,
( equal_sets(complement(complement(X1)),X1)
| ~ subset(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
subset(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_18,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
prove_involution ).
cnf(c_0_19,plain,
equal_sets(complement(complement(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET012-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:03:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.41/1.79 % Version : CSE_E---1.7
% 1.41/1.79 % Problem : theBenchmark.p
% 1.41/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.41/1.79 % SZS output start CNFRefutation
% See solution above
% 1.41/1.79 % Total time : 1.371s
%------------------------------------------------------------------------------