%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET013-1 : 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 : n019.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 2.03s 1.95s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 5 unt; 4 nHn; 15 RR)
% Number of literals : 42 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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_both_is_member_of_intersection,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_both_is_member_of_intersection) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
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(member_of_intersection_is_member_of_set2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
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_commutativity,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_7,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_8,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_9,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_10,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_11,plain,
( subset(X1,intersection(X2,X3))
| ~ member(member_of_1_not_of_2(X1,intersection(X2,X3)),X3)
| ~ member(member_of_1_not_of_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( subset(intersection(X1,X2),X3)
| member(member_of_1_not_of_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_14,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(member_of_1_not_of_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(member_of_1_not_of_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_16,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_17,plain,
subset(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
prove_commutativity ).
cnf(c_0_19,plain,
equal_sets(intersection(X1,X2),intersection(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),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
% 0.00/0.11 % Problem : SET013-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:04:14 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.03/1.95 % Version : CSE_E---1.7
% 2.03/1.95 % Problem : theBenchmark.p
% 2.03/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.95 % SZS output start CNFRefutation
% See solution above
% 2.03/1.96 % Total time : 1.369s
%------------------------------------------------------------------------------