%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET013-2 : 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 : n014.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 16.09s 11.04s
% Output : CNFRefutation 16.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 13 unt; 6 nHn; 54 RR)
% Number of literals : 120 ( 0 equ; 59 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_for_set_equal,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
cnf(intersection_of_a_and_b_is_c,hypothesis,
equal_sets(intersection(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
cnf(transitivity_for_set_equal,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',transitivity_for_set_equal) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
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_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_intersection_is_member_of_set2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
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(c_0_13,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
symmetry_for_set_equal ).
cnf(c_0_14,hypothesis,
equal_sets(intersection(bs,as),ds),
intersection_of_b_and_a_is_d ).
cnf(c_0_15,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_16,axiom,
( subset(X2,X1)
| ~ equal_sets(X1,X2) ),
set_equal_sets_are_subsets2 ).
cnf(c_0_17,hypothesis,
equal_sets(intersection(as,bs),cs),
intersection_of_a_and_b_is_c ).
cnf(c_0_18,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
transitivity_for_set_equal ).
cnf(c_0_19,hypothesis,
equal_sets(ds,intersection(bs,as)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| ~ equal_sets(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
equal_sets(cs,intersection(as,bs)),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_22,hypothesis,
( equal_sets(X1,intersection(bs,as))
| ~ equal_sets(X1,ds) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,hypothesis,
( member(X1,cs)
| ~ member(X1,intersection(as,bs)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_25,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_26,hypothesis,
( member(X1,intersection(bs,as))
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_27,hypothesis,
( equal_sets(X1,cs)
| ~ equal_sets(X1,intersection(as,bs)) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_28,hypothesis,
( equal_sets(intersection(bs,as),X1)
| ~ equal_sets(X1,ds) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_29,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_30,hypothesis,
( member(X1,cs)
| ~ member(X1,bs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
( member(X1,bs)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_33,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_34,hypothesis,
( equal_sets(intersection(bs,as),cs)
| ~ equal_sets(intersection(as,bs),ds) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,hypothesis,
( equal_sets(X1,intersection(as,bs))
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_36,hypothesis,
( subset(X1,cs)
| ~ member(member_of_1_not_of_2(X1,cs),bs)
| ~ member(member_of_1_not_of_2(X1,cs),as) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,hypothesis,
( subset(ds,X1)
| member(member_of_1_not_of_2(ds,X1),bs) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,hypothesis,
( member(X1,as)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_39,hypothesis,
( equal_sets(cs,intersection(bs,as))
| ~ equal_sets(intersection(as,bs),ds) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_40,hypothesis,
( equal_sets(intersection(as,bs),X1)
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_13,c_0_35]) ).
cnf(c_0_41,hypothesis,
( member(X1,ds)
| ~ member(X1,intersection(bs,as)) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_42,hypothesis,
( member(X1,intersection(as,bs))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_43,hypothesis,
( subset(ds,cs)
| ~ member(member_of_1_not_of_2(ds,cs),as) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,hypothesis,
( subset(ds,X1)
| member(member_of_1_not_of_2(ds,X1),as) ),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_45,hypothesis,
( equal_sets(X1,ds)
| ~ equal_sets(X1,intersection(bs,as)) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_46,hypothesis,
( equal_sets(cs,intersection(bs,as))
| ~ equal_sets(ds,cs) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
~ equal_sets(cs,ds),
prove_c_equals_d ).
cnf(c_0_48,hypothesis,
( member(X1,ds)
| ~ member(X1,as)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_41,c_0_24]) ).
cnf(c_0_49,hypothesis,
( member(X1,bs)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_50,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_51,hypothesis,
subset(ds,cs),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,hypothesis,
~ equal_sets(ds,cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_53,hypothesis,
( subset(X1,ds)
| ~ member(member_of_1_not_of_2(X1,ds),as)
| ~ member(member_of_1_not_of_2(X1,ds),bs) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_54,hypothesis,
( subset(cs,X1)
| member(member_of_1_not_of_2(cs,X1),bs) ),
inference(spm,[status(thm)],[c_0_49,c_0_32]) ).
cnf(c_0_55,hypothesis,
~ subset(cs,ds),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,hypothesis,
( member(X1,as)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_57,hypothesis,
~ member(member_of_1_not_of_2(cs,ds),as),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_58,hypothesis,
( subset(cs,X1)
| member(member_of_1_not_of_2(cs,X1),as) ),
inference(spm,[status(thm)],[c_0_56,c_0_32]) ).
cnf(c_0_59,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET013-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n014.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 02:04:22 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 16.09/11.04 % Version : CSE_E---1.7
% 16.09/11.04 % Problem : theBenchmark.p
% 16.09/11.04 % SZS status Unsatisfiable for theBenchmark.p
% 16.09/11.04 % SZS output start CNFRefutation
% See solution above
% 16.09/11.10 % Total time : 8.424s
%------------------------------------------------------------------------------