%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET015-4 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n021.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 05:06:50 PM UTC 2026
% Result : Unsatisfiable 100.28s 75.19s
% Output : CNFRefutation 100.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 59 ( 19 unt; 22 nHn; 36 RR)
% Number of literals : 117 ( 42 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
cnf(a_union_b_is_c,hypothesis,
union(as,bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_b_is_c) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
cnf(extensionality1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
cnf(b_union_a_is_d,hypothesis,
union(bs,as) = ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_a_is_d) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_13,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_14,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_15,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_16,plain,
( empty_set = X1
| member(f1(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_18,plain,
( intersection(X1,X2) = empty_set
| member(f1(empty_set,intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_20,plain,
( intersection(complement(X1),X2) = empty_set
| ~ member(f1(empty_set,intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_22,plain,
( intersection(X1,X2) = empty_set
| member(f1(empty_set,intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,plain,
( intersection(complement(intersection(X1,X2)),X3) = empty_set
| ~ member(f1(empty_set,intersection(complement(intersection(X1,X2)),X3)),X2)
| ~ member(f1(empty_set,intersection(complement(intersection(X1,X2)),X3)),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( intersection(X1,intersection(X2,X3)) = empty_set
| member(f1(empty_set,intersection(X1,intersection(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_25,plain,
( X1 = intersection(X2,X3)
| member(f1(X1,intersection(X2,X3)),X1)
| member(f1(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_26,plain,
( intersection(complement(intersection(X1,X2)),intersection(X2,X3)) = empty_set
| ~ member(f1(empty_set,intersection(complement(intersection(X1,X2)),intersection(X2,X3))),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( X1 = intersection(X2,intersection(X3,X4))
| member(f1(X1,intersection(X2,intersection(X3,X4))),X1)
| member(f1(X1,intersection(X2,intersection(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_28,hypothesis,
union(as,bs) = cs,
a_union_b_is_c ).
cnf(c_0_29,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_30,plain,
intersection(complement(intersection(X1,X2)),intersection(X2,X1)) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_13]) ).
cnf(c_0_31,hypothesis,
complement(intersection(complement(as),complement(bs))) = cs,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_33,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
extensionality1 ).
cnf(c_0_34,hypothesis,
union(bs,as) = ds,
b_union_a_is_d ).
cnf(c_0_35,plain,
( intersection(X1,X2) = X3
| member(f1(intersection(X1,X2),X3),X3)
| member(f1(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_36,hypothesis,
intersection(cs,intersection(complement(bs),complement(as))) = empty_set,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( X1 = X2
| member(f1(X1,X2),complement(X3))
| member(f1(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
complement(intersection(complement(bs),complement(as))) = ds,
inference(rw,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_39,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_40,plain,
( intersection(X1,X2) = X1
| member(f1(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
( ~ member(X1,intersection(complement(bs),complement(as)))
| ~ member(X1,cs) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_13]) ).
cnf(c_0_42,hypothesis,
( X1 = X2
| member(f1(X1,X2),intersection(complement(bs),complement(as)))
| member(f1(X1,X2),ds) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( intersection(X1,X2) = X1
| ~ member(f1(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
( X1 = X2
| member(f1(X1,X2),ds)
| ~ member(f1(X1,X2),cs) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( intersection(X1,X2) = X3
| member(f1(intersection(X1,X2),X3),X3)
| member(f1(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_46,hypothesis,
intersection(ds,intersection(complement(as),complement(bs))) = empty_set,
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_47,plain,
( intersection(X1,X2) = X1
| ~ member(f1(intersection(X1,X2),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_21]),c_0_40]) ).
cnf(c_0_48,hypothesis,
( intersection(cs,X1) = cs
| member(f1(intersection(cs,X1),cs),ds) ),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_49,plain,
( intersection(X1,X2) = X2
| member(f1(intersection(X1,X2),X2),X2) ),
inference(ef,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
( ~ member(X1,intersection(complement(as),complement(bs)))
| ~ member(X1,ds) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_46]),c_0_13]) ).
cnf(c_0_51,hypothesis,
( X1 = X2
| member(f1(X1,X2),intersection(complement(as),complement(bs)))
| member(f1(X1,X2),cs) ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_52,hypothesis,
intersection(cs,ds) = cs,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
cs != ds,
prove_c_equals_d ).
cnf(c_0_54,plain,
( intersection(X1,X2) = X2
| ~ member(f1(intersection(X1,X2),X2),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_55,hypothesis,
( X1 = X2
| member(f1(X1,X2),cs)
| ~ member(f1(X1,X2),ds) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,hypothesis,
member(f1(cs,ds),ds),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_53]) ).
cnf(c_0_57,hypothesis,
~ member(f1(cs,ds),cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_52]),c_0_53]) ).
cnf(c_0_58,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET015-4 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:08:40 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 100.28/75.19 % Version : CSE_E---1.7
% 100.28/75.19 % Problem : theBenchmark.p
% 100.28/75.19 % SZS status Unsatisfiable for theBenchmark.p
% 100.28/75.19 % SZS output start CNFRefutation
% See solution above
% 100.86/75.73 % Total time : 55.745s
%------------------------------------------------------------------------------