%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET015-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n029.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 37.38s 23.23s
% Output : CNFRefutation 37.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 54 ( 12 unt; 15 nHn; 44 RR)
% Number of literals : 119 ( 16 equ; 55 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_union_a_is_d,hypothesis,
union(bs,as) = ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(a_union_b_is_c,hypothesis,
union(as,bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset3) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',extensionality2) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',extensionality3) ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_15,hypothesis,
union(bs,as) = ds,
b_union_a_is_d ).
cnf(c_0_16,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_17,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_18,hypothesis,
complement(intersection(complement(bs),complement(as))) = ds,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
union(as,bs) = cs,
a_union_b_is_c ).
cnf(c_0_20,hypothesis,
( ~ member(X1,intersection(complement(bs),complement(as)))
| ~ member(X1,ds) ),
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,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_23,hypothesis,
complement(intersection(complement(as),complement(bs))) = cs,
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,hypothesis,
( ~ member(X1,complement(as))
| ~ member(X1,complement(bs))
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_26,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_27,hypothesis,
( member(X1,intersection(complement(as),complement(bs)))
| member(X1,cs)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_29,hypothesis,
( member(X1,bs)
| ~ member(X1,complement(as))
| ~ member(X1,ds) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_25]) ).
cnf(c_0_30,hypothesis,
( member(X1,complement(as))
| member(X1,cs)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( member(X1,complement(bs))
| member(X1,cs)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_32,hypothesis,
( member(X1,cs)
| member(X1,bs)
| ~ member(X1,ds) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25]) ).
cnf(c_0_33,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_34,hypothesis,
( member(X1,cs)
| ~ member(X1,bs) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_25]) ).
cnf(c_0_35,hypothesis,
( ~ member(X1,intersection(complement(as),complement(bs)))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_36,hypothesis,
( member(X1,intersection(complement(bs),complement(as)))
| member(X1,ds)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_37,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_38,hypothesis,
( subset(ds,X1)
| member(f17(ds,X1),cs) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,hypothesis,
( ~ member(X1,complement(bs))
| ~ member(X1,complement(as))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_40,hypothesis,
( member(X1,complement(bs))
| member(X1,ds)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_41,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_42,hypothesis,
subset(ds,cs),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
( member(X1,bs)
| ~ member(X1,complement(as))
| ~ member(X1,cs) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_25]) ).
cnf(c_0_44,hypothesis,
( member(X1,complement(as))
| member(X1,ds)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_45,hypothesis,
( member(X1,ds)
| ~ member(X1,bs) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_25]) ).
cnf(c_0_46,hypothesis,
( member(X1,cs)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_48,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_49,hypothesis,
( member(X1,ds)
| ~ member(X1,cs) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_25]),c_0_45]) ).
cnf(c_0_50,hypothesis,
( member(f1(X1,ds),cs)
| X1 = ds
| member(f1(X1,ds),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,hypothesis,
( X1 = ds
| ~ member(f1(X1,ds),X1)
| ~ member(f1(X1,ds),cs) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
cs != ds,
prove_c_equals_d ).
cnf(c_0_53,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_50,c_0_51,c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.25 % Problem : SET015-3 : TPTP v9.2.1. Released v1.0.0.
% 0.02/0.25 % 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
% 0.12/0.45 % Computer : n029.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 02:19:44 EDT 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.47 % start to proof: theBenchmark
% 37.38/23.23 % Version : CSE_E---1.7
% 37.38/23.23 % Problem : theBenchmark.p
% 37.38/23.23 % SZS status Unsatisfiable for theBenchmark.p
% 37.38/23.23 % SZS output start CNFRefutation
% See solution above
% 37.48/23.34 % Total time : 18.460s
%------------------------------------------------------------------------------