%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET010-1 : 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 : 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 05:06:47 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.70s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 56 ( 16 unt; 14 nHn; 54 RR)
% Number of literals : 127 ( 0 equ; 58 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 78 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(member_of_difference,axiom,
( member(X4,X1)
| ~ difference(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
cnf(c_minus_aIb,hypothesis,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_aIb) ).
cnf(prove_cDa_union_cDb_is_cD_aIb,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
cnf(union_axiom1,axiom,
( union(X1,X2,X3)
| member(g(X1,X2,X3),X1)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
cnf(c_minus_b,hypothesis,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_b) ).
cnf(c_minus_a,hypothesis,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_a) ).
cnf(member_of_difference_or_set2,axiom,
( member(X1,X4)
| member(X1,X3)
| ~ member(X1,X2)
| ~ difference(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
cnf(union_axiom3,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X2)
| ~ member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
cnf(a_intersection_b,hypothesis,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(X4,X3)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
cnf(not_member_of_difference,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ difference(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
cnf(union_axiom2,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X1)
| ~ member(g(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
cnf(c_0_14,axiom,
( member(X4,X1)
| ~ difference(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_difference ).
cnf(c_0_15,hypothesis,
difference(c,aIb,cD_aIb),
c_minus_aIb ).
cnf(c_0_16,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
prove_cDa_union_cDb_is_cD_aIb ).
cnf(c_0_17,axiom,
( union(X1,X2,X3)
| member(g(X1,X2,X3),X1)
| member(g(X1,X2,X3),X2)
| member(g(X1,X2,X3),X3) ),
union_axiom1 ).
cnf(c_0_18,hypothesis,
difference(c,b,cDb),
c_minus_b ).
cnf(c_0_19,hypothesis,
( member(X1,c)
| ~ member(X1,cD_aIb) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,hypothesis,
difference(c,a,cDa),
c_minus_a ).
cnf(c_0_22,axiom,
( member(X1,X4)
| member(X1,X3)
| ~ member(X1,X2)
| ~ difference(X2,X3,X4) ),
member_of_difference_or_set2 ).
cnf(c_0_23,hypothesis,
( member(X1,c)
| ~ member(X1,cDb) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_24,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),c) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
( member(X1,c)
| ~ member(X1,cDa) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_26,hypothesis,
( member(X1,aIb)
| member(X1,cD_aIb)
| ~ member(X1,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_27,hypothesis,
member(g(cDa,cDb,cD_aIb),c),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X2)
| ~ member(g(X1,X2,X3),X3) ),
union_axiom3 ).
cnf(c_0_29,hypothesis,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,hypothesis,
( member(X1,b)
| member(X1,cDb)
| ~ member(X1,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_31,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_32,hypothesis,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_33,axiom,
( member(X4,X3)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X4,X1) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_34,hypothesis,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]) ).
cnf(c_0_35,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),b) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_36,hypothesis,
( member(X1,b)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ difference(X4,X2,X3) ),
not_member_of_difference ).
cnf(c_0_38,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X1)
| ~ member(g(X1,X2,X3),X3) ),
union_axiom2 ).
cnf(c_0_39,hypothesis,
( member(X1,a)
| member(X1,cDa)
| ~ member(X1,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_40,hypothesis,
( member(X1,aIb)
| ~ member(X1,b)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_41,hypothesis,
member(g(cDa,cDb,cD_aIb),b),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_42,hypothesis,
( ~ member(X1,cD_aIb)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_43,hypothesis,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_16]) ).
cnf(c_0_44,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),a) ),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_45,hypothesis,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),a) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa)
| ~ member(g(cDa,cDb,cD_aIb),aIb) ),
inference(spm,[status(thm)],[c_0_42,c_0_20]) ).
cnf(c_0_47,hypothesis,
member(g(cDa,cDb,cD_aIb),aIb),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_49,hypothesis,
( ~ member(X1,cDb)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_18]) ).
cnf(c_0_50,hypothesis,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_51,hypothesis,
( member(X1,a)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_48,c_0_32]) ).
cnf(c_0_52,hypothesis,
( ~ member(X1,cDa)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_53,hypothesis,
member(g(cDa,cDb,cD_aIb),cDa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41])]) ).
cnf(c_0_54,hypothesis,
member(g(cDa,cDb,cD_aIb),a),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_55,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET010-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : 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 02:03:59 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.70 % Version : CSE_E---1.7
% 1.25/1.70 % Problem : theBenchmark.p
% 1.25/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.70 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------