%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET011-1 : 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 : 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 05:06:47 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 9 unt; 16 nHn; 25 RR)
% Number of literals : 85 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 60 ( 4 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(a_minus_aDb,hypothesis,
difference(a,aDb,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_aDb) ).
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(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(intersection_axiom1,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).
cnf(intersection_axiom2,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).
cnf(a_minus_b,hypothesis,
difference(a,b,aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_b) ).
cnf(intersection_axiom3,axiom,
( intersection(X1,X2,X3)
| ~ member(h(X1,X2,X3),X3)
| ~ member(h(X1,X2,X3),X2)
| ~ member(h(X1,X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',intersection_axiom3) ).
cnf(prove_a_intersection_b_is_aD_aDb,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
cnf(c_0_9,axiom,
( member(X4,X1)
| ~ difference(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_difference ).
cnf(c_0_10,hypothesis,
difference(a,aDb,aD_aDb),
a_minus_aDb ).
cnf(c_0_11,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ difference(X4,X2,X3) ),
not_member_of_difference ).
cnf(c_0_12,axiom,
( member(X1,X4)
| member(X1,X3)
| ~ member(X1,X2)
| ~ difference(X2,X3,X4) ),
member_of_difference_or_set2 ).
cnf(c_0_13,hypothesis,
( member(X1,a)
| ~ member(X1,aD_aDb) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X1) ),
intersection_axiom1 ).
cnf(c_0_15,hypothesis,
( ~ member(X1,aD_aDb)
| ~ member(X1,aDb) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X2) ),
intersection_axiom2 ).
cnf(c_0_17,hypothesis,
difference(a,b,aDb),
a_minus_b ).
cnf(c_0_18,axiom,
( intersection(X1,X2,X3)
| ~ member(h(X1,X2,X3),X3)
| ~ member(h(X1,X2,X3),X2)
| ~ member(h(X1,X2,X3),X1) ),
intersection_axiom3 ).
cnf(c_0_19,hypothesis,
( member(X1,aDb)
| member(X1,aD_aDb)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_20,hypothesis,
( intersection(X1,X2,aD_aDb)
| member(h(X1,X2,aD_aDb),a)
| member(h(X1,X2,aD_aDb),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,hypothesis,
( intersection(X1,X2,aD_aDb)
| member(h(X1,X2,aD_aDb),X2)
| ~ member(h(X1,X2,aD_aDb),aDb) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,hypothesis,
( member(X1,b)
| member(X1,aDb)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_23,hypothesis,
( intersection(X1,X2,aD_aDb)
| member(h(X1,X2,aD_aDb),a)
| member(h(X1,X2,aD_aDb),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_24,hypothesis,
( intersection(X1,X2,aD_aDb)
| member(h(X1,X2,aD_aDb),aDb)
| ~ member(h(X1,X2,aD_aDb),a)
| ~ member(h(X1,X2,aD_aDb),X2)
| ~ member(h(X1,X2,aD_aDb),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,hypothesis,
( intersection(a,X1,aD_aDb)
| member(h(a,X1,aD_aDb),a) ),
inference(ef,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
( intersection(X1,X2,aD_aDb)
| member(h(X1,X2,aD_aDb),b)
| member(h(X1,X2,aD_aDb),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,hypothesis,
( intersection(a,X1,aD_aDb)
| member(h(a,X1,aD_aDb),aDb)
| ~ member(h(a,X1,aD_aDb),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_28,hypothesis,
( intersection(X1,b,aD_aDb)
| member(h(X1,b,aD_aDb),b) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ intersection(a,b,aD_aDb),
prove_a_intersection_b_is_aD_aDb ).
cnf(c_0_30,hypothesis,
( ~ member(X1,aDb)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_31,hypothesis,
member(h(a,b,aD_aDb),aDb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,hypothesis,
~ member(h(a,b,aD_aDb),b),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET011-1 : 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
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:03:59 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.18/0.33 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------