%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET005-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n008.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 05:06:46 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 59 ( 14 unt; 17 nHn; 43 RR)
% Number of literals : 133 ( 0 equ; 54 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 : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 87 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
cnf(a_intersection_bIc,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bIc) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
cnf(b_intersection_c,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_intersection_c) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
cnf(intersection_axiom2,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
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/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
cnf(a_intersection_b,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_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/sandbox2/benchmark/Axioms/SET001-2.ax',intersection_axiom3) ).
cnf(intersection_axiom1,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).
cnf(prove_aIb_intersection_c_is_aIbIc,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
cnf(c_0_13,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_14,axiom,
intersection(a,bIc,aIbIc),
a_intersection_bIc ).
cnf(c_0_15,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_16,axiom,
intersection(b,c,bIc),
b_intersection_c ).
cnf(c_0_17,plain,
( member(X1,bIc)
| ~ member(X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_19,plain,
( member(X1,b)
| ~ member(X1,bIc) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( subset(aIbIc,X1)
| member(member_of_1_not_of_2(aIbIc,X1),bIc) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_22,plain,
( subset(aIbIc,X1)
| member(member_of_1_not_of_2(aIbIc,X1),b) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X2) ),
intersection_axiom2 ).
cnf(c_0_24,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_25,plain,
subset(aIbIc,b),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( member(X4,X3)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X4,X1) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_27,axiom,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_28,plain,
( member(X1,a)
| ~ member(X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_29,plain,
( intersection(X1,X2,X2)
| member(h(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( member(X1,b)
| ~ member(X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,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_32,plain,
( member(X1,aIb)
| ~ member(X1,b)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( intersection(X1,aIbIc,aIbIc)
| member(h(X1,aIbIc,aIbIc),a) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( intersection(X1,aIbIc,aIbIc)
| member(h(X1,aIbIc,aIbIc),b) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,plain,
( intersection(X1,X2,X2)
| ~ member(h(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_29]) ).
cnf(c_0_36,plain,
( intersection(X1,aIbIc,aIbIc)
| member(h(X1,aIbIc,aIbIc),aIb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,plain,
( member(X1,b)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_38,axiom,
( member(h(X1,X2,X3),X3)
| intersection(X1,X2,X3)
| member(h(X1,X2,X3),X1) ),
intersection_axiom1 ).
cnf(c_0_39,plain,
intersection(aIb,aIbIc,aIbIc),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( member(X1,bIc)
| ~ member(X1,c)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_41,plain,
( intersection(X1,X2,aIbIc)
| member(h(X1,X2,aIbIc),bIc)
| member(h(X1,X2,aIbIc),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_42,plain,
( intersection(aIb,X1,X2)
| member(h(aIb,X1,X2),b)
| member(h(aIb,X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( member(X1,aIb)
| ~ member(X1,aIbIc) ),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_44,plain,
( member(X1,aIbIc)
| ~ member(X1,bIc)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_45,plain,
( intersection(X1,c,aIbIc)
| member(h(X1,c,aIbIc),bIc)
| ~ member(h(X1,c,aIbIc),b) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( intersection(aIb,X1,aIbIc)
| member(h(aIb,X1,aIbIc),b) ),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
~ intersection(aIb,c,aIbIc),
prove_aIb_intersection_c_is_aIbIc ).
cnf(c_0_48,plain,
( member(X1,aIb)
| ~ member(X1,bIc)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
member(h(aIb,c,aIbIc),bIc),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,plain,
( member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),a) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,plain,
( intersection(X1,X2,aIbIc)
| member(h(X1,X2,aIbIc),a)
| member(h(X1,X2,aIbIc),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_52,plain,
( intersection(X1,X2,aIbIc)
| ~ member(h(X1,X2,aIbIc),bIc)
| ~ member(h(X1,X2,aIbIc),a)
| ~ member(h(X1,X2,aIbIc),X2)
| ~ member(h(X1,X2,aIbIc),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_44]) ).
cnf(c_0_53,plain,
member(h(aIb,c,aIbIc),aIb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47]) ).
cnf(c_0_54,plain,
( ~ member(h(aIb,c,aIbIc),a)
| ~ member(h(aIb,c,aIbIc),c) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_53])]),c_0_47]) ).
cnf(c_0_55,plain,
( member(X1,c)
| ~ member(X1,bIc) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_56,plain,
~ member(h(aIb,c,aIbIc),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_49])]) ).
cnf(c_0_57,plain,
( member(X1,a)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_58,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET005-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:03:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------