%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET007-1 : 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 : n031.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 1.73s 1.83s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 63 ( 16 unt; 12 nHn; 55 RR)
% Number of literals : 149 ( 0 equ; 72 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 : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 104 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(member_of_set2_is_member_of_union,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',member_of_set2_is_member_of_union) ).
cnf(b_union_c,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_c) ).
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_c,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_c) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
cnf(a_intersection_b,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
cnf(a_intersection_bUc,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bUc) ).
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(member_of_set1_is_member_of_union,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).
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(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
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(prove_aIb_union_aIc_is_aI_bUc,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
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(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_union_is_member_of_one_set,axiom,
( member(X4,X1)
| member(X4,X2)
| ~ union(X1,X2,X3)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',member_of_union_is_member_of_one_set) ).
cnf(c_0_17,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X2) ),
member_of_set2_is_member_of_union ).
cnf(c_0_18,axiom,
union(b,c,bUc),
b_union_c ).
cnf(c_0_19,axiom,
( member(X4,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_20,axiom,
intersection(a,c,aIc),
a_intersection_c ).
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,
( member(X1,bUc)
| ~ member(X1,c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(X1,c)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_25,axiom,
intersection(a,b,aIb),
a_intersection_b ).
cnf(c_0_26,plain,
( subset(X1,bUc)
| ~ member(member_of_1_not_of_2(X1,bUc),c) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( subset(aIc,X1)
| member(member_of_1_not_of_2(aIc,X1),c) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
intersection(a,bUc,aI_bUc),
a_intersection_bUc ).
cnf(c_0_29,plain,
( member(X1,b)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_30,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_31,axiom,
( member(X4,X3)
| ~ union(X1,X2,X3)
| ~ member(X4,X1) ),
member_of_set1_is_member_of_union ).
cnf(c_0_32,axiom,
( member(X4,X3)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X4,X1) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_33,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_34,plain,
subset(aIc,bUc),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( member(X1,bUc)
| ~ member(X1,aI_bUc) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_36,plain,
( union(aIb,X1,X2)
| member(g(aIb,X1,X2),b)
| member(g(aIb,X1,X2),X1)
| member(g(aIb,X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( member(X1,bUc)
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
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,plain,
( member(X1,aI_bUc)
| ~ member(X1,bUc)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_40,plain,
( member(X1,bUc)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( union(aIb,X1,aI_bUc)
| member(g(aIb,X1,aI_bUc),bUc)
| member(g(aIb,X1,aI_bUc),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
prove_aIb_union_aIc_is_aI_bUc ).
cnf(c_0_43,axiom,
( member(X4,X1)
| ~ intersection(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_44,axiom,
( union(X1,X2,X3)
| ~ member(g(X1,X2,X3),X2)
| ~ member(g(X1,X2,X3),X3) ),
union_axiom3 ).
cnf(c_0_45,plain,
( union(X1,X2,aI_bUc)
| ~ member(g(X1,X2,aI_bUc),bUc)
| ~ member(g(X1,X2,aI_bUc),a)
| ~ member(g(X1,X2,aI_bUc),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
member(g(aIb,aIc,aI_bUc),bUc),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,plain,
( member(X1,a)
| ~ member(X1,aIb) ),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_48,axiom,
( member(X4,X1)
| member(X4,X2)
| ~ union(X1,X2,X3)
| ~ member(X4,X3) ),
member_of_union_is_member_of_one_set ).
cnf(c_0_49,plain,
( union(X1,X2,aI_bUc)
| ~ member(g(X1,X2,aI_bUc),bUc)
| ~ member(g(X1,X2,aI_bUc),a)
| ~ member(g(X1,X2,aI_bUc),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_50,plain,
( member(X1,a)
| ~ member(X1,aIc) ),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_51,plain,
~ member(g(aIb,aIc,aI_bUc),aIb),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42]),c_0_47]) ).
cnf(c_0_52,plain,
( member(X1,aIb)
| ~ member(X1,b)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_53,plain,
( member(X1,b)
| member(X1,c)
| ~ member(X1,bUc) ),
inference(spm,[status(thm)],[c_0_48,c_0_18]) ).
cnf(c_0_54,plain,
~ member(g(aIb,aIc,aI_bUc),aIc),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_42]),c_0_50]) ).
cnf(c_0_55,plain,
( member(X1,aIc)
| ~ member(X1,c)
| ~ member(X1,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_56,plain,
( member(X1,a)
| ~ member(X1,aI_bUc) ),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_57,plain,
( ~ member(g(aIb,aIc,aI_bUc),b)
| ~ member(g(aIb,aIc,aI_bUc),a) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_59,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| ~ member(g(aIb,aIc,aI_bUc),a) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( union(X1,X2,aI_bUc)
| member(g(X1,X2,aI_bUc),a)
| member(g(X1,X2,aI_bUc),X1)
| member(g(X1,X2,aI_bUc),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_61,plain,
~ member(g(aIb,aIc,aI_bUc),a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_62,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_60]),c_0_42]),c_0_61]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET007-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:05:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.73/1.83 % Version : CSE_E---1.7
% 1.73/1.83 % Problem : theBenchmark.p
% 1.73/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 1.73/1.83 % SZS output start CNFRefutation
% See solution above
% 1.73/1.84 % Total time : 1.368s
%------------------------------------------------------------------------------