%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:45:59 PM UTC 2026
% Result : Unsatisfiable 6.36s 1.74s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 93 ( 18 unt; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 286 ( 134 ~; 152 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 152 ( 0 sgn 152 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
fof(f2,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).
fof(f25,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f26,axiom,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_a) ).
fof(f27,axiom,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_b) ).
fof(f28,axiom,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_aIb) ).
fof(f29,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_102,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[],[f25]) ).
tcf(c_103,plain,
difference(c,a,cDa),
inference(cnf_transformation,[],[f26]) ).
tcf(c_104,plain,
difference(c,b,cDb),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,plain,
difference(c,aIb,cD_aIb),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
inference(cnf_transformation,[],[f29]) ).
tcf(c_649,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolution,[status(thm)],[c_106,c_89]) ).
tcf(c_656,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[c_106,c_88]) ).
tcf(c_663,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[c_106,c_87]) ).
tcf(c_1858,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(member_of_1_not_of_2(X0_iProver_subset_1,X1_iProver_subset_1),X1_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_1859,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X1_iProver_subset_1)
| member(member_of_1_not_of_2(X0_iProver_subset_1,X1_iProver_subset_1),X0_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_79]) ).
tcf(c_1860,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_78]) ).
tcf(c_1870,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_1871,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_91]) ).
tcf(c_1872,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_90]) ).
tcf(c_1876,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X2_iProver_subset_1)
| member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_1877,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_1878,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_96]) ).
tcf(c_1880,plain,
difference(c,aIb,cD_aIb),
inference(subtyping,[status(esa)],[c_105]) ).
tcf(c_1881,plain,
difference(c,b,cDb),
inference(subtyping,[status(esa)],[c_104]) ).
tcf(c_1882,plain,
difference(c,a,cDa),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_1883,plain,
intersection(a,b,aIb),
inference(subtyping,[status(esa)],[c_102]) ).
tcf(c_1890,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( ~ difference(X1_iProver_subset_1,X0_iProver_subset_1,cDb)
| ~ member(g(cDa,cDb,cD_aIb),cDb)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1877]) ).
tcf(c_1894,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ subset(X0_iProver_subset_1,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1860]) ).
tcf(c_1925,plain,
( ~ difference(c,b,cDb)
| ~ member(g(cDa,cDb,cD_aIb),cDb)
| ~ member(g(cDa,cDb,cD_aIb),b) ),
inference(instantiation,[status(thm)],[c_1890]) ).
tcf(c_1984,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,b,X1_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1876]) ).
tcf(c_1985,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),b)
| ~ intersection(X1_iProver_subset_1,b,X0_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1871]) ).
tcf(c_2132,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),X2_iProver_subset_1)
| member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1876]) ).
tcf(c_2134,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1860]) ).
tcf(c_2144,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| ~ member(X0_iProver_member_1,cDb) ),
inference(superposition,[status(thm)],[c_1881,c_1878]) ).
tcf(c_2145,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| ~ member(X0_iProver_member_1,cD_aIb) ),
inference(superposition,[status(thm)],[c_1880,c_1878]) ).
tcf(c_2192,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(cDb,X0_iProver_subset_1)
| member(member_of_1_not_of_2(cDb,X0_iProver_subset_1),c) ),
inference(superposition,[status(thm)],[c_1859,c_2144]) ).
tcf(c_2218,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(cD_aIb,X0_iProver_subset_1)
| member(member_of_1_not_of_2(cD_aIb,X0_iProver_subset_1),c) ),
inference(superposition,[status(thm)],[c_1859,c_2145]) ).
tcf(c_2512,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1)
| ~ subset(cDb,X0_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(instantiation,[status(thm)],[c_2134]) ).
tcf(c_2513,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ subset(cDb,c)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(instantiation,[status(thm)],[c_2512]) ).
tcf(c_2569,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1,X3_iProver_subset_1: iProver_subset_1,X4_iProver_subset_1: iProver_subset_1] :
( member(g(X0_iProver_subset_1,X1_iProver_subset_1,cD_aIb),X4_iProver_subset_1)
| ~ intersection(X2_iProver_subset_1,X3_iProver_subset_1,X4_iProver_subset_1)
| ~ member(g(X0_iProver_subset_1,X1_iProver_subset_1,cD_aIb),X3_iProver_subset_1)
| ~ member(g(X0_iProver_subset_1,X1_iProver_subset_1,cD_aIb),X2_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1870]) ).
tcf(c_2696,plain,
subset(cDb,c),
inference(superposition,[status(thm)],[c_2192,c_1858]) ).
tcf(c_2698,plain,
subset(cD_aIb,c),
inference(superposition,[status(thm)],[c_2218,c_1858]) ).
tcf(c_3520,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1)
| ~ subset(cD_aIb,X0_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(instantiation,[status(thm)],[c_2134]) ).
tcf(c_3538,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ subset(cD_aIb,c)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(instantiation,[status(thm)],[c_3520]) ).
tcf(c_3555,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( ~ difference(X1_iProver_subset_1,X0_iProver_subset_1,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1877]) ).
tcf(c_3802,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ subset(cDa,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(instantiation,[status(thm)],[c_1894]) ).
tcf(c_3997,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,a)
| ~ member(X0_iProver_member_1,aIb) ),
inference(resolution,[status(thm)],[c_1872,c_1883]) ).
tcf(c_4004,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| ~ member(X0_iProver_member_1,cDa) ),
inference(resolution,[status(thm)],[c_1878,c_1882]) ).
tcf(c_4073,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,b,X1_iProver_subset_1)
| ~ member(g(cDa,cDb,cD_aIb),b)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_2569]) ).
tcf(c_4085,plain,
! [X0_iProver_member_1: iProver_member_1] :
( ~ member(X0_iProver_member_1,cDa)
| ~ member(X0_iProver_member_1,a) ),
inference(resolution,[status(thm)],[c_1877,c_1882]) ).
tcf(c_4550,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,cD_aIb)
| member(X0_iProver_member_1,aIb)
| ~ member(X0_iProver_member_1,c) ),
inference(resolution,[status(thm)],[c_1876,c_1880]) ).
tcf(c_4855,plain,
( member(g(cDa,cDb,cD_aIb),b)
| ~ intersection(a,b,aIb)
| ~ member(g(cDa,cDb,cD_aIb),aIb) ),
inference(instantiation,[status(thm)],[c_1985]) ).
tcf(c_4866,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(cDa,X0_iProver_subset_1)
| member(member_of_1_not_of_2(cDa,X0_iProver_subset_1),c) ),
inference(resolution,[status(thm)],[c_4004,c_1859]) ).
tcf(c_5272,plain,
( ~ difference(c,aIb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),aIb) ),
inference(instantiation,[status(thm)],[c_3555]) ).
tcf(c_5551,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,cDa)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_2132]) ).
tcf(c_5579,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),X1_iProver_subset_1)
| ~ difference(X0_iProver_subset_1,X1_iProver_subset_1,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_2132]) ).
tcf(c_5847,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),b)
| ~ difference(X0_iProver_subset_1,b,cDb)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1984]) ).
tcf(c_5848,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),b)
| ~ difference(c,b,cDb)
| ~ member(g(cDa,cDb,cD_aIb),c) ),
inference(instantiation,[status(thm)],[c_5847]) ).
tcf(c_6638,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(cDa,X0_iProver_subset_1)
| ~ member(member_of_1_not_of_2(cDa,X0_iProver_subset_1),a) ),
inference(resolution,[status(thm)],[c_4085,c_1859]) ).
tcf(c_7423,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ intersection(X0_iProver_subset_1,b,aIb)
| ~ member(g(cDa,cDb,cD_aIb),b)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_4073]) ).
tcf(c_11501,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb)
| ~ difference(c,aIb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),c) ),
inference(instantiation,[status(thm)],[c_5579]) ).
tcf(c_12990,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,cD_aIb)
| member(member_of_1_not_of_2(X0_iProver_subset_1,cD_aIb),aIb)
| ~ member(member_of_1_not_of_2(X0_iProver_subset_1,cD_aIb),c) ),
inference(resolution,[status(thm)],[c_4550,c_1858]) ).
tcf(c_15553,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ intersection(a,b,aIb)
| ~ member(g(cDa,cDb,cD_aIb),b)
| ~ member(g(cDa,cDb,cD_aIb),a) ),
inference(instantiation,[status(thm)],[c_7423]) ).
tcf(c_17510,plain,
( subset(cDa,cD_aIb)
| member(member_of_1_not_of_2(cDa,cD_aIb),aIb) ),
inference(resolution,[status(thm)],[c_12990,c_4866]) ).
tcf(c_19283,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),a)
| ~ difference(X0_iProver_subset_1,a,cDa)
| ~ member(g(cDa,cDb,cD_aIb),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_5551]) ).
tcf(c_19320,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),a)
| ~ difference(c,a,cDa)
| ~ member(g(cDa,cDb,cD_aIb),c) ),
inference(instantiation,[status(thm)],[c_19283]) ).
tcf(c_19386,plain,
( subset(cDa,cD_aIb)
| member(member_of_1_not_of_2(cDa,cD_aIb),a) ),
inference(resolution,[status(thm)],[c_17510,c_3997]) ).
tcf(c_19606,plain,
subset(cDa,cD_aIb),
inference(forward_subsumption_resolution,[status(thm)],[c_19386,c_6638]) ).
tcf(c_19607,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19606,c_19320,c_15553,c_11501,c_5848,c_5272,c_4855,c_3802,c_3538,c_2698,c_2696,c_2513,c_1925,c_663,c_656,c_649,c_102,c_103,c_104,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:04:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 6.36/1.74 % SZS status Started for theBenchmark.p
% 6.36/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 6.36/1.74
% 6.36/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.36/1.74
% 6.36/1.74 % ------ iProver source info
% 6.36/1.74
% 6.36/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 6.36/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.36/1.74 % git: non_committed_changes: false
% 6.36/1.74
% 6.36/1.74 % ------ Parsing...% successful
% 6.36/1.74
% 6.36/1.74
% 6.36/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.36/1.74
% 6.36/1.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.36/1.74
% 6.36/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.36/1.74 % ------ Proving...
% 6.36/1.74 % ------ Problem Properties
% 6.36/1.74
% 6.36/1.74 %
% 6.36/1.74 % clauses 26
% 6.36/1.74 % conjectures 1
% 6.36/1.74 % EPR 15
% 6.36/1.74 % Horn 17
% 6.36/1.74 % unary 5
% 6.36/1.74 % binary 2
% 6.36/1.74 % lits 72
% 6.36/1.74 % lits eq 0
% 6.36/1.74 % fd_pure 0
% 6.36/1.74 % fd_pseudo 0
% 6.36/1.74 % fd_cond 0
% 6.36/1.74 % fd_pseudo_cond 0
% 6.36/1.74 % AC symbols 0
% 6.36/1.74
% 6.36/1.74 % ------ Input Options Time Limit: Unbounded
% 6.36/1.74
% 6.36/1.74
% 6.36/1.74 % ------
% 6.36/1.74 % Current options:
% 6.36/1.74 % ------
% 6.36/1.74
% 6.36/1.74
% 6.36/1.74 %
% 6.36/1.74
% 6.36/1.74 % ------ Proving...
% 6.36/1.74 %
% 6.36/1.74
% 6.36/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 6.36/1.74
% 6.36/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.36/1.74
% 6.36/1.74
%------------------------------------------------------------------------------