%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET144+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:46:44 PM UTC 2026
% Result : Theorem 16.25s 3.48s
% Output : CNFRefutation 16.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 113 ( 27 unt; 4 def)
% Number of atoms : 490 ( 38 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 282 ( 107 ~; 140 |; 26 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 151 !; 7 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> union(X0,intersection(X2,X1)) = intersection(union(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th44) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> union(X0,intersection(X2,X1)) = intersection(union(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& union(X0,intersection(X2,X1)) != intersection(union(X0,X2),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
( subset(sK2,sK3)
& union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3),
inference(cnf_transformation,[],[f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,negated_conjecture,
union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3),
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f45]) ).
tcf(c_188,plain,
union(sK2,intersection(sK3,sK4)) != intersection(sK3,union(sK2,sK4)),
inference(demodulation,[status(thm)],[c_66,c_62]) ).
tcf(c_349,definition,
iPr_def_10 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_350,definition,
iPr_def_11 = union(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_351,definition,
iPr_def_12 = union(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_352,definition,
iPr_def_13 = intersection(sK3,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_353,plain,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_188,c_351,c_352,c_349,c_350]) ).
tcf(c_354,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_594,plain,
union(iPr_def_10,sK2) = iPr_def_11,
inference(demodulation,[status(thm)],[c_350,c_61]) ).
tcf(c_595,plain,
intersection(iPr_def_12,sK3) = iPr_def_13,
inference(demodulation,[status(thm)],[c_352,c_62]) ).
tcf(c_604,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_351,c_49]) ).
tcf(c_605,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_594,c_49]) ).
tcf(c_619,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_594,c_50]) ).
tcf(c_633,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_349,c_53]) ).
tcf(c_634,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_595,c_53]) ).
tcf(c_671,plain,
! [X0: $i] :
( subset(sK2,X0)
| member(sK0(sK2,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_56,c_619]) ).
tcf(c_725,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK2)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_351,c_51]) ).
tcf(c_726,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK2)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_594,c_51]) ).
tcf(c_746,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_349,c_54]) ).
tcf(c_747,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_595,c_54]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,union(X1,X2))
| ~ member(sK0(X0,union(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_49,c_55]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,union(X1,X2))
| ~ member(sK0(X0,union(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_766,plain,
subset(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_671,c_55]) ).
tcf(c_823,plain,
( ( iPr_def_11 = iPr_def_13 )
| ~ member(sK1(iPr_def_11,iPr_def_13),iPr_def_13)
| ~ member(sK1(iPr_def_11,iPr_def_13),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_921,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_349,c_52]) ).
tcf(c_922,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| ~ member(X0,iPr_def_12)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_595,c_52]) ).
tcf(c_962,plain,
! [X0: $i] :
( member(sK1(X0,iPr_def_13),sK3)
| member(sK1(X0,iPr_def_13),X0)
| ( X0 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_65,c_747]) ).
tcf(c_963,plain,
! [X0: $i] :
( member(sK1(X0,iPr_def_13),iPr_def_12)
| member(sK1(X0,iPr_def_13),X0)
| ( X0 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_65,c_634]) ).
tcf(c_1302,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),iPr_def_10)
| member(sK0(iPr_def_11,X0),sK2) ),
inference(superposition,[status(thm)],[c_56,c_726]) ).
tcf(c_1648,plain,
! [X0: $i,X1: $i] :
( member(sK1(iPr_def_11,iPr_def_13),X1)
| ~ subset(X0,X1)
| ~ member(sK1(iPr_def_11,iPr_def_13),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_5486,plain,
! [X0: $i] :
( subset(X0,union(sK2,sK4))
| ~ member(sK0(X0,iPr_def_12),sK2) ),
inference(superposition,[status(thm)],[c_351,c_760]) ).
tcf(c_5561,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ member(sK0(X0,iPr_def_12),sK2) ),
inference(light_normalisation,[status(thm)],[c_5486,c_351]) ).
tcf(c_5862,plain,
! [X0: $i] :
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_11)
| ~ subset(X0,iPr_def_11)
| ~ member(sK1(iPr_def_11,iPr_def_13),X0) ),
inference(instantiation,[status(thm)],[c_1648]) ).
tcf(c_5863,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_11)
| ~ subset(sK2,iPr_def_11)
| ~ member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(instantiation,[status(thm)],[c_5862]) ).
tcf(c_9411,plain,
! [X0: $i] :
( subset(X0,union(sK2,sK4))
| ~ member(sK0(X0,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_351,c_761]) ).
tcf(c_9416,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ member(sK0(X0,iPr_def_12),sK4) ),
inference(light_normalisation,[status(thm)],[c_9411,c_351]) ).
tcf(c_12929,plain,
( subset(iPr_def_11,iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1302,c_5561]) ).
tcf(c_13039,plain,
( subset(iPr_def_11,iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_12929,c_746]) ).
tcf(c_13158,plain,
subset(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_13039,c_9416]) ).
tcf(c_28521,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK3)
| member(sK1(iPr_def_11,iPr_def_13),sK2)
| ( iPr_def_11 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_962,c_726]) ).
tcf(c_28576,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK3)
| member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28521,c_353]) ).
tcf(c_28845,plain,
( member(sK1(iPr_def_11,iPr_def_13),sK3)
| member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28576,c_633]) ).
tcf(c_31285,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_12)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK2)
| ( iPr_def_11 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_963,c_726]) ).
tcf(c_31339,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_12)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31285,c_353]) ).
tcf(c_31734,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_12)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31339,c_604]) ).
tcf(c_31742,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_13)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| ~ member(sK1(iPr_def_11,iPr_def_13),sK3) ),
inference(superposition,[status(thm)],[c_31734,c_922]) ).
tcf(c_31743,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK4)
| member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(superposition,[status(thm)],[c_31734,c_725]) ).
tcf(c_33254,plain,
( member(sK1(iPr_def_11,iPr_def_13),sK4)
| member(sK1(iPr_def_11,iPr_def_13),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31743,c_746]) ).
tcf(c_33263,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| member(sK1(iPr_def_11,iPr_def_13),sK2)
| ~ member(sK1(iPr_def_11,iPr_def_13),sK3) ),
inference(superposition,[status(thm)],[c_33254,c_921]) ).
tcf(c_33278,plain,
( ~ member(sK1(iPr_def_11,iPr_def_13),sK3)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_31742,c_353,c_766,c_823,c_5863,c_31742,c_33263]) ).
tcf(c_33279,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| ~ member(sK1(iPr_def_11,iPr_def_13),sK3) ),
inference(renaming,[status(thm)],[c_33278]) ).
tcf(c_33290,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_11)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10)
| ( iPr_def_11 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_962,c_33279]) ).
tcf(c_33303,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_11)
| member(sK1(iPr_def_11,iPr_def_13),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33290,c_353]) ).
tcf(c_33581,plain,
member(sK1(iPr_def_11,iPr_def_13),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_33303,c_605]) ).
tcf(c_33582,plain,
! [X0: $i] :
( member(sK1(iPr_def_11,iPr_def_13),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_33581,c_57]) ).
tcf(c_33583,plain,
( ( iPr_def_11 = iPr_def_13 )
| ~ member(sK1(iPr_def_11,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_33581,c_64]) ).
tcf(c_33587,plain,
~ member(sK1(iPr_def_11,iPr_def_13),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_33583,c_353]) ).
tcf(c_33646,plain,
( member(sK1(iPr_def_11,iPr_def_13),iPr_def_13)
| ~ subset(iPr_def_11,iPr_def_12)
| ~ member(sK1(iPr_def_11,iPr_def_13),sK3) ),
inference(superposition,[status(thm)],[c_33582,c_922]) ).
tcf(c_33696,plain,
~ member(sK1(iPr_def_11,iPr_def_13),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_33646,c_33587,c_13158]) ).
tcf(c_33702,plain,
member(sK1(iPr_def_11,iPr_def_13),sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_28845,c_33696]) ).
tcf(c_33809,plain,
! [X0: $i] :
( member(sK1(iPr_def_11,iPr_def_13),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_33702,c_57]) ).
tcf(c_33869,plain,
~ subset(sK2,sK3),
inference(superposition,[status(thm)],[c_33809,c_33696]) ).
tcf(c_33870,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_33869,c_354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET144+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Thu Sep 24 10:01:29 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.49 Running first-order theorem proving
% 0.15/0.49 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 16.25/3.48 % SZS status Started for theBenchmark.p
% 16.25/3.48 % SZS status Theorem for theBenchmark.p
% 16.25/3.48
% 16.25/3.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.25/3.48
% 16.25/3.48 % ------ iProver source info
% 16.25/3.48
% 16.25/3.48 % git: date: 2026-07-19 20:42:38 +0200
% 16.25/3.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.25/3.48 % git: non_committed_changes: false
% 16.25/3.48
% 16.25/3.48 % ------ Parsing...
% 16.25/3.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.25/3.48
% 16.25/3.48 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 16.25/3.48
% 16.25/3.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.25/3.48
% 16.25/3.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.25/3.48 % ------ Proving...
% 16.25/3.48 % ------ Problem Properties
% 16.25/3.48
% 16.25/3.48 %
% 16.25/3.48 % clauses 21
% 16.25/3.48 % conjectures 1
% 16.25/3.48 % EPR 5
% 16.25/3.48 % Horn 18
% 16.25/3.48 % unary 9
% 16.25/3.48 % binary 6
% 16.25/3.48 % lits 39
% 16.25/3.48 % lits eq 10
% 16.25/3.48 % fd_pure 0
% 16.25/3.48 % fd_pseudo 0
% 16.25/3.48 % fd_cond 0
% 16.25/3.48 % fd_pseudo_cond 3
% 16.25/3.48 % AC symbols 0
% 16.25/3.48
% 16.25/3.48 % ------ Schedule dynamic 5 is on
% 16.25/3.48
% 16.25/3.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.25/3.48
% 16.25/3.48
% 16.25/3.48 % ------
% 16.25/3.48 % Current options:
% 16.25/3.48 % ------
% 16.25/3.48
% 16.25/3.48
% 16.25/3.48 %
% 16.25/3.48
% 16.25/3.48 % ------ Proving...
% 16.25/3.48 %
% 16.25/3.48
% 16.25/3.48 % SZS status Theorem for theBenchmark.p
% 16.25/3.48
% 16.25/3.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.25/3.48
% 16.25/3.48
%------------------------------------------------------------------------------