%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV542+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 03:02:31 PM UTC 2026
% Result : Theorem 2.23s 1.21s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 136 ( 48 unt; 8 def)
% Number of atoms : 420 ( 49 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 248 ( 102 ~; 116 |; 18 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 148 !; 6 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',subq_def) ).
fof(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',setext) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X2)
| mem(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',p_ax) ).
fof(f11,axiom,
! [X0] :
( atleast2p(X0)
<=> ? [X1] :
( ~ subq(X0,p(X1))
& mem(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast2p_def) ).
fof(f12,axiom,
! [X0] :
( atleast3p(X0)
<=> ? [X1] :
( ~ subq(X0,X1)
& atleast2p(X1)
& subq(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast3p_def) ).
fof(f26,conjecture,
atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3_81) ).
fof(f27,negated_conjecture,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( ~ subq(X0,X1)
& atleast2p(X1)
& subq(X1,X0) )
=> atleast3p(X0) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( ~ subq(X0,p(X1))
& mem(X1,X0) )
=> atleast2p(X0) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f31,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( ~ mem(X2,X0)
| mem(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( subq(X0,p(X1))
| ~ mem(X1,X0) )
| atleast2p(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( subq(X0,X1)
| ~ atleast2p(X1)
| ~ subq(X1,X0) )
| atleast3p(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X2] :
( ~ mem(X2,X0)
| mem(X2,X1) ) )
& ( ? [X2] :
( mem(X2,X0)
& ~ mem(X2,X1) )
| subq(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X3] :
( ~ mem(X3,X0)
| mem(X3,X1) ) )
& ( ? [X2] :
( mem(X2,X0)
& ~ mem(X2,X1) )
| subq(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X3] :
( ~ mem(X3,X0)
| mem(X3,X1) ) )
& ( ( mem(sK0(X0,X1),X0)
& ~ mem(sK0(X0,X1),X1) )
| subq(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ mem(X0,s(X1))
| X0 = X1 )
& ( X0 != X1
| mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) )
& ( ( ~ mem(X0,X2)
& ~ mem(X0,X1) )
| mem(X0,u(X1,X2)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) )
& ( ( ~ mem(X0,X2)
& ~ mem(X0,X1) )
| mem(X0,u(X1,X2)) ) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ mem(X0,p(X1))
| subq(X0,X1) )
& ( ~ subq(X0,X1)
| mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subq(X0,X1)
| ~ mem(X3,X0)
| mem(X3,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f47,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f51,plain,
! [X0,X1] :
( X0 != X1
| mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f58,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f60,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| mem(X0,p(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f62,plain,
! [X0,X1] :
( subq(X0,p(X1))
| ~ mem(X1,X0)
| atleast2p(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f63,plain,
! [X0,X1] :
( subq(X0,X1)
| ~ atleast2p(X1)
| ~ subq(X1,X0)
| atleast3p(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f64,plain,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f59,f58]) ).
fof(f66,plain,
~ atleast3p(u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),
inference(definition_unfolding,[],[f64,f58,f65,f65,f65]) ).
fof(f67,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f51]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_53,plain,
! [X0: $i] : ~ mem(X0,e),
inference(cnf_transformation,[],[f49]) ).
tcf(c_54,plain,
! [X0: $i] : mem(X0,s(X0)),
inference(cnf_transformation,[],[f67]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X2,X1))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| mem(X0,X1)
| ~ mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(X0,p(X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( atleast2p(X1)
| subq(X1,p(X0))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( atleast3p(X1)
| subq(X1,X0)
| ~ atleast2p(X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_66,negated_conjecture,
~ atleast3p(u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),
inference(cnf_transformation,[],[f66]) ).
tcf(c_68,plain,
~ mem(e,e),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ atleast2p(X1)
| ~ subq(X1,X0)
| ( u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_66]) ).
tcf(c_301,plain,
! [X0: $i] :
( subq(u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),X0)
| ~ atleast2p(X0)
| ~ subq(X0,u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))) ),
inference(unflattening,[status(thm)],[c_300]) ).
tcf(c_566,definition,
iPr_def_10 = s(e),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_567,definition,
iPr_def_11 = u(e,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_568,definition,
iPr_def_12 = s(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_569,definition,
iPr_def_13 = s(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_570,definition,
iPr_def_14 = p(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_571,definition,
iPr_def_15 = u(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_572,definition,
iPr_def_16 = s(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_573,definition,
iPr_def_17 = u(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_574,plain,
! [X0: $i] :
( subq(iPr_def_17,X0)
| ~ atleast2p(X0)
| ~ subq(X0,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_301,c_571,c_572,c_566,c_567,c_568,c_569,c_570,c_573]) ).
tcf(c_1031,plain,
mem(e,iPr_def_10),
inference(superposition,[status(thm)],[c_566,c_54]) ).
tcf(c_1032,plain,
mem(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_568,c_54]) ).
tcf(c_1033,plain,
mem(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_569,c_54]) ).
tcf(c_1034,plain,
mem(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_572,c_54]) ).
tcf(c_1039,plain,
! [X0: $i] : subq(e,X0),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_1052,plain,
! [X0: $i] :
( mem(X0,iPr_def_14)
| ~ subq(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_570,c_62]) ).
tcf(c_1060,plain,
mem(e,iPr_def_14),
inference(superposition,[status(thm)],[c_1039,c_1052]) ).
tcf(c_1067,plain,
! [X0: $i] :
( subq(X0,iPr_def_13)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_570,c_63]) ).
tcf(c_1108,plain,
! [X0: $i] : subq(X0,X0),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_1117,plain,
! [X0: $i,X1: $i] :
( subq(s(X0),X1)
| ( sK0(s(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_1121,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ mem(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_569,c_55]) ).
tcf(c_1142,plain,
! [X0: $i] :
( mem(X0,iPr_def_15)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_571,c_56]) ).
tcf(c_1143,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_573,c_56]) ).
tcf(c_1158,plain,
! [X0: $i] :
( mem(X0,iPr_def_11)
| ~ mem(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_567,c_57]) ).
tcf(c_1160,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_16) ),
inference(superposition,[status(thm)],[c_573,c_57]) ).
tcf(c_1174,plain,
mem(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_1108,c_1052]) ).
tcf(c_1181,plain,
mem(iPr_def_11,iPr_def_15),
inference(superposition,[status(thm)],[c_1032,c_1142]) ).
tcf(c_1195,plain,
! [X0: $i] :
( subq(iPr_def_14,X0)
| mem(sK0(iPr_def_14,X0),iPr_def_17) ),
inference(superposition,[status(thm)],[c_50,c_1143]) ).
tcf(c_1213,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| mem(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_50,c_1158]) ).
tcf(c_1290,plain,
! [X0: $i] :
( mem(e,X0)
| ~ subq(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1031,c_51]) ).
tcf(c_1292,plain,
! [X0: $i] :
( mem(iPr_def_12,X0)
| ~ subq(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_1033,c_51]) ).
tcf(c_1297,plain,
! [X0: $i] :
( mem(iPr_def_13,X0)
| ~ subq(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_1174,c_51]) ).
tcf(c_1298,plain,
! [X0: $i] :
( mem(iPr_def_11,X0)
| ~ subq(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_1181,c_51]) ).
tcf(c_1347,plain,
( mem(e,e)
| ~ subq(iPr_def_10,e) ),
inference(instantiation,[status(thm)],[c_1290]) ).
tcf(c_1381,plain,
mem(iPr_def_15,iPr_def_17),
inference(superposition,[status(thm)],[c_1034,c_1160]) ).
tcf(c_1385,plain,
! [X0: $i] :
( mem(iPr_def_15,X0)
| ~ subq(iPr_def_17,X0) ),
inference(superposition,[status(thm)],[c_1381,c_51]) ).
tcf(c_1509,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| ( sK0(s(e),X0) = e ) ),
inference(superposition,[status(thm)],[c_566,c_1117]) ).
tcf(c_1524,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| ( sK0(iPr_def_10,X0) = e ) ),
inference(light_normalisation,[status(thm)],[c_1509,c_566]) ).
tcf(c_1532,plain,
( subq(iPr_def_10,e)
| ( sK0(iPr_def_10,e) = e ) ),
inference(instantiation,[status(thm)],[c_1524]) ).
tcf(c_1560,plain,
! [X0: $i] :
( ( X0 = e )
| ~ subq(X0,e) ),
inference(superposition,[status(thm)],[c_1039,c_52]) ).
tcf(c_1602,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| mem(X0,e)
| ~ mem(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_567,c_58]) ).
tcf(c_1611,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| ~ mem(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1602,c_53]) ).
tcf(c_1657,plain,
! [X0: $i] :
( atleast2p(iPr_def_14)
| mem(iPr_def_13,p(X0))
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_64,c_1297]) ).
tcf(c_2062,plain,
! [X0: $i] :
( subq(iPr_def_11,X0)
| mem(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_1611]) ).
tcf(c_2129,plain,
subq(iPr_def_14,iPr_def_17),
inference(superposition,[status(thm)],[c_1195,c_49]) ).
tcf(c_2336,plain,
! [X0: $i] :
( ( s(X0) = e )
| ( sK0(s(X0),e) = X0 ) ),
inference(superposition,[status(thm)],[c_1117,c_1560]) ).
tcf(c_2337,plain,
( ( e = iPr_def_10 )
| ( sK0(iPr_def_10,e) = e ) ),
inference(superposition,[status(thm)],[c_1524,c_1560]) ).
tcf(c_2347,plain,
( subq(iPr_def_17,iPr_def_14)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2129,c_574]) ).
tcf(c_2372,plain,
subq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1213,c_49]) ).
tcf(c_2416,plain,
( mem(iPr_def_15,iPr_def_14)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2347,c_1385]) ).
tcf(c_2430,plain,
( subq(iPr_def_15,iPr_def_13)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2416,c_1067]) ).
tcf(c_2444,plain,
( mem(iPr_def_11,iPr_def_13)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2430,c_1298]) ).
tcf(c_2608,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2444,c_1121]) ).
tcf(c_2830,plain,
sK0(iPr_def_10,e) = e,
inference(global_subsumption_just,[status(thm)],[c_2337,c_68,c_1347,c_1532]) ).
tcf(c_2840,plain,
subq(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_2062,c_49]) ).
tcf(c_2857,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subq(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2840,c_52]) ).
tcf(c_2859,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_2857,c_2372]) ).
tcf(c_2863,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ atleast2p(iPr_def_14) ),
inference(demodulation,[status(thm)],[c_2608,c_2859]) ).
tcf(c_2877,plain,
mem(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1032,c_2859]) ).
tcf(c_2878,plain,
s(iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_568,c_2859]) ).
tcf(c_2905,plain,
( ( s(iPr_def_10) = e )
| ( sK0(iPr_def_12,e) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2878,c_2336]) ).
tcf(c_2922,plain,
( ( e = iPr_def_12 )
| ( sK0(iPr_def_12,e) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_2905,c_2878]) ).
tcf(c_5165,plain,
! [X0: $i] :
( atleast2p(iPr_def_14)
| subq(iPr_def_13,X0)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1657,c_63]) ).
tcf(c_5220,plain,
( atleast2p(iPr_def_14)
| subq(iPr_def_13,e) ),
inference(superposition,[status(thm)],[c_1060,c_5165]) ).
tcf(c_5311,plain,
( atleast2p(iPr_def_14)
| mem(iPr_def_12,e) ),
inference(superposition,[status(thm)],[c_5220,c_1292]) ).
tcf(c_5313,plain,
atleast2p(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_5311,c_53]) ).
tcf(c_5317,plain,
iPr_def_10 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_2863,c_5313]) ).
tcf(c_5345,plain,
( ( e = iPr_def_10 )
| ( sK0(iPr_def_10,e) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_2922,c_5317]) ).
tcf(c_5361,plain,
mem(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_2877,c_5317]) ).
tcf(c_5424,plain,
e = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_5345,c_2830]) ).
tcf(c_5467,plain,
! [X0: $i] : ~ mem(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_5424]) ).
tcf(c_5468,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_5361,c_5467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV542+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 15:00:09 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 2.23/1.21 % SZS status Started for theBenchmark.p
% 2.23/1.21 % SZS status Theorem for theBenchmark.p
% 2.23/1.21
% 2.23/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.23/1.21
% 2.23/1.21 % ------ iProver source info
% 2.23/1.21
% 2.23/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.23/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.23/1.21 % git: non_committed_changes: false
% 2.23/1.21
% 2.23/1.21 % ------ Parsing...
% 2.23/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.23/1.21
% 2.23/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.23/1.21
% 2.23/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.23/1.21
% 2.23/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.23/1.21 % ------ Proving...
% 2.23/1.21 % ------ Problem Properties
% 2.23/1.21
% 2.23/1.21 %
% 2.23/1.21 % clauses 25
% 2.23/1.21 % conjectures 0
% 2.23/1.21 % EPR 4
% 2.23/1.21 % Horn 21
% 2.23/1.21 % unary 10
% 2.23/1.21 % binary 9
% 2.23/1.21 % lits 46
% 2.23/1.21 % lits eq 10
% 2.23/1.21 % fd_pure 0
% 2.23/1.21 % fd_pseudo 0
% 2.23/1.21 % fd_cond 0
% 2.23/1.21 % fd_pseudo_cond 2
% 2.23/1.21 % AC symbols 0
% 2.23/1.21
% 2.23/1.21 % ------ Schedule dynamic 5 is on
% 2.23/1.21
% 2.23/1.21 % ------ no conjectures: strip conj schedule
% 2.23/1.21
% 2.23/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.23/1.21
% 2.23/1.21
% 2.23/1.21 % ------
% 2.23/1.21 % Current options:
% 2.23/1.21 % ------
% 2.23/1.21
% 2.23/1.21
% 2.23/1.21 %
% 2.23/1.21
% 2.23/1.21 % ------ Proving...
% 2.23/1.21 %
% 2.23/1.21
% 2.23/1.21 % SZS status Theorem for theBenchmark.p
% 2.23/1.21
% 2.23/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.23/1.22
% 2.23/1.22
%------------------------------------------------------------------------------