%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV540+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 : n001.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 2.57s 1.08s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 140 ( 50 unt; 9 def)
% Number of atoms : 435 ( 49 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 251 ( 103 ~; 118 |; 18 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 151 !; 6 ?; 65 :)
% 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(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3_83) ).
fof(f27,negated_conjecture,
~ atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ atleast3p(u(s(n(e)),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(u(s(n(e)),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(s(u(e,s(e))),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,f65,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(s(u(e,s(e))),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(s(u(e,s(e))),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(s(u(e,s(e))),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(s(u(e,s(e))),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,definition,
iPr_def_18 = u(iPr_def_12,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_575,plain,
! [X0: $i] :
( subq(iPr_def_18,X0)
| ~ atleast2p(X0)
| ~ subq(X0,iPr_def_18) ),
inference(demodulation,[status(thm)],[c_301,c_571,c_572,c_569,c_570,c_573,c_566,c_567,c_568,c_574]) ).
tcf(c_1038,plain,
mem(e,iPr_def_10),
inference(superposition,[status(thm)],[c_566,c_54]) ).
tcf(c_1039,plain,
mem(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_568,c_54]) ).
tcf(c_1040,plain,
mem(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_569,c_54]) ).
tcf(c_1041,plain,
mem(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_572,c_54]) ).
tcf(c_1046,plain,
! [X0: $i] : subq(e,X0),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_1059,plain,
! [X0: $i] :
( mem(X0,iPr_def_14)
| ~ subq(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_570,c_62]) ).
tcf(c_1067,plain,
mem(e,iPr_def_14),
inference(superposition,[status(thm)],[c_1046,c_1059]) ).
tcf(c_1074,plain,
! [X0: $i] :
( subq(X0,iPr_def_13)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_570,c_63]) ).
tcf(c_1115,plain,
! [X0: $i] : subq(X0,X0),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( subq(s(X0),X1)
| ( sK0(s(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_1128,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ mem(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_569,c_55]) ).
tcf(c_1149,plain,
! [X0: $i] :
( mem(X0,iPr_def_15)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_571,c_56]) ).
tcf(c_1150,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_573,c_56]) ).
tcf(c_1169,plain,
! [X0: $i] :
( mem(X0,iPr_def_11)
| ~ mem(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_567,c_57]) ).
tcf(c_1171,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_16) ),
inference(superposition,[status(thm)],[c_573,c_57]) ).
tcf(c_1172,plain,
! [X0: $i] :
( mem(X0,iPr_def_18)
| ~ mem(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_574,c_57]) ).
tcf(c_1189,plain,
mem(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_1115,c_1059]) ).
tcf(c_1196,plain,
mem(iPr_def_11,iPr_def_15),
inference(superposition,[status(thm)],[c_1039,c_1149]) ).
tcf(c_1214,plain,
! [X0: $i] :
( subq(iPr_def_14,X0)
| mem(sK0(iPr_def_14,X0),iPr_def_17) ),
inference(superposition,[status(thm)],[c_50,c_1150]) ).
tcf(c_1241,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| mem(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_50,c_1169]) ).
tcf(c_1309,plain,
! [X0: $i] :
( mem(e,X0)
| ~ subq(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1038,c_51]) ).
tcf(c_1311,plain,
! [X0: $i] :
( mem(iPr_def_12,X0)
| ~ subq(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_1040,c_51]) ).
tcf(c_1316,plain,
! [X0: $i] :
( mem(iPr_def_13,X0)
| ~ subq(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_1189,c_51]) ).
tcf(c_1317,plain,
! [X0: $i] :
( mem(iPr_def_11,X0)
| ~ subq(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_1196,c_51]) ).
tcf(c_1366,plain,
( mem(e,e)
| ~ subq(iPr_def_10,e) ),
inference(instantiation,[status(thm)],[c_1309]) ).
tcf(c_1426,plain,
mem(iPr_def_15,iPr_def_17),
inference(superposition,[status(thm)],[c_1041,c_1171]) ).
tcf(c_1441,plain,
mem(iPr_def_15,iPr_def_18),
inference(superposition,[status(thm)],[c_1426,c_1172]) ).
tcf(c_1453,plain,
! [X0: $i] :
( mem(iPr_def_15,X0)
| ~ subq(iPr_def_18,X0) ),
inference(superposition,[status(thm)],[c_1441,c_51]) ).
tcf(c_1516,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| ( sK0(s(e),X0) = e ) ),
inference(superposition,[status(thm)],[c_566,c_1124]) ).
tcf(c_1531,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| ( sK0(iPr_def_10,X0) = e ) ),
inference(light_normalisation,[status(thm)],[c_1516,c_566]) ).
tcf(c_1539,plain,
( subq(iPr_def_10,e)
| ( sK0(iPr_def_10,e) = e ) ),
inference(instantiation,[status(thm)],[c_1531]) ).
tcf(c_1557,plain,
! [X0: $i] :
( ( X0 = e )
| ~ subq(X0,e) ),
inference(superposition,[status(thm)],[c_1046,c_52]) ).
tcf(c_1615,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_1628,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| ~ mem(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1615,c_53]) ).
tcf(c_1704,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_1316]) ).
tcf(c_2151,plain,
! [X0: $i] :
( subq(iPr_def_11,X0)
| mem(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_1628]) ).
tcf(c_2323,plain,
! [X0: $i] :
( ( s(X0) = e )
| ( sK0(s(X0),e) = X0 ) ),
inference(superposition,[status(thm)],[c_1124,c_1557]) ).
tcf(c_2324,plain,
( ( e = iPr_def_10 )
| ( sK0(iPr_def_10,e) = e ) ),
inference(superposition,[status(thm)],[c_1531,c_1557]) ).
tcf(c_2394,plain,
! [X0: $i] :
( subq(iPr_def_14,X0)
| mem(sK0(iPr_def_14,X0),iPr_def_18) ),
inference(superposition,[status(thm)],[c_1214,c_1172]) ).
tcf(c_2807,plain,
subq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1241,c_49]) ).
tcf(c_2967,plain,
sK0(iPr_def_10,e) = e,
inference(global_subsumption_just,[status(thm)],[c_2324,c_68,c_1366,c_1539]) ).
tcf(c_3185,plain,
subq(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_2151,c_49]) ).
tcf(c_3199,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subq(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3185,c_52]) ).
tcf(c_3201,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3199,c_2807]) ).
tcf(c_3219,plain,
! [X0: $i] :
( mem(iPr_def_10,X0)
| ~ subq(iPr_def_15,X0) ),
inference(demodulation,[status(thm)],[c_1317,c_3201]) ).
tcf(c_3227,plain,
mem(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1039,c_3201]) ).
tcf(c_3228,plain,
s(iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_568,c_3201]) ).
tcf(c_3282,plain,
( ( s(iPr_def_10) = e )
| ( sK0(iPr_def_12,e) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3228,c_2323]) ).
tcf(c_3299,plain,
( ( e = iPr_def_12 )
| ( sK0(iPr_def_12,e) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_3282,c_3228]) ).
tcf(c_3506,plain,
subq(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_2394,c_49]) ).
tcf(c_3513,plain,
( subq(iPr_def_18,iPr_def_14)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_3506,c_575]) ).
tcf(c_3526,plain,
( mem(iPr_def_15,iPr_def_14)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_3513,c_1453]) ).
tcf(c_3557,plain,
( subq(iPr_def_15,iPr_def_13)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_3526,c_1074]) ).
tcf(c_3592,plain,
( mem(iPr_def_10,iPr_def_13)
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_3557,c_3219]) ).
tcf(c_3662,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ atleast2p(iPr_def_14) ),
inference(superposition,[status(thm)],[c_3592,c_1128]) ).
tcf(c_7270,plain,
! [X0: $i] :
( atleast2p(iPr_def_14)
| subq(iPr_def_13,X0)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1704,c_63]) ).
tcf(c_7293,plain,
( atleast2p(iPr_def_14)
| subq(iPr_def_13,e) ),
inference(superposition,[status(thm)],[c_1067,c_7270]) ).
tcf(c_7366,plain,
( atleast2p(iPr_def_14)
| mem(iPr_def_12,e) ),
inference(superposition,[status(thm)],[c_7293,c_1311]) ).
tcf(c_7368,plain,
atleast2p(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_7366,c_53]) ).
tcf(c_7370,plain,
iPr_def_10 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_3662,c_7368]) ).
tcf(c_7462,plain,
( ( e = iPr_def_10 )
| ( sK0(iPr_def_10,e) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_3299,c_7370]) ).
tcf(c_7471,plain,
mem(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_3227,c_7370]) ).
tcf(c_7517,plain,
e = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_7462,c_2967]) ).
tcf(c_7551,plain,
! [X0: $i] : ~ mem(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_7517]) ).
tcf(c_7552,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_7471,c_7551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV540+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 15:03:23 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 2.57/1.08 % SZS status Started for theBenchmark.p
% 2.57/1.08 % SZS status Theorem for theBenchmark.p
% 2.57/1.08
% 2.57/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.57/1.08
% 2.57/1.08 % ------ iProver source info
% 2.57/1.08
% 2.57/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.57/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.57/1.08 % git: non_committed_changes: false
% 2.57/1.08
% 2.57/1.08 % ------ Parsing...
% 2.57/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.57/1.08
% 2.57/1.08 % ------ 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 %
% 2.57/1.08
% 2.57/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.57/1.08
% 2.57/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.57/1.08 % ------ Proving...
% 2.57/1.08 % ------ Problem Properties
% 2.57/1.08
% 2.57/1.08 %
% 2.57/1.08 % clauses 26
% 2.57/1.08 % conjectures 0
% 2.57/1.08 % EPR 4
% 2.57/1.08 % Horn 22
% 2.57/1.08 % unary 11
% 2.57/1.08 % binary 9
% 2.57/1.08 % lits 47
% 2.57/1.08 % lits eq 11
% 2.57/1.08 % fd_pure 0
% 2.57/1.08 % fd_pseudo 0
% 2.57/1.08 % fd_cond 0
% 2.57/1.08 % fd_pseudo_cond 2
% 2.57/1.08 % AC symbols 0
% 2.57/1.08
% 2.57/1.08 % ------ Schedule dynamic 5 is on
% 2.57/1.08
% 2.57/1.08 % ------ no conjectures: strip conj schedule
% 2.57/1.08
% 2.57/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.57/1.08
% 2.57/1.08
% 2.57/1.08 % ------
% 2.57/1.08 % Current options:
% 2.57/1.08 % ------
% 2.57/1.08
% 2.57/1.08
% 2.57/1.08 %
% 2.57/1.08
% 2.57/1.08 % ------ Proving...
% 2.57/1.08 %
% 2.57/1.08
% 2.57/1.08 % SZS status Theorem for theBenchmark.p
% 2.57/1.08
% 2.57/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.35/1.09
% 4.35/1.09
%------------------------------------------------------------------------------