%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV539+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 : n015.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 1.02s 1.74s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 125 ( 48 unt; 11 def)
% Number of atoms : 382 ( 33 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 234 ( 99 ~; 105 |; 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 : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 149 ( 0 sgn 143 !; 6 ?; 57 :)
% 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(n(n(s(n(e)))),p(s(n(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3_327) ).
fof(f27,negated_conjecture,
~ atleast3p(u(n(n(s(n(e)))),p(s(n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ atleast3p(u(n(n(s(n(e)))),p(s(n(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(n(n(s(n(e)))),p(s(n(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(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),s(u(e,s(e)))))))),
inference(definition_unfolding,[],[f64,f65,f65,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(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),s(u(e,s(e)))))))),
inference(cnf_transformation,[],[f66]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ atleast2p(X1)
| ~ subq(X1,X0)
| ( u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),s(u(e,s(e))))))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_66]) ).
tcf(c_301,plain,
! [X0: $i] :
( subq(u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),s(u(e,s(e))))))),X0)
| ~ atleast2p(X0)
| ~ subq(X0,u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(s(u(u(e,s(e)),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 = u(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_571,definition,
iPr_def_15 = s(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_572,definition,
iPr_def_16 = u(iPr_def_14,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_573,definition,
iPr_def_17 = u(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_574,definition,
iPr_def_18 = s(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_575,definition,
iPr_def_19 = p(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_576,definition,
iPr_def_20 = u(iPr_def_16,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_577,plain,
! [X0: $i] :
( subq(iPr_def_20,X0)
| ~ atleast2p(X0)
| ~ subq(X0,iPr_def_20) ),
inference(demodulation,[status(thm)],[c_301,c_573,c_574,c_575,c_571,c_569,c_566,c_567,c_568,c_570,c_572,c_576]) ).
tcf(c_1052,plain,
mem(e,iPr_def_10),
inference(superposition,[status(thm)],[c_566,c_54]) ).
tcf(c_1053,plain,
mem(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_568,c_54]) ).
tcf(c_1056,plain,
mem(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_574,c_54]) ).
tcf(c_1061,plain,
! [X0: $i] : subq(e,X0),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_1074,plain,
! [X0: $i] :
( mem(X0,iPr_def_19)
| ~ subq(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_575,c_62]) ).
tcf(c_1082,plain,
mem(e,iPr_def_19),
inference(superposition,[status(thm)],[c_1061,c_1074]) ).
tcf(c_1102,plain,
! [X0: $i] :
( subq(X0,iPr_def_18)
| ~ mem(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_575,c_63]) ).
tcf(c_1113,plain,
! [X0: $i] : subq(X0,X0),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_1128,plain,
! [X0: $i] :
( ( X0 = iPr_def_17 )
| ~ mem(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_574,c_55]) ).
tcf(c_1151,plain,
! [X0: $i] :
( mem(X0,iPr_def_14)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_570,c_56]) ).
tcf(c_1152,plain,
! [X0: $i] :
( mem(X0,iPr_def_16)
| ~ mem(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_572,c_56]) ).
tcf(c_1154,plain,
! [X0: $i] :
( mem(X0,iPr_def_20)
| ~ mem(X0,iPr_def_16) ),
inference(superposition,[status(thm)],[c_576,c_56]) ).
tcf(c_1173,plain,
mem(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_1113,c_1074]) ).
tcf(c_1193,plain,
mem(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_1053,c_1151]) ).
tcf(c_1202,plain,
mem(iPr_def_11,iPr_def_16),
inference(superposition,[status(thm)],[c_1193,c_1152]) ).
tcf(c_1223,plain,
mem(iPr_def_11,iPr_def_20),
inference(superposition,[status(thm)],[c_1202,c_1154]) ).
tcf(c_1270,plain,
! [X0: $i] :
( mem(X0,iPr_def_11)
| ~ mem(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_567,c_57]) ).
tcf(c_1273,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_573,c_57]) ).
tcf(c_1274,plain,
! [X0: $i] :
( mem(X0,iPr_def_20)
| ~ mem(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_576,c_57]) ).
tcf(c_1341,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| mem(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_50,c_1270]) ).
tcf(c_1342,plain,
mem(e,iPr_def_11),
inference(superposition,[status(thm)],[c_1052,c_1270]) ).
tcf(c_1443,plain,
! [X0: $i] :
( mem(iPr_def_17,X0)
| ~ subq(iPr_def_18,X0) ),
inference(superposition,[status(thm)],[c_1056,c_51]) ).
tcf(c_1445,plain,
! [X0: $i] :
( mem(e,X0)
| ~ subq(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_1342,c_51]) ).
tcf(c_1447,plain,
! [X0: $i] :
( mem(iPr_def_18,X0)
| ~ subq(iPr_def_19,X0) ),
inference(superposition,[status(thm)],[c_1173,c_51]) ).
tcf(c_1450,plain,
! [X0: $i] :
( mem(iPr_def_11,X0)
| ~ subq(iPr_def_20,X0) ),
inference(superposition,[status(thm)],[c_1223,c_51]) ).
tcf(c_1566,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_1583,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| ~ mem(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1566,c_53]) ).
tcf(c_1631,plain,
mem(iPr_def_11,iPr_def_17),
inference(superposition,[status(thm)],[c_1053,c_1273]) ).
tcf(c_1644,plain,
! [X0: $i] :
( subq(iPr_def_19,X0)
| mem(sK0(iPr_def_19,X0),iPr_def_20) ),
inference(superposition,[status(thm)],[c_50,c_1274]) ).
tcf(c_1840,plain,
! [X0: $i] :
( atleast2p(iPr_def_19)
| mem(iPr_def_18,p(X0))
| ~ mem(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_64,c_1447]) ).
tcf(c_2304,plain,
! [X0: $i] :
( subq(iPr_def_11,X0)
| mem(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_1583]) ).
tcf(c_3412,plain,
subq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1341,c_49]) ).
tcf(c_3676,plain,
subq(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_1644,c_49]) ).
tcf(c_3683,plain,
( subq(iPr_def_20,iPr_def_19)
| ~ atleast2p(iPr_def_19) ),
inference(superposition,[status(thm)],[c_3676,c_577]) ).
tcf(c_3713,plain,
( mem(iPr_def_11,iPr_def_19)
| ~ atleast2p(iPr_def_19) ),
inference(superposition,[status(thm)],[c_3683,c_1450]) ).
tcf(c_3777,plain,
( subq(iPr_def_11,iPr_def_18)
| ~ atleast2p(iPr_def_19) ),
inference(superposition,[status(thm)],[c_3713,c_1102]) ).
tcf(c_3842,plain,
( mem(e,iPr_def_18)
| ~ atleast2p(iPr_def_19) ),
inference(superposition,[status(thm)],[c_3777,c_1445]) ).
tcf(c_3900,plain,
subq(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_2304,c_49]) ).
tcf(c_3929,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subq(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3900,c_52]) ).
tcf(c_3931,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3929,c_3412]) ).
tcf(c_3959,plain,
mem(iPr_def_10,iPr_def_17),
inference(demodulation,[status(thm)],[c_1631,c_3931]) ).
tcf(c_4103,plain,
( ( e = iPr_def_17 )
| ~ atleast2p(iPr_def_19) ),
inference(superposition,[status(thm)],[c_3842,c_1128]) ).
tcf(c_9229,plain,
! [X0: $i] :
( atleast2p(iPr_def_19)
| subq(iPr_def_18,X0)
| ~ mem(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_1840,c_63]) ).
tcf(c_9542,plain,
( atleast2p(iPr_def_19)
| subq(iPr_def_18,e) ),
inference(superposition,[status(thm)],[c_1082,c_9229]) ).
tcf(c_9695,plain,
( atleast2p(iPr_def_19)
| mem(iPr_def_17,e) ),
inference(superposition,[status(thm)],[c_9542,c_1443]) ).
tcf(c_9696,plain,
atleast2p(iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_9695,c_53]) ).
tcf(c_9701,plain,
e = iPr_def_17,
inference(backward_subsumption_resolution,[status(thm)],[c_4103,c_9696]) ).
tcf(c_9803,plain,
! [X0: $i] : ~ mem(X0,iPr_def_17),
inference(demodulation,[status(thm)],[c_53,c_9701]) ).
tcf(c_9804,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_3959,c_9803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV539+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n015.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 15:01:11 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.40 Running first-order theorem proving
% 0.07/0.40 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
% 0.07/0.41
% 0.07/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.41
% 0.07/0.41 % Detected problem language: tptp
% 0.07/0.42 % Proving...
% 1.02/1.74 % SZS status Started for theBenchmark.p
% 1.02/1.74 % SZS status Theorem for theBenchmark.p
% 1.02/1.74
% 1.02/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.02/1.74
% 1.02/1.74 % ------ iProver source info
% 1.02/1.74
% 1.02/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.02/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.02/1.74 % git: non_committed_changes: false
% 1.02/1.74
% 1.02/1.74 % ------ Parsing...
% 1.02/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.02/1.74
% 1.02/1.74 % ------ 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 %
% 1.02/1.74
% 1.02/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.02/1.74
% 1.02/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.02/1.74 % ------ Proving...
% 1.02/1.74 % ------ Problem Properties
% 1.02/1.74
% 1.02/1.74 %
% 1.02/1.74 % clauses 28
% 1.02/1.74 % conjectures 0
% 1.02/1.74 % EPR 4
% 1.02/1.74 % Horn 24
% 1.02/1.74 % unary 13
% 1.02/1.74 % binary 9
% 1.02/1.74 % lits 49
% 1.02/1.74 % lits eq 13
% 1.02/1.74 % fd_pure 0
% 1.02/1.74 % fd_pseudo 0
% 1.02/1.74 % fd_cond 0
% 1.02/1.74 % fd_pseudo_cond 2
% 1.02/1.74 % AC symbols 0
% 1.02/1.74
% 1.02/1.74 % ------ Schedule dynamic 5 is on
% 1.02/1.74
% 1.02/1.74 % ------ no conjectures: strip conj schedule
% 1.02/1.74
% 1.02/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.02/1.74
% 1.02/1.74
% 1.02/1.74 % ------
% 1.02/1.74 % Current options:
% 1.02/1.74 % ------
% 1.02/1.74
% 1.02/1.74
% 1.02/1.74 %
% 1.02/1.74
% 1.02/1.74 % ------ Proving...
% 1.02/1.74 %
% 1.02/1.74
% 1.02/1.74 % SZS status Theorem for theBenchmark.p
% 1.02/1.74
% 1.02/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.02/1.74
% 1.02/1.74
%------------------------------------------------------------------------------