%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 03:32:49 PM UTC 2026
% Result : Theorem 5.98s 2.28s
% Output : CNFRefutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 21
% Syntax : Number of formulae : 134 ( 67 unt; 3 def)
% Number of atoms : 604 ( 114 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 364 ( 130 ~; 211 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 178 ( 0 sgn 176 !; 2 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : proj1S(s(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f5,axiom,
! [X0] : z != s(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f6,axiom,
! [X0] : leqNat(z,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f7,axiom,
! [X0] : ~ leqNat(s(X0),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f8,axiom,
! [X0,X1] :
( leqNat(s(X0),s(X1))
<=> leqNat(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f10,axiom,
! [X0] : sorted(cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f11,axiom,
! [X0,X1,X2] :
( sorted(cons(X0,cons(X1,X2)))
<=> ( sorted(cons(X1,X2))
& leqNat(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f12,axiom,
lengthNat(nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f13,axiom,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f14,axiom,
! [X0] : ~ elemNat(X0,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(f15,axiom,
! [X0,X1,X2] :
( elemNat(X0,cons(X1,X2))
<=> ( elemNat(X0,X2)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,axiom,
unique(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f17,axiom,
! [X0,X1] :
( unique(cons(X0,X1))
<=> ( unique(X1)
& ~ elemNat(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(f18,axiom,
! [X0] : append(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(f19,axiom,
! [X0,X1,X2] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f20,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f21,axiom,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(f22,conjecture,
? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_022) ).
fof(f23,negated_conjecture,
~ ? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ sorted(rev(X0))
| ~ unique(X0)
| leqNat(lengthNat(X0),s(s(s(z)))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ sorted(rev(X0))
| ~ unique(X0)
| leqNat(lengthNat(X0),s(s(s(z)))) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ leqNat(s(X0),s(X1))
| leqNat(X0,X1) )
& ( ~ leqNat(X0,X1)
| leqNat(s(X0),s(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ sorted(cons(X0,cons(X1,X2)))
| ( sorted(cons(X1,X2))
& leqNat(X0,X1) ) )
& ( ~ sorted(cons(X1,X2))
| ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,X2))) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ sorted(cons(X0,cons(X1,X2)))
| ( sorted(cons(X1,X2))
& leqNat(X0,X1) ) )
& ( ~ sorted(cons(X1,X2))
| ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,X2))) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ~ elemNat(X0,cons(X1,X2))
| elemNat(X0,X2)
| X0 = X1 )
& ( ( ~ elemNat(X0,X2)
& X0 != X1 )
| elemNat(X0,cons(X1,X2)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ~ elemNat(X0,cons(X1,X2))
| elemNat(X0,X2)
| X0 = X1 )
& ( ( ~ elemNat(X0,X2)
& X0 != X1 )
| elemNat(X0,cons(X1,X2)) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( ~ unique(cons(X0,X1))
| ( unique(X1)
& ~ elemNat(X0,X1) ) )
& ( ~ unique(X1)
| elemNat(X0,X1)
| unique(cons(X0,X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ unique(cons(X0,X1))
| ( unique(X1)
& ~ elemNat(X0,X1) ) )
& ( ~ unique(X1)
| elemNat(X0,X1)
| unique(cons(X0,X1)) ) ),
inference(flattening,[],[f31]) ).
fof(f36,plain,
! [X0] : proj1S(s(X0)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0] : leqNat(z,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0,X1] :
( ~ leqNat(s(X0),s(X1))
| leqNat(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leqNat(X0,X1)
| leqNat(s(X0),s(X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0] : sorted(cons(X0,nil)),
inference(cnf_transformation,[],[f10]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ sorted(cons(X1,X2))
| ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
z = lengthNat(nil),
inference(cnf_transformation,[],[f12]) ).
fof(f48,plain,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f49,plain,
! [X0] : ~ elemNat(X0,nil),
inference(cnf_transformation,[],[f14]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ elemNat(X0,cons(X1,X2))
| elemNat(X0,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
unique(nil),
inference(cnf_transformation,[],[f16]) ).
fof(f56,plain,
! [X0,X1] :
( ~ unique(X1)
| elemNat(X0,X1)
| unique(cons(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X0] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f18]) ).
fof(f58,plain,
! [X2,X0,X1] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f59,plain,
nil = rev(nil),
inference(cnf_transformation,[],[f20]) ).
fof(f60,plain,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
inference(cnf_transformation,[],[f21]) ).
fof(f61,plain,
! [X0] :
( ~ sorted(rev(X0))
| ~ unique(X0)
| leqNat(lengthNat(X0),s(s(s(z)))) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i] : proj1S(s(X0)) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0: $i] : s(X0) != z,
inference(cnf_transformation,[],[f37]) ).
tcf(c_54,plain,
! [X0: $i] : leqNat(z,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[],[f39]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( leqNat(s(X0),s(X1))
| ~ leqNat(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( leqNat(X0,X1)
| ~ leqNat(s(X0),s(X1)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,plain,
! [X0: $i] : sorted(cons(X0,nil)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( sorted(cons(X2,cons(X0,X1)))
| ~ leqNat(X2,X0)
| ~ sorted(cons(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_63,plain,
lengthNat(nil) = z,
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_65,plain,
! [X0: $i] : ~ elemNat(X0,nil),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( elemNat(X0,X2)
| ( X0 = X1 )
| ~ elemNat(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_69,plain,
unique(nil),
inference(cnf_transformation,[],[f53]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( elemNat(X1,X0)
| unique(cons(X1,X0))
| ~ unique(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_73,plain,
! [X0: $i] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f57]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,append(X1,X2)) = append(cons(X0,X1),X2),
inference(cnf_transformation,[],[f58]) ).
tcf(c_75,plain,
rev(nil) = nil,
inference(cnf_transformation,[],[f59]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : append(rev(X0),cons(X1,nil)) = rev(cons(X1,X0)),
inference(cnf_transformation,[],[f60]) ).
tcf(c_77,negated_conjecture,
! [X0: $i] :
( leqNat(lengthNat(X0),s(s(s(z))))
| ~ unique(X0)
| ~ sorted(rev(X0)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_317,definition,
iPr_def_10 = s(z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_318,definition,
iPr_def_11 = s(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_319,definition,
iPr_def_12 = s(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_320,negated_conjecture,
! [X0: $i] :
( leqNat(lengthNat(X0),iPr_def_12)
| ~ unique(X0)
| ~ sorted(rev(X0)) ),
inference(demodulation,[status(thm)],[c_77,c_317,c_318,c_319]) ).
tcf(c_913,plain,
proj1S(iPr_def_10) = z,
inference(superposition,[status(thm)],[c_317,c_52]) ).
tcf(c_914,plain,
~ leqNat(iPr_def_10,z),
inference(superposition,[status(thm)],[c_317,c_55]) ).
tcf(c_915,plain,
proj1S(iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_318,c_52]) ).
tcf(c_919,plain,
z != iPr_def_10,
inference(superposition,[status(thm)],[c_317,c_53]) ).
tcf(c_920,plain,
z != iPr_def_11,
inference(superposition,[status(thm)],[c_318,c_53]) ).
tcf(c_921,plain,
z != iPr_def_12,
inference(superposition,[status(thm)],[c_319,c_53]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i] :
( leqNat(s(lengthNat(X1)),iPr_def_12)
| ~ unique(cons(X0,X1))
| ~ sorted(rev(cons(X0,X1))) ),
inference(superposition,[status(thm)],[c_64,c_320]) ).
tcf(c_935,plain,
! [X0: $i] :
( leqNat(iPr_def_10,s(X0))
| ~ leqNat(z,X0) ),
inference(superposition,[status(thm)],[c_317,c_56]) ).
tcf(c_936,plain,
! [X0: $i] :
( leqNat(iPr_def_11,s(X0))
| ~ leqNat(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_318,c_56]) ).
tcf(c_951,plain,
! [X0: $i] : leqNat(iPr_def_10,s(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_935,c_54]) ).
tcf(c_958,plain,
leqNat(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_317,c_951]) ).
tcf(c_959,plain,
leqNat(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_318,c_951]) ).
tcf(c_972,plain,
( leqNat(iPr_def_11,iPr_def_11)
| ~ leqNat(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_318,c_936]) ).
tcf(c_973,plain,
( leqNat(iPr_def_11,iPr_def_12)
| ~ leqNat(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_319,c_936]) ).
tcf(c_974,plain,
leqNat(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_973,c_959]) ).
tcf(c_975,plain,
leqNat(iPr_def_11,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_972,c_958]) ).
tcf(c_1003,plain,
! [X0: $i] :
( leqNat(iPr_def_10,X0)
| ~ leqNat(iPr_def_11,s(X0)) ),
inference(superposition,[status(thm)],[c_318,c_57]) ).
tcf(c_1004,plain,
! [X0: $i] :
( leqNat(iPr_def_11,X0)
| ~ leqNat(iPr_def_12,s(X0)) ),
inference(superposition,[status(thm)],[c_319,c_57]) ).
tcf(c_1007,plain,
! [X0: $i] :
( leqNat(X0,iPr_def_11)
| ~ leqNat(s(X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_319,c_57]) ).
tcf(c_1054,plain,
( leqNat(iPr_def_10,z)
| ~ leqNat(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_317,c_1003]) ).
tcf(c_1057,plain,
~ leqNat(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1054,c_914]) ).
tcf(c_1064,plain,
( leqNat(iPr_def_11,iPr_def_10)
| ~ leqNat(iPr_def_12,iPr_def_11) ),
inference(superposition,[status(thm)],[c_318,c_1004]) ).
tcf(c_1066,plain,
~ leqNat(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1064,c_1057]) ).
tcf(c_1104,plain,
! [X0: $i] : append(nil,cons(X0,nil)) = rev(cons(X0,nil)),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_1122,plain,
! [X0: $i] : rev(cons(X0,nil)) = cons(X0,nil),
inference(demodulation,[status(thm)],[c_1104,c_73]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] : append(cons(X0,nil),cons(X1,nil)) = rev(cons(X1,cons(X0,nil))),
inference(superposition,[status(thm)],[c_1122,c_76]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i] : rev(cons(X0,cons(X1,nil))) = cons(X1,cons(X0,nil)),
inference(demodulation,[status(thm)],[c_1124,c_73,c_74]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i,X2: $i] : append(cons(X0,cons(X1,nil)),cons(X2,nil)) = rev(cons(X2,cons(X1,cons(X0,nil)))),
inference(superposition,[status(thm)],[c_1127,c_76]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i] : rev(cons(X0,cons(X1,cons(X2,nil)))) = cons(X2,cons(X1,cons(X0,nil))),
inference(demodulation,[status(thm)],[c_1129,c_73,c_74]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : append(cons(X0,cons(X1,cons(X2,nil))),cons(X3,nil)) = rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))),
inference(superposition,[status(thm)],[c_1135,c_76]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rev(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) = cons(X3,cons(X2,cons(X1,cons(X0,nil)))),
inference(demodulation,[status(thm)],[c_1137,c_73,c_74]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(lengthNat(cons(X2,cons(X1,cons(X0,nil))))),iPr_def_12)
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) ),
inference(superposition,[status(thm)],[c_1144,c_922]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) ),
inference(demodulation,[status(thm)],[c_1145,c_63,c_64,c_317,c_318,c_319]) ).
tcf(c_1163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| ~ leqNat(X3,X2)
| ~ sorted(cons(X2,cons(X1,cons(X0,nil))))
| ~ unique(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) ),
inference(superposition,[status(thm)],[c_60,c_1153]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X2,cons(X1,cons(X0,cons(X3,nil))))
| ~ leqNat(X3,X0)
| ~ unique(cons(X1,cons(X0,cons(X3,nil))))
| ~ sorted(cons(X0,cons(X1,cons(X2,nil)))) ),
inference(superposition,[status(thm)],[c_70,c_1163]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X2,cons(X0,cons(X3,nil)))
| ( X1 = X2 )
| ~ leqNat(X3,X0)
| ~ unique(cons(X1,cons(X0,cons(X3,nil))))
| ~ sorted(cons(X0,cons(X1,cons(X2,nil)))) ),
inference(superposition,[status(thm)],[c_1177,c_68]) ).
tcf(c_1213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X3,cons(X1,cons(X2,nil)))
| ( X0 = X3 )
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X0)
| ~ sorted(cons(X0,cons(X3,nil)))
| ~ unique(cons(X0,cons(X1,cons(X2,nil)))) ),
inference(superposition,[status(thm)],[c_60,c_1194]) ).
tcf(c_1235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X1,cons(X2,cons(X3,nil)))
| elemNat(X0,cons(X2,cons(X3,nil)))
| ( X0 = X1 )
| ~ leqNat(X3,X2)
| ~ leqNat(X2,X0)
| ~ unique(cons(X2,cons(X3,nil)))
| ~ sorted(cons(X0,cons(X1,nil))) ),
inference(superposition,[status(thm)],[c_70,c_1213]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X3,cons(X0,cons(X1,nil)))
| elemNat(X2,cons(X0,cons(X1,nil)))
| ( X2 = X3 )
| ~ leqNat(X3,X2)
| ~ leqNat(X1,X0)
| ~ leqNat(X0,X3)
| ~ sorted(cons(X2,nil))
| ~ unique(cons(X0,cons(X1,nil))) ),
inference(superposition,[status(thm)],[c_60,c_1235]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(X3,cons(X0,cons(X1,nil)))
| elemNat(X2,cons(X0,cons(X1,nil)))
| ( X2 = X3 )
| ~ leqNat(X2,X3)
| ~ leqNat(X1,X0)
| ~ leqNat(X0,X2)
| ~ unique(cons(X0,cons(X1,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1260,c_59]) ).
tcf(c_1299,plain,
! [X0: $i,X1: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X0,cons(X1,nil)))
| elemNat(iPr_def_11,cons(X0,cons(X1,nil)))
| ( iPr_def_11 = iPr_def_12 )
| ~ leqNat(X0,iPr_def_11)
| ~ leqNat(X1,X0)
| ~ unique(cons(X0,cons(X1,nil))) ),
inference(superposition,[status(thm)],[c_974,c_1261]) ).
tcf(c_1559,plain,
! [X0: $i,X1: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X1,nil))
| elemNat(iPr_def_11,cons(X0,cons(X1,nil)))
| ( iPr_def_11 = iPr_def_12 )
| ( X0 = iPr_def_12 )
| ~ leqNat(X0,iPr_def_11)
| ~ leqNat(X1,X0)
| ~ unique(cons(X0,cons(X1,nil))) ),
inference(superposition,[status(thm)],[c_1299,c_68]) ).
tcf(c_2462,plain,
! [X0: $i,X1: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X1,nil))
| elemNat(iPr_def_11,cons(X1,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( X0 = iPr_def_12 )
| ( X0 = iPr_def_11 )
| ~ leqNat(X0,iPr_def_11)
| ~ leqNat(X1,X0)
| ~ unique(cons(X0,cons(X1,nil))) ),
inference(superposition,[status(thm)],[c_1559,c_68]) ).
tcf(c_3144,plain,
! [X0: $i,X1: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X0,nil))
| elemNat(iPr_def_11,cons(X0,nil))
| elemNat(X1,cons(X0,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( X1 = iPr_def_12 )
| ( X1 = iPr_def_11 )
| ~ leqNat(X1,iPr_def_11)
| ~ leqNat(X0,X1)
| ~ unique(cons(X0,nil)) ),
inference(superposition,[status(thm)],[c_70,c_2462]) ).
tcf(c_9339,plain,
! [X0: $i,X1: $i] :
( elemNat(X1,nil)
| leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X0,nil))
| elemNat(iPr_def_11,cons(X0,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( X1 = iPr_def_12 )
| ( X1 = iPr_def_11 )
| ( X0 = X1 )
| ~ leqNat(X1,iPr_def_11)
| ~ leqNat(X0,X1)
| ~ unique(cons(X0,nil)) ),
inference(superposition,[status(thm)],[c_3144,c_68]) ).
tcf(c_9342,plain,
! [X0: $i,X1: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(X0,nil))
| elemNat(iPr_def_11,cons(X0,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( X1 = iPr_def_12 )
| ( X1 = iPr_def_11 )
| ( X0 = X1 )
| ~ leqNat(X1,iPr_def_11)
| ~ leqNat(X0,X1)
| ~ unique(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9339,c_65]) ).
tcf(c_9384,plain,
! [X0: $i] :
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(z,nil))
| elemNat(iPr_def_11,cons(z,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( X0 = iPr_def_12 )
| ( X0 = iPr_def_11 )
| ( X0 = z )
| ~ leqNat(X0,iPr_def_11)
| ~ unique(cons(z,nil)) ),
inference(superposition,[status(thm)],[c_54,c_9342]) ).
tcf(c_9494,plain,
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(z,nil))
| elemNat(iPr_def_11,cons(z,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ( z = iPr_def_10 )
| ~ unique(cons(z,nil)) ),
inference(superposition,[status(thm)],[c_959,c_9384]) ).
tcf(c_9496,plain,
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_12,cons(z,nil))
| elemNat(iPr_def_11,cons(z,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ~ unique(cons(z,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9494,c_919]) ).
tcf(c_9584,plain,
( elemNat(iPr_def_12,nil)
| leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_11,cons(z,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ( z = iPr_def_12 )
| ~ unique(cons(z,nil)) ),
inference(superposition,[status(thm)],[c_9496,c_68]) ).
tcf(c_9585,plain,
( leqNat(s(iPr_def_12),iPr_def_12)
| elemNat(iPr_def_11,cons(z,nil))
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ~ unique(cons(z,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9584,c_65,c_921]) ).
tcf(c_9610,plain,
( elemNat(iPr_def_11,nil)
| leqNat(s(iPr_def_12),iPr_def_12)
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ( z = iPr_def_11 )
| ~ unique(cons(z,nil)) ),
inference(superposition,[status(thm)],[c_9585,c_68]) ).
tcf(c_9611,plain,
( leqNat(s(iPr_def_12),iPr_def_12)
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ~ unique(cons(z,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9610,c_65,c_920]) ).
tcf(c_9632,plain,
( elemNat(z,nil)
| leqNat(s(iPr_def_12),iPr_def_12)
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ~ unique(nil) ),
inference(superposition,[status(thm)],[c_70,c_9611]) ).
tcf(c_9633,plain,
( leqNat(s(iPr_def_12),iPr_def_12)
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9632,c_65,c_69]) ).
tcf(c_9664,plain,
( leqNat(iPr_def_12,iPr_def_11)
| ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_9633,c_1007]) ).
tcf(c_9666,plain,
( ( iPr_def_11 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9664,c_1066]) ).
tcf(c_10149,plain,
( ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 )
| ~ leqNat(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_9666,c_1066]) ).
tcf(c_10159,plain,
( ( iPr_def_10 = iPr_def_12 )
| ( iPr_def_10 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10149,c_975]) ).
tcf(c_10183,plain,
( leqNat(iPr_def_11,iPr_def_10)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_10159,c_974]) ).
tcf(c_10188,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_10183,c_1057]) ).
tcf(c_10219,plain,
proj1S(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_915,c_10188]) ).
tcf(c_10223,plain,
z = iPr_def_10,
inference(demodulation,[status(thm)],[c_913,c_10219]) ).
tcf(c_10224,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10223,c_919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 23:38:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 5.98/2.28 % SZS status Started for theBenchmark.p
% 5.98/2.28 % SZS status Theorem for theBenchmark.p
% 5.98/2.28
% 5.98/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.98/2.28
% 5.98/2.28 % ------ iProver source info
% 5.98/2.28
% 5.98/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 5.98/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.98/2.28 % git: non_committed_changes: false
% 5.98/2.28
% 5.98/2.28 % ------ Parsing...
% 5.98/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.98/2.28
% 5.98/2.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.98/2.28
% 5.98/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.98/2.28
% 5.98/2.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.98/2.28 % ------ Proving...
% 5.98/2.28 % ------ Problem Properties
% 5.98/2.28
% 5.98/2.28 %
% 5.98/2.28 % clauses 32
% 5.98/2.28 % conjectures 1
% 5.98/2.28 % EPR 4
% 5.98/2.28 % Horn 30
% 5.98/2.28 % unary 21
% 5.98/2.28 % binary 7
% 5.98/2.28 % lits 47
% 5.98/2.28 % lits eq 15
% 5.98/2.28 % fd_pure 0
% 5.98/2.28 % fd_pseudo 0
% 5.98/2.28 % fd_cond 0
% 5.98/2.28 % fd_pseudo_cond 1
% 5.98/2.28 % AC symbols 0
% 5.98/2.28
% 5.98/2.28 % ------ Schedule dynamic 5 is on
% 5.98/2.28
% 5.98/2.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.98/2.28
% 5.98/2.28
% 5.98/2.28 % ------
% 5.98/2.28 % Current options:
% 5.98/2.28 % ------
% 5.98/2.28
% 5.98/2.28
% 5.98/2.28 %
% 5.98/2.28
% 5.98/2.28 % ------ Proving...
% 5.98/2.28 %
% 5.98/2.28
% 5.98/2.28 % SZS status Theorem for theBenchmark.p
% 5.98/2.28
% 5.98/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.98/2.28
% 5.98/2.28
%------------------------------------------------------------------------------