%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL890-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 11:56:56 AM UTC 2026
% Result : Unsatisfiable 36.15s 12.54s
% Output : Refutation 80.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 132 ( 101 unt; 10 def)
% Number of atoms : 177 ( 113 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 89 ( 44 ~; 39 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 181 ( 0 sgn 181 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f4,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f5,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f8,axiom,
! [X0] : '>='(X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f11,axiom,
! [X0,X1] : ifeq2('>='(X0,X1),true,ifeq2('>='(X1,X0),true,X1,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f12,axiom,
! [X2,X0,X1] : ifeq('>='('+'(X0,X1),X2),true,'>='(X1,'==>'(X0,X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08_1) ).
fof(f13,plain,
! [X2,X0,X1] : true = ifeq('>='('+'(X0,X1),X2),true,'>='(X1,'==>'(X0,X2)),true),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] : ifeq('>='(X0,'==>'(X1,X2)),true,'>='('+'(X1,X0),X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f15,plain,
! [X2,X0,X1] : true = ifeq('>='(X0,'==>'(X1,X2)),true,'>='('+'(X1,X0),X2),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] : '>='(X0,'0') = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(f17,plain,
! [X0] : true = '>='(X0,'0'),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X2,X0,X1] : ifeq('>='(X0,X1),true,'>='('+'(X0,X2),'+'(X1,X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(f19,plain,
! [X2,X0,X1] : true = ifeq('>='(X0,X1),true,'>='('+'(X0,X2),'+'(X1,X2)),true),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X2,X0,X1] : ifeq('>='(X0,X1),true,'>='('==>'(X1,X2),'==>'(X0,X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(f21,plain,
! [X2,X0,X1] : true = ifeq('>='(X0,X1),true,'>='('==>'(X1,X2),'==>'(X0,X2)),true),
inference(reorient_equations,[],[f20]) ).
fof(f24,axiom,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(f25,negated_conjecture,
sK2_goals_14_X19 = '==>'(sK2_goals_14_X19,sK3_goals_14_X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f26,negated_conjecture,
'>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14_1) ).
fof(f27,plain,
true = '>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
'>='(sK2_goals_14_X19,sK1_goals_14_X17) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14_2) ).
fof(f29,plain,
true != '>='(sK2_goals_14_X19,sK1_goals_14_X17),
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF0 = '==>'(sK2_goals_14_X19,sK3_goals_14_X18),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f31,plain,
'==>'(sK2_goals_14_X19,sK3_goals_14_X18) = sF0,
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
sK2_goals_14_X19 = sF0,
inference(definition_folding,[],[f25,f31]) ).
fof(f33,definition,
sF1 = '==>'(sK1_goals_14_X17,sK3_goals_14_X18),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f34,plain,
'==>'(sK1_goals_14_X17,sK3_goals_14_X18) = sF1,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF2 = '>='(sF1,sK1_goals_14_X17),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
'>='(sF1,sK1_goals_14_X17) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
true = sF2,
inference(definition_folding,[],[f27,f36,f34]) ).
fof(f38,definition,
sF3 = '>='(sK2_goals_14_X19,sK1_goals_14_X17),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
'>='(sK2_goals_14_X19,sK1_goals_14_X17) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,plain,
true != sF3,
inference(definition_folding,[],[f29,f39]) ).
fof(f41,plain,
sF2 != sF3,
inference(backward_demodulation,[],[f40,f37]) ).
fof(f43,plain,
! [X2,X0,X1] : sF2 = ifeq('>='(X0,X1),sF2,'>='('==>'(X1,X2),'==>'(X0,X2)),sF2),
inference(forward_demodulation,[],[f21,f37]) ).
fof(f44,plain,
! [X2,X0,X1] : sF2 = ifeq('>='(X0,X1),sF2,'>='('+'(X0,X2),'+'(X1,X2)),sF2),
inference(forward_demodulation,[],[f19,f37]) ).
fof(f45,plain,
! [X0] : '>='(X0,'0') = sF2,
inference(forward_demodulation,[],[f17,f37]) ).
fof(f46,plain,
! [X2,X0,X1] : sF2 = ifeq('>='(X0,'==>'(X1,X2)),sF2,'>='('+'(X1,X0),X2),sF2),
inference(forward_demodulation,[],[f15,f37]) ).
fof(f47,plain,
! [X2,X0,X1] : sF2 = ifeq('>='('+'(X0,X1),X2),sF2,'>='(X1,'==>'(X0,X2)),sF2),
inference(forward_demodulation,[],[f13,f37]) ).
fof(f48,plain,
! [X0,X1] : ifeq2('>='(X0,X1),sF2,ifeq2('>='(X1,X0),sF2,X1,X0),X0) = X0,
inference(forward_demodulation,[],[f11,f37]) ).
fof(f50,plain,
! [X0] : '>='(X0,X0) = sF2,
inference(forward_demodulation,[],[f8,f37]) ).
fof(f51,plain,
sF0 = '==>'(sF0,sK3_goals_14_X18),
inference(forward_demodulation,[],[f31,f32]) ).
fof(f52,plain,
sF3 = '>='(sF0,sK1_goals_14_X17),
inference(forward_demodulation,[],[f39,f32]) ).
fof(f54,definition,
( spl4_1
<=> sF2 = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f56,plain,
( sF2 != sF3
| spl4_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f41,f54]) ).
fof(f64,definition,
( spl4_3
<=> sF3 = '>='(sF0,sK1_goals_14_X17) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f66,plain,
( sF3 = '>='(sF0,sK1_goals_14_X17)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
spl4_3,
inference(avatar_split_clause,[],[f52,f64]) ).
fof(f70,definition,
( spl4_4
<=> sF0 = '==>'(sF0,sK3_goals_14_X18) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f72,plain,
( sF0 = '==>'(sF0,sK3_goals_14_X18)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
spl4_4,
inference(avatar_split_clause,[],[f51,f70]) ).
fof(f80,plain,
! [X0,X1] : sF2 = ifeq(sF2,sF2,'>='('+'(X0,'==>'(X0,X1)),X1),sF2),
inference(superposition,[],[f46,f50]) ).
fof(f82,plain,
! [X2,X0,X1] : sF2 = ifeq('>='(X0,'==>'(X1,X2)),sF2,'>='('+'(X0,X1),X2),sF2),
inference(superposition,[],[f46,f4]) ).
fof(f86,plain,
! [X0,X1] : sF2 = '>='('+'(X0,'==>'(X0,X1)),X1),
inference(forward_demodulation,[],[f80,f2]) ).
fof(f92,definition,
( spl4_6
<=> '==>'(sK1_goals_14_X17,sK3_goals_14_X18) = sF1 ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f94,plain,
( '==>'(sK1_goals_14_X17,sK3_goals_14_X18) = sF1
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
spl4_6,
inference(avatar_split_clause,[],[f34,f92]) ).
fof(f102,definition,
( spl4_7
<=> '>='(sF1,sK1_goals_14_X17) = sF2 ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f104,plain,
( '>='(sF1,sK1_goals_14_X17) = sF2
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
spl4_7,
inference(avatar_split_clause,[],[f36,f102]) ).
fof(f110,plain,
! [X0] : '+'('0',X0) = X0,
inference(superposition,[],[f4,f5]) ).
fof(f147,plain,
( ! [X0] : sF2 = ifeq(sF2,sF2,'>='('==>'(sK1_goals_14_X17,X0),'==>'(sF1,X0)),sF2)
| ~ spl4_7 ),
inference(superposition,[],[f43,f104]) ).
fof(f154,plain,
( ! [X0] : sF2 = '>='('==>'(sK1_goals_14_X17,X0),'==>'(sF1,X0))
| ~ spl4_7 ),
inference(forward_demodulation,[],[f147,f2]) ).
fof(f197,plain,
! [X0,X1] : sF2 = ifeq('>='(X1,'0'),sF2,'>='('+'(X1,X0),X0),sF2),
inference(superposition,[],[f44,f110]) ).
fof(f200,plain,
! [X0,X1] : sF2 = ifeq(sF2,sF2,'>='('+'(X1,X0),X0),sF2),
inference(forward_demodulation,[],[f197,f45]) ).
fof(f207,plain,
! [X0,X1] : sF2 = '>='('+'(X1,X0),X0),
inference(forward_demodulation,[],[f200,f2]) ).
fof(f213,plain,
! [X2,X0,X1] : sF2 = '>='('+'(X0,'+'(X1,'==>'('+'(X0,X1),X2))),X2),
inference(superposition,[],[f86,f3]) ).
fof(f219,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('+'(X1,'+'(X0,'==>'(X0,'==>'(X1,X2)))),X2),sF2),
inference(superposition,[],[f46,f86]) ).
fof(f220,plain,
! [X2,X0,X1] : sF2 = '>='('+'(X1,'+'(X0,'==>'(X0,'==>'(X1,X2)))),X2),
inference(forward_demodulation,[],[f219,f2]) ).
fof(f231,plain,
! [X2,X3,X0,X1] : sF2 = ifeq('>='('+'(X0,'+'(X1,X2)),X3),sF2,'>='(X2,'==>'('+'(X0,X1),X3)),sF2),
inference(superposition,[],[f47,f3]) ).
fof(f306,plain,
! [X0] : ifeq2(sF2,sF2,ifeq2('>='('0',X0),sF2,'0',X0),X0) = X0,
inference(superposition,[],[f48,f45]) ).
fof(f315,plain,
( ! [X0] : '==>'(sF1,X0) = ifeq2('>='('==>'(sF1,X0),'==>'(sK1_goals_14_X17,X0)),sF2,ifeq2(sF2,sF2,'==>'(sK1_goals_14_X17,X0),'==>'(sF1,X0)),'==>'(sF1,X0))
| ~ spl4_7 ),
inference(superposition,[],[f48,f154]) ).
fof(f322,plain,
( ! [X0] : '==>'(sF1,X0) = ifeq2('>='('==>'(sF1,X0),'==>'(sK1_goals_14_X17,X0)),sF2,'==>'(sK1_goals_14_X17,X0),'==>'(sF1,X0))
| ~ spl4_7 ),
inference(forward_demodulation,[],[f315,f1]) ).
fof(f330,plain,
! [X0] : ifeq2('>='('0',X0),sF2,'0',X0) = X0,
inference(forward_demodulation,[],[f306,f1]) ).
fof(f577,plain,
! [X0,X1] : sF2 = ifeq(sF2,sF2,'>='(X1,'==>'(X0,X1)),sF2),
inference(superposition,[],[f47,f207]) ).
fof(f598,plain,
! [X0,X1] : sF2 = '>='(X1,'==>'(X0,X1)),
inference(forward_demodulation,[],[f577,f2]) ).
fof(f605,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('==>'('==>'(X1,X0),X2),'==>'(X0,X2)),sF2),
inference(superposition,[],[f43,f598]) ).
fof(f612,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='(X1,'==>'(X0,'==>'(X2,'+'(X0,X1)))),sF2),
inference(superposition,[],[f47,f598]) ).
fof(f621,plain,
! [X2,X0,X1] : sF2 = '>='(X1,'==>'(X0,'==>'(X2,'+'(X0,X1)))),
inference(forward_demodulation,[],[f612,f2]) ).
fof(f628,plain,
! [X2,X0,X1] : sF2 = '>='('==>'('==>'(X1,X0),X2),'==>'(X0,X2)),
inference(forward_demodulation,[],[f605,f2]) ).
fof(f2353,plain,
! [X2,X0,X1] : sF2 = ifeq('>='(X1,'==>'('==>'(X1,X0),X2)),sF2,'>='('+'(X0,'==>'(X0,X1)),X2),sF2),
inference(superposition,[],[f82,f24]) ).
fof(f10828,plain,
! [X0,X1] : '==>'(X0,'==>'(X1,'+'(X0,'0'))) = ifeq2(sF2,sF2,'0','==>'(X0,'==>'(X1,'+'(X0,'0')))),
inference(superposition,[],[f330,f621]) ).
fof(f10854,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X0,'0'))),
inference(forward_demodulation,[],[f10828,f1]) ).
fof(f10887,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,X0)),
inference(forward_demodulation,[],[f10854,f5]) ).
fof(f12555,plain,
( ! [X0] : '==>'(sF1,'==>'(X0,sK1_goals_14_X17)) = ifeq2('>='('==>'(sF1,'==>'(X0,sK1_goals_14_X17)),'0'),sF2,'0','==>'(sF1,'==>'(X0,sK1_goals_14_X17)))
| ~ spl4_7 ),
inference(superposition,[],[f322,f10887]) ).
fof(f12566,plain,
( ! [X0] : '==>'(sF1,'==>'(X0,sK1_goals_14_X17)) = ifeq2(sF2,sF2,'0','==>'(sF1,'==>'(X0,sK1_goals_14_X17)))
| ~ spl4_7 ),
inference(forward_demodulation,[],[f12555,f45]) ).
fof(f12572,plain,
( ! [X0] : '0' = '==>'(sF1,'==>'(X0,sK1_goals_14_X17))
| ~ spl4_7 ),
inference(forward_demodulation,[],[f12566,f1]) ).
fof(f14884,plain,
! [X2,X3,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('==>'('==>'(X1,X2),X3),'==>'('==>'('==>'(X0,X1),X2),X3)),sF2),
inference(superposition,[],[f43,f628]) ).
fof(f14918,plain,
! [X2,X3,X0,X1] : sF2 = '>='('==>'('==>'(X1,X2),X3),'==>'('==>'('==>'(X0,X1),X2),X3)),
inference(forward_demodulation,[],[f14884,f2]) ).
fof(f23820,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('+'(X1,'==>'('+'(X0,X1),X2)),'==>'(X0,X2)),sF2),
inference(superposition,[],[f47,f213]) ).
fof(f23919,plain,
! [X2,X0,X1] : sF2 = '>='('+'(X1,'==>'('+'(X0,X1),X2)),'==>'(X0,X2)),
inference(forward_demodulation,[],[f23820,f2]) ).
fof(f24062,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('==>'('+'(X1,X0),X2),'==>'(X0,'==>'(X1,X2))),sF2),
inference(superposition,[],[f47,f23919]) ).
fof(f24122,plain,
! [X2,X0,X1] : sF2 = '>='('==>'('+'(X1,X0),X2),'==>'(X0,'==>'(X1,X2))),
inference(forward_demodulation,[],[f24062,f2]) ).
fof(f24282,plain,
! [X2,X0,X1] : '==>'(X0,'==>'(X1,X2)) = ifeq2('>='('==>'(X0,'==>'(X1,X2)),'==>'('+'(X1,X0),X2)),sF2,ifeq2(sF2,sF2,'==>'('+'(X1,X0),X2),'==>'(X0,'==>'(X1,X2))),'==>'(X0,'==>'(X1,X2))),
inference(superposition,[],[f48,f24122]) ).
fof(f24313,plain,
! [X2,X0,X1] : '==>'(X0,'==>'(X1,X2)) = ifeq2('>='('==>'(X0,'==>'(X1,X2)),'==>'('+'(X1,X0),X2)),sF2,'==>'('+'(X1,X0),X2),'==>'(X0,'==>'(X1,X2))),
inference(forward_demodulation,[],[f24282,f1]) ).
fof(f28345,plain,
! [X0,X1] : sF2 = ifeq(sF2,sF2,'>='('+'(X1,'==>'(X1,'==>'('==>'(X0,X1),X0))),X0),sF2),
inference(superposition,[],[f2353,f14918]) ).
fof(f28397,plain,
! [X0,X1] : sF2 = '>='('+'(X1,'==>'(X1,'==>'('==>'(X0,X1),X0))),X0),
inference(forward_demodulation,[],[f28345,f2]) ).
fof(f29887,plain,
! [X2,X0,X1] : sF2 = ifeq(sF2,sF2,'>='('==>'(X1,'==>'(X0,X2)),'==>'('+'(X0,X1),X2)),sF2),
inference(superposition,[],[f231,f220]) ).
fof(f30134,plain,
! [X2,X0,X1] : sF2 = '>='('==>'(X1,'==>'(X0,X2)),'==>'('+'(X0,X1),X2)),
inference(forward_demodulation,[],[f29887,f2]) ).
fof(f30171,plain,
! [X2,X0,X1] : '==>'(X0,'==>'(X1,X2)) = ifeq2(sF2,sF2,'==>'('+'(X1,X0),X2),'==>'(X0,'==>'(X1,X2))),
inference(backward_demodulation,[],[f24313,f30134]) ).
fof(f30178,plain,
! [X2,X0,X1] : '==>'('+'(X1,X0),X2) = '==>'(X0,'==>'(X1,X2)),
inference(forward_demodulation,[],[f30171,f1]) ).
fof(f31927,plain,
! [X2,X0,X1] : '==>'('+'(X0,X1),X2) = '==>'(X0,'==>'(X1,X2)),
inference(superposition,[],[f30178,f4]) ).
fof(f31937,plain,
! [X2,X0,X1] : '==>'('+'(X0,'==>'(X0,X1)),X2) = '==>'('==>'(X1,X0),'==>'(X1,X2)),
inference(superposition,[],[f30178,f24]) ).
fof(f32338,plain,
! [X2,X0,X1] : '==>'('==>'(X1,X0),'==>'(X1,X2)) = '==>'('==>'(X0,X1),'==>'(X0,X2)),
inference(forward_demodulation,[],[f31937,f30178]) ).
fof(f32347,plain,
! [X2,X0,X1] : '==>'(X0,'==>'(X1,X2)) = '==>'(X1,'==>'(X0,X2)),
inference(forward_demodulation,[],[f31927,f30178]) ).
fof(f32464,plain,
( ! [X0] : '==>'(X0,sF1) = '==>'(sK1_goals_14_X17,'==>'(X0,sK3_goals_14_X18))
| ~ spl4_6 ),
inference(superposition,[],[f32347,f94]) ).
fof(f33014,plain,
( '==>'(sF0,sF1) = '==>'(sK1_goals_14_X17,sF0)
| ~ spl4_4
| ~ spl4_6 ),
inference(superposition,[],[f32464,f72]) ).
fof(f33230,definition,
( spl4_48
<=> '==>'(sF0,sF1) = '==>'(sK1_goals_14_X17,sF0) ),
introduced(definition,[new_symbols(definition,[spl4_48])],[avatar_definition]) ).
fof(f33232,plain,
( '==>'(sF0,sF1) = '==>'(sK1_goals_14_X17,sF0)
| ~ spl4_48 ),
inference(avatar_component_clause,[],[f33230]) ).
fof(f33233,plain,
( spl4_48
| ~ spl4_4
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f33014,f92,f70,f33230]) ).
fof(f35228,plain,
! [X2,X0,X1] : '==>'('==>'(X0,X1),'==>'(X0,X2)) = '==>'(X1,'==>'('==>'(X1,X0),X2)),
inference(superposition,[],[f32347,f32338]) ).
fof(f35451,plain,
! [X2,X0,X1] : '==>'(X0,'==>'('==>'(X0,X1),X2)) = '==>'(X1,'==>'('==>'(X1,X0),X2)),
inference(forward_demodulation,[],[f35228,f32347]) ).
fof(f61632,plain,
( sF2 = '>='('+'(sF0,'==>'(sF0,'==>'('==>'(sF0,sF1),sK1_goals_14_X17))),sK1_goals_14_X17)
| ~ spl4_48 ),
inference(superposition,[],[f28397,f33232]) ).
fof(f61808,plain,
( sF2 = '>='('+'(sF0,'==>'(sF1,'==>'('==>'(sF1,sF0),sK1_goals_14_X17))),sK1_goals_14_X17)
| ~ spl4_48 ),
inference(forward_demodulation,[],[f61632,f35451]) ).
fof(f61878,plain,
( sF2 = '>='('+'(sF0,'0'),sK1_goals_14_X17)
| ~ spl4_7
| ~ spl4_48 ),
inference(forward_demodulation,[],[f61808,f12572]) ).
fof(f61916,plain,
( sF2 = '>='(sF0,sK1_goals_14_X17)
| ~ spl4_7
| ~ spl4_48 ),
inference(forward_demodulation,[],[f61878,f5]) ).
fof(f61931,plain,
( sF2 = sF3
| ~ spl4_3
| ~ spl4_7
| ~ spl4_48 ),
inference(forward_demodulation,[],[f61916,f66]) ).
fof(f61934,plain,
( $false
| spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_48 ),
inference(forward_subsumption_resolution,[],[f61931,f56]) ).
fof(f61935,plain,
( spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_48 ),
inference(avatar_contradiction_clause,[],[f61934]) ).
cnf(s1,plain,
~ spl4_1,
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
spl4_6,
inference(sat_conversion,[],[f95]) ).
cnf(s7,plain,
spl4_7,
inference(sat_conversion,[],[f105]) ).
cnf(s48,plain,
( ~ spl4_4
| ~ spl4_6
| spl4_48 ),
inference(sat_conversion,[],[f33233]) ).
cnf(s65,plain,
( spl4_1
| ~ spl4_3
| ~ spl4_7
| ~ spl4_48 ),
inference(sat_conversion,[],[f61935]) ).
cnf(s102,plain,
spl4_48,
inference(rat,[],[s48,s6,s4]) ).
cnf(s116,plain,
spl4_1,
inference(rat,[],[s65,s102,s7,s3]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s1,s116]) ).
fof(f61940,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL890-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 % Computer : n004.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sun Sep 27 17:04:37 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.54 Running first-order theorem proving
% 0.28/0.54 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.15/12.54 % (3749220)Detected a unit-equality problem, will run specialized UEQ schedule.
% 36.15/12.54 % (3749228)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2950533512:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 36.15/12.54 % (3749225)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3732810309:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 36.15/12.54 % (3749226)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2512257063:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 36.15/12.54 % (3749227)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=397570771:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 36.15/12.54 % (3749229)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1157628423:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 36.15/12.54 % (3749228)Instruction limit reached!
% 36.15/12.54 % (3749228)------------------------------
% 36.15/12.54 % (3749228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749228)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749228)Termination reason: Instruction limit
% 36.15/12.54 % (3749228)Termination phase: Saturation
% 36.15/12.54 % (3749228)Time elapsed: 0.072 s
% 36.15/12.54 % (3749228)Peak memory usage: 88 MB
% 36.15/12.54 % (3749228)Instructions burned: 138 (million)
% 36.15/12.54 % (3749231)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1955912283:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 36.15/12.54 % (3749230)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2961442615:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 36.15/12.54 % (3749237)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2903930410:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 36.15/12.54 % (3749229)Instruction limit reached!
% 36.15/12.54 % (3749229)------------------------------
% 36.15/12.54 % (3749229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749229)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749229)Termination reason: Instruction limit
% 36.15/12.54 % (3749229)Termination phase: Saturation
% 36.15/12.54 % (3749229)Time elapsed: 0.179 s
% 36.15/12.54 % (3749229)Peak memory usage: 90 MB
% 36.15/12.54 % (3749229)Instructions burned: 181 (million)
% 36.15/12.54 % (3749230)Instruction limit reached!
% 36.15/12.54 % (3749230)------------------------------
% 36.15/12.54 % (3749230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749230)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749230)Termination reason: Instruction limit
% 36.15/12.54 % (3749230)Termination phase: Saturation
% 36.15/12.54 % (3749230)Time elapsed: 0.254 s
% 36.15/12.54 % (3749230)Peak memory usage: 90 MB
% 36.15/12.54 % (3749230)Instructions burned: 258 (million)
% 36.15/12.54 % (3749241)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=348398584:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 36.15/12.54 % (3749242)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=683880012:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 36.15/12.54 % (3749242)Instruction limit reached!
% 36.15/12.54 % (3749242)------------------------------
% 36.15/12.54 % (3749242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749242)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749242)Termination reason: Instruction limit
% 36.15/12.54 % (3749242)Termination phase: Saturation
% 36.15/12.54 % (3749242)Time elapsed: 0.179 s
% 36.15/12.54 % (3749242)Peak memory usage: 91 MB
% 36.15/12.54 % (3749242)Instructions burned: 216 (million)
% 36.15/12.54 % (3749245)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1350110045:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 36.15/12.54 % (3749245)Instruction limit reached!
% 36.15/12.54 % (3749245)------------------------------
% 36.15/12.54 % (3749245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749245)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749245)Termination reason: Instruction limit
% 36.15/12.54 % (3749245)Termination phase: Saturation
% 36.15/12.54 % (3749245)Time elapsed: 0.153 s
% 36.15/12.54 % (3749245)Peak memory usage: 90 MB
% 36.15/12.54 % (3749245)Instructions burned: 319 (million)
% 36.15/12.54 % (3749231)Instruction limit reached!
% 36.15/12.54 % (3749231)------------------------------
% 36.15/12.54 % (3749231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749231)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749231)Termination reason: Instruction limit
% 36.15/12.54 % (3749231)Termination phase: Saturation
% 36.15/12.54 % (3749231)Time elapsed: 1.089 s
% 36.15/12.54 % (3749231)Peak memory usage: 102 MB
% 36.15/12.54 % (3749231)Instructions burned: 1187 (million)
% 36.15/12.54 % (3749247)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2857521961:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 36.15/12.54 % (3749248)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2747470107:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 36.15/12.54 % (3749237)Instruction limit reached!
% 36.15/12.54 % (3749237)------------------------------
% 36.15/12.54 % (3749237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749237)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749237)Termination reason: Instruction limit
% 36.15/12.54 % (3749237)Termination phase: Saturation
% 36.15/12.54 % (3749237)Time elapsed: 1.995 s
% 36.15/12.54 % (3749237)Peak memory usage: 142 MB
% 36.15/12.54 % (3749237)Instructions burned: 2051 (million)
% 36.15/12.54 % (3749251)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2229289603:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2975 on theBenchmark for (2975ds/14534Mi)
% 36.15/12.54 % (3749248)Instruction limit reached!
% 36.15/12.54 % (3749248)------------------------------
% 36.15/12.54 % (3749248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749248)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749248)Termination reason: Instruction limit
% 36.15/12.54 % (3749248)Termination phase: Saturation
% 36.15/12.54 % (3749248)Time elapsed: 2.991 s
% 36.15/12.54 % (3749248)Peak memory usage: 125 MB
% 36.15/12.54 % (3749248)Instructions burned: 2836 (million)
% 36.15/12.54 % (3749253)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=2116090662:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2954 on theBenchmark for (2954ds/11832Mi)
% 36.15/12.54 % (3749241)Instruction limit reached!
% 36.15/12.54 % (3749241)------------------------------
% 36.15/12.54 % (3749241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749241)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749241)Termination reason: Instruction limit
% 36.15/12.54 % (3749241)Termination phase: Saturation
% 36.15/12.54 % (3749241)Time elapsed: 5.107 s
% 36.15/12.54 % (3749241)Peak memory usage: 170 MB
% 36.15/12.54 % (3749241)Instructions burned: 4949 (million)
% 36.15/12.54 % (3749255)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=2345027144:i=2279:fgj=on:bd=all_2942 on theBenchmark for (2942ds/2279Mi)
% 36.15/12.54 % (3749247)Instruction limit reached!
% 36.15/12.54 % (3749247)------------------------------
% 36.15/12.54 % (3749247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749247)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749247)Termination reason: Instruction limit
% 36.15/12.54 % (3749247)Termination phase: Saturation
% 36.15/12.54 % (3749247)Time elapsed: 6.623 s
% 36.15/12.54 % (3749247)Peak memory usage: 251 MB
% 36.15/12.54 % (3749247)Instructions burned: 12127 (million)
% 36.15/12.54 % (3749257)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=3566057205:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2919 on theBenchmark for (2919ds/6225Mi)
% 36.15/12.54 % (3749255)Instruction limit reached!
% 36.15/12.54 % (3749255)------------------------------
% 36.15/12.54 % (3749255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.15/12.54 % (3749255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.15/12.54 % (3749255)CaDiCaL version: 2.1.3
% 36.15/12.54 % (3749255)Termination reason: Instruction limit
% 36.15/12.54 % (3749255)Termination phase: Saturation
% 36.15/12.54 % (3749255)Time elapsed: 2.404 s
% 36.15/12.54 % (3749255)Peak memory usage: 141 MB
% 36.15/12.54 % (3749255)Instructions burned: 2279 (million)
% 36.15/12.54 % (3749259)lrs-1010_1_sil=32000:tgt=ground:etr=on:sp=const_frequency:spb=goal_then_units:rnwc=on:lwlo=on:random_seed=1772967312:lrd=on:i=21755:kws=frequency:fgj=on:bd=preordered:nm=4:ins=20:av=off_2915 on theBenchmark for (2915ds/21755Mi)
% 36.15/12.54 % (3749225)First to succeed.
% 36.15/12.54 % (3749225)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3749220"
% 36.15/12.54 % (3749225)Refutation found. Thanks to Tanya!
% 36.15/12.54 % SZS status Unsatisfiable for theBenchmark
% 36.15/12.54 % SZS output start Proof for theBenchmark
% See solution above
% 80.66/12.76 % (3749225)------------------------------
% 80.66/12.76 % (3749225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 80.66/12.76 % (3749225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.66/12.76 % (3749225)CaDiCaL version: 2.1.3
% 80.66/12.76 % (3749225)Termination reason: Refutation
% 80.66/12.76 % (3749225)Time elapsed: 10.518 s
% 80.66/12.76 % (3749225)Peak memory usage: 221 MB
% 80.66/12.76 % (3749225)Instructions burned: 9942 (million)
% 80.66/12.76 % (3749225)------------------------------
% 80.66/12.76 % (3749225)------------------------------
% 80.66/12.76 % (3749220)Success in time 11.23 s
% 80.66/12.76 % Vampire exiting
%------------------------------------------------------------------------------