%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL224-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:51:38 AM UTC 2026
% Result : Unsatisfiable 12.59s 2.67s
% Output : Refutation 14.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 38
% Syntax : Number of formulae : 191 ( 109 unt; 28 def)
% Number of atoms : 331 ( 142 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 268 ( 128 ~; 122 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 14 con; 0-4 aty)
% Number of variables : 133 ( 0 sgn 133 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f4,plain,
! [X0,X1] : true = axiom(implies(X0,or(X1,X0))),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f6,plain,
! [X0,X1] : true = axiom(implies(or(X0,X1),or(X1,X0))),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f8,plain,
! [X2,X0,X1] : true = axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f10,plain,
! [X2,X0,X1] : true = axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f12,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f13,plain,
! [X0] : true = ifeq(axiom(X0),true,theorem(X0),true),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] : ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f15,plain,
! [X0,X1] : true = ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f17,plain,
true != theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : true = axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f2,f11]) ).
fof(f19,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f4,f11]) ).
fof(f20,plain,
! [X0,X1] : true = axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f6,f11]) ).
fof(f21,plain,
! [X2,X0,X1] : true = axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f8,f11]) ).
fof(f22,plain,
! [X2,X0,X1] : true = axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f10,f11,f11,f11]) ).
fof(f23,plain,
! [X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(definition_unfolding,[],[f15,f11]) ).
fof(f24,plain,
true != theorem(or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))),
inference(definition_unfolding,[],[f17,f11,f11,f11]) ).
fof(f25,definition,
sF0 = not(q),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f26,plain,
not(q) = sF0,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF1 = or(sF0,r),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f28,plain,
or(sF0,r) = sF1,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF2 = or(p,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f30,plain,
or(p,sF1) = sF2,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF3 = not(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f32,plain,
not(sF2) = sF3,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF4 = or(p,q),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f34,plain,
or(p,q) = sF4,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF5 = not(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f36,plain,
not(sF4) = sF5,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF6 = or(p,r),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f38,plain,
or(p,r) = sF6,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF7 = or(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f40,plain,
or(sF5,sF6) = sF7,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF8 = or(sF3,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f42,plain,
or(sF3,sF7) = sF8,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF9 = theorem(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f44,plain,
theorem(sF8) = sF9,
inference(reorient_equations,[],[f43]) ).
fof(f45,plain,
true != sF9,
inference(definition_folding,[],[f24,f44,f42,f40,f38,f36,f34,f32,f30,f28,f26]) ).
fof(f47,definition,
( spl10_1
<=> theorem(sF8) = sF9 ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f49,plain,
( theorem(sF8) = sF9
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
spl10_1,
inference(avatar_split_clause,[],[f44,f47]) ).
fof(f54,definition,
( spl10_2
<=> true = sF9 ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f56,plain,
( true != sF9
| spl10_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
~ spl10_2,
inference(avatar_split_clause,[],[f45,f54]) ).
fof(f59,definition,
( spl10_3
<=> not(q) = sF0 ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f61,plain,
( not(q) = sF0
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
spl10_3,
inference(avatar_split_clause,[],[f26,f59]) ).
fof(f66,definition,
( spl10_4
<=> not(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f68,plain,
( not(sF2) = sF3
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
spl10_4,
inference(avatar_split_clause,[],[f32,f66]) ).
fof(f73,definition,
( spl10_5
<=> not(sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f75,plain,
( not(sF4) = sF5
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
spl10_5,
inference(avatar_split_clause,[],[f36,f73]) ).
fof(f83,definition,
( spl10_6
<=> or(sF3,sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f85,plain,
( or(sF3,sF7) = sF8
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
spl10_6,
inference(avatar_split_clause,[],[f42,f83]) ).
fof(f94,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true),
inference(superposition,[],[f13,f20]) ).
fof(f95,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X1,X0))),true),
inference(superposition,[],[f13,f19]) ).
fof(f96,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),true),
inference(superposition,[],[f13,f21]) ).
fof(f97,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),true),
inference(superposition,[],[f13,f22]) ).
fof(f98,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,X0)),X0)),true),
inference(superposition,[],[f13,f18]) ).
fof(f100,plain,
! [X0] : true = theorem(or(not(or(X0,X0)),X0)),
inference(forward_demodulation,[],[f98,f1]) ).
fof(f101,plain,
! [X2,X0,X1] : true = theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(forward_demodulation,[],[f97,f1]) ).
fof(f102,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(forward_demodulation,[],[f96,f1]) ).
fof(f103,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X1,X0))),
inference(forward_demodulation,[],[f95,f1]) ).
fof(f104,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(forward_demodulation,[],[f94,f1]) ).
fof(f118,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),true),
inference(superposition,[],[f23,f102]) ).
fof(f124,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),
inference(forward_demodulation,[],[f118,f1]) ).
fof(f139,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),true),
inference(superposition,[],[f23,f104]) ).
fof(f148,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),
inference(forward_demodulation,[],[f139,f1]) ).
fof(f150,plain,
! [X0] : true = ifeq(true,true,ifeq(theorem(or(X0,X0)),true,theorem(X0),true),true),
inference(superposition,[],[f23,f100]) ).
fof(f159,plain,
! [X0] : true = ifeq(theorem(or(X0,X0)),true,theorem(X0),true),
inference(forward_demodulation,[],[f150,f1]) ).
fof(f162,definition,
( spl10_7
<=> or(p,sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f164,plain,
( or(p,sF1) = sF2
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
spl10_7,
inference(avatar_split_clause,[],[f30,f162]) ).
fof(f184,definition,
( spl10_8
<=> or(p,q) = sF4 ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f186,plain,
( or(p,q) = sF4
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
spl10_8,
inference(avatar_split_clause,[],[f34,f184]) ).
fof(f193,plain,
( ! [X0] : true = axiom(or(not(or(not(q),X0)),or(not(sF4),or(p,X0))))
| ~ spl10_8 ),
inference(superposition,[],[f22,f186]) ).
fof(f204,plain,
( ! [X0] : true = axiom(or(not(or(not(q),X0)),or(sF5,or(p,X0))))
| ~ spl10_5
| ~ spl10_8 ),
inference(forward_demodulation,[],[f193,f75]) ).
fof(f207,plain,
( ! [X0] : true = axiom(or(not(or(sF0,X0)),or(sF5,or(p,X0))))
| ~ spl10_3
| ~ spl10_5
| ~ spl10_8 ),
inference(forward_demodulation,[],[f204,f61]) ).
fof(f209,definition,
( spl10_9
<=> or(sF5,sF6) = sF7 ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f211,plain,
( or(sF5,sF6) = sF7
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
spl10_9,
inference(avatar_split_clause,[],[f40,f209]) ).
fof(f228,definition,
( spl10_10
<=> or(p,r) = sF6 ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f230,plain,
( or(p,r) = sF6
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
spl10_10,
inference(avatar_split_clause,[],[f38,f228]) ).
fof(f247,definition,
( spl10_11
<=> or(sF0,r) = sF1 ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f249,plain,
( or(sF0,r) = sF1
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,plain,
spl10_11,
inference(avatar_split_clause,[],[f28,f247]) ).
fof(f280,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(not(X0),X1)),true,theorem(or(not(or(X2,X0)),or(X2,X1))),true),true),
inference(superposition,[],[f23,f101]) ).
fof(f289,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,theorem(or(not(or(X2,X0)),or(X2,X1))),true),
inference(forward_demodulation,[],[f280,f1]) ).
fof(f297,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,X0)),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f289,f103]) ).
fof(f299,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f289,f104]) ).
fof(f302,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF1),X0)),true,theorem(or(not(sF2),or(p,X0))),true)
| ~ spl10_7 ),
inference(superposition,[],[f289,f164]) ).
fof(f321,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF1),X0)),true,theorem(or(sF3,or(p,X0))),true)
| ~ spl10_4
| ~ spl10_7 ),
inference(forward_demodulation,[],[f302,f68]) ).
fof(f324,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f299,f1]) ).
fof(f326,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,X0)),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f297,f1]) ).
fof(f342,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),true),
inference(superposition,[],[f23,f324]) ).
fof(f350,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f342,f1]) ).
fof(f368,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X2,X1))),true),true),
inference(superposition,[],[f23,f326]) ).
fof(f376,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f368,f1]) ).
fof(f560,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X0,X1))),true),
inference(superposition,[],[f350,f103]) ).
fof(f596,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X0,X1))),
inference(forward_demodulation,[],[f560,f1]) ).
fof(f691,plain,
( ! [X0] : true = ifeq(theorem(or(X0,sF7)),true,theorem(or(X0,sF8)),true)
| ~ spl10_6 ),
inference(superposition,[],[f376,f85]) ).
fof(f692,plain,
( ! [X0] : true = ifeq(theorem(or(X0,sF6)),true,theorem(or(X0,sF7)),true)
| ~ spl10_9 ),
inference(superposition,[],[f376,f211]) ).
fof(f725,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,X0)),or(X2,or(X0,X1)))),true),
inference(superposition,[],[f289,f596]) ).
fof(f751,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,X0)),or(X2,or(X0,X1)))),
inference(forward_demodulation,[],[f725,f1]) ).
fof(f755,plain,
( true = axiom(or(not(or(sF0,r)),or(sF5,sF6)))
| ~ spl10_3
| ~ spl10_5
| ~ spl10_8
| ~ spl10_10 ),
inference(superposition,[],[f207,f230]) ).
fof(f758,plain,
( true = axiom(or(not(or(sF0,r)),sF7))
| ~ spl10_3
| ~ spl10_5
| ~ spl10_8
| ~ spl10_9
| ~ spl10_10 ),
inference(forward_demodulation,[],[f755,f211]) ).
fof(f760,plain,
( true = axiom(or(not(sF1),sF7))
| ~ spl10_3
| ~ spl10_5
| ~ spl10_8
| ~ spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(forward_demodulation,[],[f758,f249]) ).
fof(f763,definition,
( spl10_12
<=> true = axiom(or(not(sF1),sF7)) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
fof(f765,plain,
( true = axiom(or(not(sF1),sF7))
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f766,plain,
( spl10_12
| ~ spl10_3
| ~ spl10_5
| ~ spl10_8
| ~ spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(avatar_split_clause,[],[f760,f247,f228,f209,f184,f73,f59,f763]) ).
fof(f799,plain,
( true = ifeq(true,true,theorem(or(not(sF1),sF7)),true)
| ~ spl10_12 ),
inference(superposition,[],[f13,f765]) ).
fof(f800,plain,
( true = theorem(or(not(sF1),sF7))
| ~ spl10_12 ),
inference(forward_demodulation,[],[f799,f1]) ).
fof(f802,plain,
( true = ifeq(theorem(or(sF8,sF8)),true,sF9,true)
| ~ spl10_1 ),
inference(superposition,[],[f159,f49]) ).
fof(f883,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X1,X2))),true),true),
inference(superposition,[],[f23,f751]) ).
fof(f907,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X1,X2))),true),
inference(forward_demodulation,[],[f883,f1]) ).
fof(f934,plain,
( ! [X0] : true = ifeq(theorem(or(X0,p)),true,theorem(or(X0,sF6)),true)
| ~ spl10_10 ),
inference(superposition,[],[f907,f230]) ).
fof(f970,definition,
( spl10_13
<=> true = theorem(or(not(sF1),sF7)) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
fof(f972,plain,
( true = theorem(or(not(sF1),sF7))
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f973,plain,
( spl10_13
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f800,f763,f970]) ).
fof(f1025,plain,
( true = ifeq(true,true,theorem(or(sF3,or(p,sF7))),true)
| ~ spl10_4
| ~ spl10_7
| ~ spl10_13 ),
inference(superposition,[],[f321,f972]) ).
fof(f1050,plain,
( true = theorem(or(sF3,or(p,sF7)))
| ~ spl10_4
| ~ spl10_7
| ~ spl10_13 ),
inference(forward_demodulation,[],[f1025,f1]) ).
fof(f1099,definition,
( spl10_14
<=> true = theorem(or(sF3,or(p,sF7))) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
fof(f1101,plain,
( true = theorem(or(sF3,or(p,sF7)))
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1102,plain,
( spl10_14
| ~ spl10_4
| ~ spl10_7
| ~ spl10_13 ),
inference(avatar_split_clause,[],[f1050,f970,f162,f66,f1099]) ).
fof(f1109,plain,
( true = ifeq(true,true,theorem(or(p,or(sF3,sF7))),true)
| ~ spl10_14 ),
inference(superposition,[],[f124,f1101]) ).
fof(f1128,plain,
( true = theorem(or(p,or(sF3,sF7)))
| ~ spl10_14 ),
inference(forward_demodulation,[],[f1109,f1]) ).
fof(f1130,plain,
( true = theorem(or(p,sF8))
| ~ spl10_6
| ~ spl10_14 ),
inference(forward_demodulation,[],[f1128,f85]) ).
fof(f1132,definition,
( spl10_15
<=> true = theorem(or(p,sF8)) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
fof(f1134,plain,
( true = theorem(or(p,sF8))
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1135,plain,
( spl10_15
| ~ spl10_6
| ~ spl10_14 ),
inference(avatar_split_clause,[],[f1130,f1099,f83,f1132]) ).
fof(f1141,plain,
( true = ifeq(true,true,theorem(or(sF8,p)),true)
| ~ spl10_15 ),
inference(superposition,[],[f148,f1134]) ).
fof(f1150,plain,
( true = theorem(or(sF8,p))
| ~ spl10_15 ),
inference(forward_demodulation,[],[f1141,f1]) ).
fof(f1204,definition,
( spl10_16
<=> true = theorem(or(sF8,p)) ),
introduced(definition,[new_symbols(definition,[spl10_16])],[avatar_definition]) ).
fof(f1206,plain,
( true = theorem(or(sF8,p))
| ~ spl10_16 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1207,plain,
( spl10_16
| ~ spl10_15 ),
inference(avatar_split_clause,[],[f1150,f1132,f1204]) ).
fof(f1915,plain,
( true = ifeq(true,true,theorem(or(sF8,sF6)),true)
| ~ spl10_10
| ~ spl10_16 ),
inference(superposition,[],[f934,f1206]) ).
fof(f1920,plain,
( true = theorem(or(sF8,sF6))
| ~ spl10_10
| ~ spl10_16 ),
inference(forward_demodulation,[],[f1915,f1]) ).
fof(f1924,definition,
( spl10_26
<=> true = theorem(or(sF8,sF6)) ),
introduced(definition,[new_symbols(definition,[spl10_26])],[avatar_definition]) ).
fof(f1926,plain,
( true = theorem(or(sF8,sF6))
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f1924]) ).
fof(f1927,plain,
( spl10_26
| ~ spl10_10
| ~ spl10_16 ),
inference(avatar_split_clause,[],[f1920,f1204,f228,f1924]) ).
fof(f2343,plain,
( true = ifeq(true,true,theorem(or(sF8,sF7)),true)
| ~ spl10_9
| ~ spl10_26 ),
inference(superposition,[],[f692,f1926]) ).
fof(f2366,plain,
( true = theorem(or(sF8,sF7))
| ~ spl10_9
| ~ spl10_26 ),
inference(forward_demodulation,[],[f2343,f1]) ).
fof(f2369,definition,
( spl10_33
<=> true = theorem(or(sF8,sF7)) ),
introduced(definition,[new_symbols(definition,[spl10_33])],[avatar_definition]) ).
fof(f2371,plain,
( true = theorem(or(sF8,sF7))
| ~ spl10_33 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f2372,plain,
( spl10_33
| ~ spl10_9
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f2366,f1924,f209,f2369]) ).
fof(f2526,plain,
( true = ifeq(true,true,theorem(or(sF8,sF8)),true)
| ~ spl10_6
| ~ spl10_33 ),
inference(superposition,[],[f691,f2371]) ).
fof(f2551,plain,
( true = theorem(or(sF8,sF8))
| ~ spl10_6
| ~ spl10_33 ),
inference(forward_demodulation,[],[f2526,f1]) ).
fof(f2552,plain,
( true = ifeq(true,true,sF9,true)
| ~ spl10_1
| ~ spl10_6
| ~ spl10_33 ),
inference(backward_demodulation,[],[f802,f2551]) ).
fof(f2553,plain,
( true = sF9
| ~ spl10_1
| ~ spl10_6
| ~ spl10_33 ),
inference(forward_demodulation,[],[f2552,f1]) ).
fof(f2554,plain,
( $false
| ~ spl10_1
| spl10_2
| ~ spl10_6
| ~ spl10_33 ),
inference(forward_subsumption_resolution,[],[f2553,f56]) ).
fof(f2555,plain,
( ~ spl10_1
| spl10_2
| ~ spl10_6
| ~ spl10_33 ),
inference(avatar_contradiction_clause,[],[f2554]) ).
cnf(s1,plain,
spl10_1,
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
~ spl10_2,
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
spl10_3,
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
spl10_4,
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
spl10_5,
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
spl10_6,
inference(sat_conversion,[],[f86]) ).
cnf(s7,plain,
spl10_7,
inference(sat_conversion,[],[f165]) ).
cnf(s8,plain,
spl10_8,
inference(sat_conversion,[],[f187]) ).
cnf(s9,plain,
spl10_9,
inference(sat_conversion,[],[f212]) ).
cnf(s10,plain,
spl10_10,
inference(sat_conversion,[],[f231]) ).
cnf(s11,plain,
spl10_11,
inference(sat_conversion,[],[f250]) ).
cnf(s12,plain,
( ~ spl10_3
| ~ spl10_5
| ~ spl10_8
| ~ spl10_9
| ~ spl10_10
| ~ spl10_11
| spl10_12 ),
inference(sat_conversion,[],[f766]) ).
cnf(s13,plain,
( ~ spl10_12
| spl10_13 ),
inference(sat_conversion,[],[f973]) ).
cnf(s14,plain,
( ~ spl10_4
| ~ spl10_7
| ~ spl10_13
| spl10_14 ),
inference(sat_conversion,[],[f1102]) ).
cnf(s15,plain,
( ~ spl10_6
| ~ spl10_14
| spl10_15 ),
inference(sat_conversion,[],[f1135]) ).
cnf(s16,plain,
( ~ spl10_15
| spl10_16 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s26,plain,
( ~ spl10_10
| ~ spl10_16
| spl10_26 ),
inference(sat_conversion,[],[f1927]) ).
cnf(s33,plain,
( ~ spl10_9
| ~ spl10_26
| spl10_33 ),
inference(sat_conversion,[],[f2372]) ).
cnf(s34,plain,
( ~ spl10_1
| spl10_2
| ~ spl10_6
| ~ spl10_33 ),
inference(sat_conversion,[],[f2555]) ).
cnf(s40,plain,
spl10_12,
inference(rat,[],[s12,s5,s11,s10,s9,s8,s3]) ).
cnf(s42,plain,
spl10_13,
inference(rat,[],[s13,s40]) ).
cnf(s46,plain,
spl10_14,
inference(rat,[],[s14,s4,s7,s42]) ).
cnf(s51,plain,
spl10_15,
inference(rat,[],[s15,s6,s46]) ).
cnf(s54,plain,
spl10_16,
inference(rat,[],[s16,s51]) ).
cnf(s55,plain,
spl10_26,
inference(rat,[],[s26,s10,s54]) ).
cnf(s56,plain,
spl10_33,
inference(rat,[],[s33,s9,s55]) ).
cnf(s57,plain,
~ spl10_1,
inference(rat,[],[s34,s56,s6,s2]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s1,s57]) ).
fof(f2556,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL224-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 15:30:24 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.59/2.67 % (2516078)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.59/2.67 % (2516101)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3319242328:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 12.59/2.67 % (2516104)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1699915660:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 12.59/2.67 % (2516099)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=2536347132:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 12.59/2.67 % (2516102)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4174845763:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 12.59/2.67 % (2516103)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=79325259:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 12.59/2.67 % (2516105)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2809117845:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 12.59/2.67 % (2516100)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=2189865296:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 12.59/2.67 % (2516104)Instruction limit reached!
% 12.59/2.67 % (2516104)------------------------------
% 12.59/2.67 % (2516104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516104)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516104)Termination reason: Instruction limit
% 12.59/2.67 % (2516104)Termination phase: Saturation
% 12.59/2.67 % (2516104)Time elapsed: 0.114 s
% 12.59/2.67 % (2516104)Peak memory usage: 91 MB
% 12.59/2.67 % (2516104)Instructions burned: 259 (million)
% 12.59/2.67 % (2516102)Instruction limit reached!
% 12.59/2.67 % (2516102)------------------------------
% 12.59/2.67 % (2516102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516102)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516102)Termination reason: Instruction limit
% 12.59/2.67 % (2516102)Termination phase: Saturation
% 12.59/2.67 % (2516102)Time elapsed: 0.137 s
% 12.59/2.67 % (2516102)Peak memory usage: 89 MB
% 12.59/2.67 % (2516102)Instructions burned: 136 (million)
% 12.59/2.67 % (2516103)Instruction limit reached!
% 12.59/2.67 % (2516103)------------------------------
% 12.59/2.67 % (2516103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516103)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516103)Termination reason: Instruction limit
% 12.59/2.67 % (2516103)Termination phase: Saturation
% 12.59/2.67 % (2516103)Time elapsed: 0.158 s
% 12.59/2.67 % (2516103)Peak memory usage: 89 MB
% 12.59/2.67 % (2516103)Instructions burned: 182 (million)
% 12.59/2.67 % (2516118)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2327023863:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 12.59/2.67 % (2516121)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4061604102:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 12.59/2.67 % (2516122)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1662722426:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 12.59/2.67 % (2516122)Instruction limit reached!
% 12.59/2.67 % (2516122)------------------------------
% 12.59/2.67 % (2516122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516122)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516122)Termination reason: Instruction limit
% 12.59/2.67 % (2516122)Termination phase: Saturation
% 12.59/2.67 % (2516122)Time elapsed: 0.176 s
% 12.59/2.67 % (2516122)Peak memory usage: 88 MB
% 12.59/2.67 % (2516122)Instructions burned: 215 (million)
% 12.59/2.67 % (2516131)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=871141829:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 12.59/2.67 % (2516131)Instruction limit reached!
% 12.59/2.67 % (2516131)------------------------------
% 12.59/2.67 % (2516131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516131)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516131)Termination reason: Instruction limit
% 12.59/2.67 % (2516131)Termination phase: Saturation
% 12.59/2.67 % (2516131)Time elapsed: 0.299 s
% 12.59/2.67 % (2516131)Peak memory usage: 94 MB
% 12.59/2.67 % (2516131)Instructions burned: 317 (million)
% 12.59/2.67 % (2516105)Instruction limit reached!
% 12.59/2.67 % (2516105)------------------------------
% 12.59/2.67 % (2516105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516105)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516105)Termination reason: Instruction limit
% 12.59/2.67 % (2516105)Termination phase: Saturation
% 12.59/2.67 % (2516105)Time elapsed: 1.108 s
% 12.59/2.67 % (2516105)Peak memory usage: 101 MB
% 12.59/2.67 % (2516105)Instructions burned: 1191 (million)
% 12.59/2.67 % (2516118)Instruction limit reached!
% 12.59/2.67 % (2516118)------------------------------
% 12.59/2.67 % (2516118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.59/2.67 % (2516118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.59/2.67 % (2516118)CaDiCaL version: 2.1.3
% 12.59/2.67 % (2516118)Termination reason: Instruction limit
% 12.59/2.67 % (2516118)Termination phase: Saturation
% 12.59/2.67 % (2516118)Time elapsed: 0.933 s
% 12.59/2.67 % (2516118)Peak memory usage: 143 MB
% 12.59/2.67 % (2516118)Instructions burned: 2054 (million)
% 12.59/2.67 % (2516145)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1146154647:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2986 on theBenchmark for (2986ds/14534Mi)
% 12.59/2.67 % (2516141)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=975173847:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 12.59/2.67 % (2516144)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2711891644:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 12.59/2.67 % (2516099)First to succeed.
% 12.59/2.67 % (2516099)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2516078"
% 12.59/2.67 % (2516099)Refutation found. Thanks to Tanya!
% 12.59/2.67 % SZS status Unsatisfiable for theBenchmark
% 12.59/2.67 % SZS output start Proof for theBenchmark
% See solution above
% 14.21/2.76 % (2516099)------------------------------
% 14.21/2.76 % (2516099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.21/2.76 % (2516099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.21/2.76 % (2516099)CaDiCaL version: 2.1.3
% 14.21/2.76 % (2516099)Termination reason: Refutation
% 14.21/2.76 % (2516099)Time elapsed: 1.529 s
% 14.21/2.76 % (2516099)Peak memory usage: 136 MB
% 14.21/2.76 % (2516099)Instructions burned: 1635 (million)
% 14.21/2.76 % (2516099)------------------------------
% 14.21/2.76 % (2516099)------------------------------
% 14.21/2.76 % (2516078)Success in time 1.964 s
% 14.21/2.76 % Vampire exiting
%------------------------------------------------------------------------------