%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL306-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:51:55 AM UTC 2026
% Result : Unsatisfiable 9.66s 2.42s
% Output : Refutation 11.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 43
% Syntax : Number of formulae : 198 ( 123 unt; 31 def)
% Number of atoms : 358 ( 152 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 308 ( 148 ~; 142 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 16 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,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f17,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f18,negated_conjecture,
theorem(implies(not(p),equivalent(q,or(p,q)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f19,plain,
true != theorem(implies(not(p),equivalent(q,or(p,q)))),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f17,f16,f11,f11]) ).
fof(f21,plain,
! [X0] : true = axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f2,f11]) ).
fof(f22,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f4,f11]) ).
fof(f23,plain,
! [X0,X1] : true = axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f6,f11]) ).
fof(f24,plain,
! [X2,X0,X1] : true = axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f8,f11]) ).
fof(f25,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(f26,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(f27,plain,
true != theorem(or(not(not(p)),not(or(not(or(not(q),or(p,q))),not(or(not(or(p,q)),q)))))),
inference(definition_unfolding,[],[f19,f11,f20]) ).
fof(f28,definition,
sF0 = not(p),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f29,plain,
not(p) = sF0,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF1 = not(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f31,plain,
not(sF0) = sF1,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF2 = not(q),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f33,plain,
not(q) = sF2,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF3 = or(p,q),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f35,plain,
or(p,q) = sF3,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF4 = or(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f37,plain,
or(sF2,sF3) = sF4,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF5 = not(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f39,plain,
not(sF4) = sF5,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF6 = not(sF3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f41,plain,
not(sF3) = sF6,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF7 = or(sF6,q),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f43,plain,
or(sF6,q) = sF7,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF8 = not(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f45,plain,
not(sF7) = sF8,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF9 = or(sF5,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f47,plain,
or(sF5,sF8) = sF9,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF10 = not(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f49,plain,
not(sF9) = sF10,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF11 = or(sF1,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f51,plain,
or(sF1,sF10) = sF11,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF12 = theorem(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f53,plain,
theorem(sF11) = sF12,
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
true != sF12,
inference(definition_folding,[],[f27,f53,f51,f49,f47,f45,f43,f41,f35,f39,f37,f35,f33,f31,f29]) ).
fof(f56,definition,
( spl13_1
<=> theorem(sF11) = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f58,plain,
( theorem(sF11) = sF12
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
spl13_1,
inference(avatar_split_clause,[],[f53,f56]) ).
fof(f63,definition,
( spl13_2
<=> true = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f65,plain,
( true != sF12
| spl13_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
~ spl13_2,
inference(avatar_split_clause,[],[f54,f63]) ).
fof(f68,definition,
( spl13_3
<=> not(p) = sF0 ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f70,plain,
( not(p) = sF0
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
spl13_3,
inference(avatar_split_clause,[],[f29,f68]) ).
fof(f73,definition,
( spl13_4
<=> not(q) = sF2 ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f75,plain,
( not(q) = sF2
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
spl13_4,
inference(avatar_split_clause,[],[f33,f73]) ).
fof(f82,definition,
( spl13_5
<=> not(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f84,plain,
( not(sF0) = sF1
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
spl13_5,
inference(avatar_split_clause,[],[f31,f82]) ).
fof(f89,definition,
( spl13_6
<=> not(sF3) = sF6 ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f91,plain,
( not(sF3) = sF6
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
spl13_6,
inference(avatar_split_clause,[],[f41,f89]) ).
fof(f96,definition,
( spl13_7
<=> not(sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f98,plain,
( not(sF7) = sF8
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
spl13_7,
inference(avatar_split_clause,[],[f45,f96]) ).
fof(f103,definition,
( spl13_8
<=> not(sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f105,plain,
( not(sF4) = sF5
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
spl13_8,
inference(avatar_split_clause,[],[f39,f103]) ).
fof(f107,plain,
( ! [X0] : true = ifeq(theorem(or(sF5,X0)),true,ifeq(theorem(sF4),true,theorem(X0),true),true)
| ~ spl13_8 ),
inference(superposition,[],[f26,f105]) ).
fof(f110,definition,
( spl13_9
<=> not(sF9) = sF10 ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f112,plain,
( not(sF9) = sF10
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
spl13_9,
inference(avatar_split_clause,[],[f49,f110]) ).
fof(f116,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true),
inference(superposition,[],[f13,f23]) ).
fof(f117,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X1,X0))),true),
inference(superposition,[],[f13,f22]) ).
fof(f118,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,f24]) ).
fof(f119,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,X0)),X0)),true),
inference(superposition,[],[f13,f21]) ).
fof(f121,plain,
! [X0] : true = theorem(or(not(or(X0,X0)),X0)),
inference(forward_demodulation,[],[f119,f1]) ).
fof(f122,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(forward_demodulation,[],[f118,f1]) ).
fof(f123,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X1,X0))),
inference(forward_demodulation,[],[f117,f1]) ).
fof(f124,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(forward_demodulation,[],[f116,f1]) ).
fof(f125,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),true),
inference(superposition,[],[f26,f124]) ).
fof(f131,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),
inference(forward_demodulation,[],[f125,f1]) ).
fof(f146,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,[],[f26,f122]) ).
fof(f152,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),
inference(forward_demodulation,[],[f146,f1]) ).
fof(f179,definition,
( spl13_10
<=> or(sF2,sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f181,plain,
( or(sF2,sF3) = sF4
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
spl13_10,
inference(avatar_split_clause,[],[f37,f179]) ).
fof(f200,definition,
( spl13_11
<=> or(p,q) = sF3 ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f202,plain,
( or(p,q) = sF3
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
spl13_11,
inference(avatar_split_clause,[],[f35,f200]) ).
fof(f211,plain,
( true = theorem(or(not(q),sF3))
| ~ spl13_11 ),
inference(superposition,[],[f123,f202]) ).
fof(f217,plain,
( true = theorem(or(sF2,sF3))
| ~ spl13_4
| ~ spl13_11 ),
inference(forward_demodulation,[],[f211,f75]) ).
fof(f220,plain,
( true = theorem(sF4)
| ~ spl13_4
| ~ spl13_10
| ~ spl13_11 ),
inference(forward_demodulation,[],[f217,f181]) ).
fof(f222,plain,
( ! [X0] : true = ifeq(theorem(or(sF5,X0)),true,ifeq(true,true,theorem(X0),true),true)
| ~ spl13_4
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11 ),
inference(backward_demodulation,[],[f107,f220]) ).
fof(f223,plain,
( ! [X0] : true = ifeq(theorem(or(sF5,X0)),true,theorem(X0),true)
| ~ spl13_4
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11 ),
inference(forward_demodulation,[],[f222,f1]) ).
fof(f225,definition,
( spl13_12
<=> or(sF5,sF8) = sF9 ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f227,plain,
( or(sF5,sF8) = sF9
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
spl13_12,
inference(avatar_split_clause,[],[f47,f225]) ).
fof(f244,definition,
( spl13_13
<=> or(sF6,q) = sF7 ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f246,plain,
( or(sF6,q) = sF7
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,plain,
spl13_13,
inference(avatar_split_clause,[],[f43,f244]) ).
fof(f259,plain,
( ! [X0] : true = ifeq(theorem(or(sF6,or(X0,q))),true,theorem(or(X0,sF7)),true)
| ~ spl13_13 ),
inference(superposition,[],[f152,f246]) ).
fof(f265,definition,
( spl13_14
<=> or(sF1,sF10) = sF11 ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f267,plain,
( or(sF1,sF10) = sF11
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
spl13_14,
inference(avatar_split_clause,[],[f51,f265]) ).
fof(f298,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,f25]) ).
fof(f299,plain,
! [X2,X0,X1] : true = theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(forward_demodulation,[],[f298,f1]) ).
fof(f358,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,[],[f26,f299]) ).
fof(f370,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,[],[f358,f1]) ).
fof(f387,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f370,f124]) ).
fof(f391,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),true),
inference(superposition,[],[f370,f121]) ).
fof(f395,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF8),X0)),true,theorem(or(not(sF9),or(sF5,X0))),true)
| ~ spl13_12 ),
inference(superposition,[],[f370,f227]) ).
fof(f409,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF8),X0)),true,theorem(or(sF10,or(sF5,X0))),true)
| ~ spl13_9
| ~ spl13_12 ),
inference(forward_demodulation,[],[f395,f112]) ).
fof(f412,plain,
! [X0,X1] : true = theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),
inference(forward_demodulation,[],[f391,f1]) ).
fof(f416,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f387,f1]) ).
fof(f427,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),true),
inference(superposition,[],[f26,f412]) ).
fof(f438,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),
inference(forward_demodulation,[],[f427,f1]) ).
fof(f528,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,[],[f26,f416]) ).
fof(f539,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f528,f1]) ).
fof(f545,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(X0),X0)),true),
inference(superposition,[],[f438,f123]) ).
fof(f574,plain,
! [X0] : true = theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f545,f1]) ).
fof(f580,plain,
( true = theorem(or(sF6,sF3))
| ~ spl13_6 ),
inference(superposition,[],[f574,f91]) ).
fof(f592,plain,
! [X0] : true = ifeq(true,true,theorem(or(X0,not(X0))),true),
inference(superposition,[],[f131,f574]) ).
fof(f598,plain,
! [X0] : true = theorem(or(X0,not(X0))),
inference(forward_demodulation,[],[f592,f1]) ).
fof(f665,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X1,X0)),or(X1,not(not(X0))))),true),
inference(superposition,[],[f370,f598]) ).
fof(f677,plain,
! [X0,X1] : true = theorem(or(not(or(X1,X0)),or(X1,not(not(X0))))),
inference(forward_demodulation,[],[f665,f1]) ).
fof(f887,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(not(not(X1)),X0))),true),
inference(superposition,[],[f539,f677]) ).
fof(f906,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(not(not(X1)),X0))),
inference(forward_demodulation,[],[f887,f1]) ).
fof(f1362,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(not(not(X1)),X0)),true),true),
inference(superposition,[],[f26,f906]) ).
fof(f1391,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(not(not(X1)),X0)),true),
inference(forward_demodulation,[],[f1362,f1]) ).
fof(f1538,plain,
( ! [X0] : true = ifeq(theorem(or(X0,p)),true,theorem(or(not(sF0),X0)),true)
| ~ spl13_3 ),
inference(superposition,[],[f1391,f70]) ).
fof(f1553,plain,
( ! [X0] : true = ifeq(theorem(or(X0,p)),true,theorem(or(sF1,X0)),true)
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_demodulation,[],[f1538,f84]) ).
fof(f2152,plain,
( true = ifeq(theorem(or(sF10,p)),true,theorem(sF11),true)
| ~ spl13_3
| ~ spl13_5
| ~ spl13_14 ),
inference(superposition,[],[f1553,f267]) ).
fof(f2158,plain,
( true = ifeq(theorem(or(sF10,p)),true,sF12,true)
| ~ spl13_1
| ~ spl13_3
| ~ spl13_5
| ~ spl13_14 ),
inference(forward_demodulation,[],[f2152,f58]) ).
fof(f2446,plain,
( true = ifeq(theorem(or(sF6,sF3)),true,theorem(or(p,sF7)),true)
| ~ spl13_11
| ~ spl13_13 ),
inference(superposition,[],[f259,f202]) ).
fof(f2456,plain,
( true = ifeq(true,true,theorem(or(p,sF7)),true)
| ~ spl13_6
| ~ spl13_11
| ~ spl13_13 ),
inference(forward_demodulation,[],[f2446,f580]) ).
fof(f2458,plain,
( true = theorem(or(p,sF7))
| ~ spl13_6
| ~ spl13_11
| ~ spl13_13 ),
inference(forward_demodulation,[],[f2456,f1]) ).
fof(f2461,definition,
( spl13_25
<=> true = theorem(or(p,sF7)) ),
introduced(definition,[new_symbols(definition,[spl13_25])],[avatar_definition]) ).
fof(f2463,plain,
( true = theorem(or(p,sF7))
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f2461]) ).
fof(f2464,plain,
( spl13_25
| ~ spl13_6
| ~ spl13_11
| ~ spl13_13 ),
inference(avatar_split_clause,[],[f2458,f244,f200,f89,f2461]) ).
fof(f2476,plain,
( true = ifeq(true,true,theorem(or(not(not(sF7)),p)),true)
| ~ spl13_25 ),
inference(superposition,[],[f1391,f2463]) ).
fof(f2487,plain,
( true = theorem(or(not(not(sF7)),p))
| ~ spl13_25 ),
inference(forward_demodulation,[],[f2476,f1]) ).
fof(f2493,plain,
( true = theorem(or(not(sF8),p))
| ~ spl13_7
| ~ spl13_25 ),
inference(forward_demodulation,[],[f2487,f98]) ).
fof(f2788,definition,
( spl13_30
<=> true = theorem(or(not(sF8),p)) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f2790,plain,
( true = theorem(or(not(sF8),p))
| ~ spl13_30 ),
inference(avatar_component_clause,[],[f2788]) ).
fof(f2791,plain,
( spl13_30
| ~ spl13_7
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f2493,f2461,f96,f2788]) ).
fof(f2792,plain,
( true = ifeq(true,true,theorem(or(sF10,or(sF5,p))),true)
| ~ spl13_9
| ~ spl13_12
| ~ spl13_30 ),
inference(superposition,[],[f409,f2790]) ).
fof(f2828,plain,
( true = theorem(or(sF10,or(sF5,p)))
| ~ spl13_9
| ~ spl13_12
| ~ spl13_30 ),
inference(forward_demodulation,[],[f2792,f1]) ).
fof(f2891,definition,
( spl13_31
<=> true = theorem(or(sF10,or(sF5,p))) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f2893,plain,
( true = theorem(or(sF10,or(sF5,p)))
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f2891]) ).
fof(f2894,plain,
( spl13_31
| ~ spl13_9
| ~ spl13_12
| ~ spl13_30 ),
inference(avatar_split_clause,[],[f2828,f2788,f225,f110,f2891]) ).
fof(f2902,plain,
( true = ifeq(true,true,theorem(or(sF5,or(sF10,p))),true)
| ~ spl13_31 ),
inference(superposition,[],[f152,f2893]) ).
fof(f2928,plain,
( true = theorem(or(sF5,or(sF10,p)))
| ~ spl13_31 ),
inference(forward_demodulation,[],[f2902,f1]) ).
fof(f2932,definition,
( spl13_32
<=> true = theorem(or(sF5,or(sF10,p))) ),
introduced(definition,[new_symbols(definition,[spl13_32])],[avatar_definition]) ).
fof(f2934,plain,
( true = theorem(or(sF5,or(sF10,p)))
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f2932]) ).
fof(f2935,plain,
( spl13_32
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f2928,f2891,f2932]) ).
fof(f2938,plain,
( true = ifeq(true,true,theorem(or(sF10,p)),true)
| ~ spl13_4
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_32 ),
inference(superposition,[],[f223,f2934]) ).
fof(f2972,plain,
( true = theorem(or(sF10,p))
| ~ spl13_4
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_32 ),
inference(forward_demodulation,[],[f2938,f1]) ).
fof(f2975,plain,
( true = ifeq(true,true,sF12,true)
| ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_32 ),
inference(backward_demodulation,[],[f2158,f2972]) ).
fof(f2976,plain,
( true = sF12
| ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_32 ),
inference(forward_demodulation,[],[f2975,f1]) ).
fof(f2977,plain,
( $false
| ~ spl13_1
| spl13_2
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_32 ),
inference(forward_subsumption_resolution,[],[f2976,f65]) ).
fof(f2978,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_32 ),
inference(avatar_contradiction_clause,[],[f2977]) ).
cnf(s1,plain,
spl13_1,
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
~ spl13_2,
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
spl13_3,
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
spl13_4,
inference(sat_conversion,[],[f76]) ).
cnf(s5,plain,
spl13_5,
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
spl13_6,
inference(sat_conversion,[],[f92]) ).
cnf(s7,plain,
spl13_7,
inference(sat_conversion,[],[f99]) ).
cnf(s8,plain,
spl13_8,
inference(sat_conversion,[],[f106]) ).
cnf(s9,plain,
spl13_9,
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
spl13_10,
inference(sat_conversion,[],[f182]) ).
cnf(s11,plain,
spl13_11,
inference(sat_conversion,[],[f203]) ).
cnf(s12,plain,
spl13_12,
inference(sat_conversion,[],[f228]) ).
cnf(s13,plain,
spl13_13,
inference(sat_conversion,[],[f247]) ).
cnf(s14,plain,
spl13_14,
inference(sat_conversion,[],[f268]) ).
cnf(s25,plain,
( ~ spl13_6
| ~ spl13_11
| ~ spl13_13
| spl13_25 ),
inference(sat_conversion,[],[f2464]) ).
cnf(s30,plain,
( ~ spl13_7
| ~ spl13_25
| spl13_30 ),
inference(sat_conversion,[],[f2791]) ).
cnf(s31,plain,
( ~ spl13_9
| ~ spl13_12
| ~ spl13_30
| spl13_31 ),
inference(sat_conversion,[],[f2894]) ).
cnf(s32,plain,
( ~ spl13_31
| spl13_32 ),
inference(sat_conversion,[],[f2935]) ).
cnf(s33,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_32 ),
inference(sat_conversion,[],[f2978]) ).
cnf(s34,plain,
spl13_25,
inference(rat,[],[s25,s11,s13,s6]) ).
cnf(s36,plain,
spl13_30,
inference(rat,[],[s30,s7,s34]) ).
cnf(s38,plain,
spl13_31,
inference(rat,[],[s31,s9,s12,s36]) ).
cnf(s40,plain,
spl13_32,
inference(rat,[],[s32,s38]) ).
cnf(s52,plain,
~ spl13_1,
inference(rat,[],[s33,s40,s14,s11,s10,s8,s5,s4,s3,s2]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s1,s52]) ).
fof(f2979,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL306-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 15:33:48 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 9.66/2.42 % (3215122)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.66/2.42 % (3215177)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2114215015:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.66/2.42 % (3215172)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=1971535197:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.66/2.42 % (3215173)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=808226686:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.66/2.42 % (3215174)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3843567216:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.66/2.42 % (3215176)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1070864904:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.66/2.42 % (3215179)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1600724353:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.66/2.42 % (3215175)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2475660997:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.66/2.42 % (3215177)Instruction limit reached!
% 9.66/2.42 % (3215177)------------------------------
% 9.66/2.42 % (3215177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215177)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215177)Termination reason: Instruction limit
% 9.66/2.42 % (3215177)Termination phase: Saturation
% 9.66/2.42 % (3215177)Time elapsed: 0.091 s
% 9.66/2.42 % (3215177)Peak memory usage: 90 MB
% 9.66/2.42 % (3215177)Instructions burned: 258 (million)
% 9.66/2.42 % (3215175)Instruction limit reached!
% 9.66/2.42 % (3215175)------------------------------
% 9.66/2.42 % (3215175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215175)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215175)Termination reason: Instruction limit
% 9.66/2.42 % (3215175)Termination phase: Saturation
% 9.66/2.42 % (3215175)Time elapsed: 0.084 s
% 9.66/2.42 % (3215175)Peak memory usage: 89 MB
% 9.66/2.42 % (3215175)Instructions burned: 136 (million)
% 9.66/2.42 % (3215176)Instruction limit reached!
% 9.66/2.42 % (3215176)------------------------------
% 9.66/2.42 % (3215176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215176)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215176)Termination reason: Instruction limit
% 9.66/2.42 % (3215176)Termination phase: Saturation
% 9.66/2.42 % (3215176)Time elapsed: 0.105 s
% 9.66/2.42 % (3215176)Peak memory usage: 89 MB
% 9.66/2.42 % (3215176)Instructions burned: 182 (million)
% 9.66/2.42 % (3215196)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2829980274:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 9.66/2.42 % (3215197)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2346891752:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 9.66/2.42 % (3215200)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=4002342301:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 9.66/2.42 % (3215200)Instruction limit reached!
% 9.66/2.42 % (3215200)------------------------------
% 9.66/2.42 % (3215200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215200)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215200)Termination reason: Instruction limit
% 9.66/2.42 % (3215200)Termination phase: Saturation
% 9.66/2.42 % (3215200)Time elapsed: 0.110 s
% 9.66/2.42 % (3215200)Peak memory usage: 88 MB
% 9.66/2.42 % (3215200)Instructions burned: 217 (million)
% 9.66/2.42 % (3215300)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=1261413601:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 9.66/2.42 % (3215179)Instruction limit reached!
% 9.66/2.42 % (3215179)------------------------------
% 9.66/2.42 % (3215179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215179)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215179)Termination reason: Instruction limit
% 9.66/2.42 % (3215179)Termination phase: Saturation
% 9.66/2.42 % (3215179)Time elapsed: 0.690 s
% 9.66/2.42 % (3215179)Peak memory usage: 101 MB
% 9.66/2.42 % (3215179)Instructions burned: 1188 (million)
% 9.66/2.42 % (3215300)Instruction limit reached!
% 9.66/2.42 % (3215300)------------------------------
% 9.66/2.42 % (3215300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.66/2.42 % (3215300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.66/2.42 % (3215300)CaDiCaL version: 2.1.3
% 9.66/2.42 % (3215300)Termination reason: Instruction limit
% 9.66/2.42 % (3215300)Termination phase: Saturation
% 9.66/2.42 % (3215300)Time elapsed: 0.196 s
% 9.66/2.42 % (3215300)Peak memory usage: 94 MB
% 9.66/2.42 % (3215300)Instructions burned: 318 (million)
% 9.66/2.42 % (3215356)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=1960798879:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 9.66/2.42 % (3215357)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2792029056:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 9.66/2.42 % (3215172)First to succeed.
% 9.66/2.42 % (3215172)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3215122"
% 9.66/2.42 % (3215172)Refutation found. Thanks to Tanya!
% 9.66/2.42 % SZS status Unsatisfiable for theBenchmark
% 9.66/2.42 % SZS output start Proof for theBenchmark
% See solution above
% 11.43/2.51 % (3215172)------------------------------
% 11.43/2.51 % (3215172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.43/2.51 % (3215172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.43/2.51 % (3215172)CaDiCaL version: 2.1.3
% 11.43/2.51 % (3215172)Termination reason: Refutation
% 11.43/2.51 % (3215172)Time elapsed: 1.078 s
% 11.43/2.51 % (3215172)Peak memory usage: 137 MB
% 11.43/2.51 % (3215172)Instructions burned: 1667 (million)
% 11.43/2.51 % (3215172)------------------------------
% 11.43/2.51 % (3215172)------------------------------
% 11.43/2.51 % (3215122)Success in time 1.532 s
% 11.43/2.51 % Vampire exiting
%------------------------------------------------------------------------------