%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL341-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 11:52:02 AM UTC 2026
% Result : Unsatisfiable 8.79s 2.33s
% Output : Refutation 10.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 38
% Syntax : Number of formulae : 176 ( 111 unt; 26 def)
% Number of atoms : 324 ( 140 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 288 ( 140 ~; 134 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-4 aty)
% Number of variables : 132 ( 0 sgn 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))) = true,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f12,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f17,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f18,negated_conjecture,
theorem(implies(p,equivalent(implies(p,q),q))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f19,plain,
true != theorem(implies(p,equivalent(implies(p,q),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(p),not(or(not(or(not(or(not(p),q)),q)),not(or(not(q),or(not(p),q))))))),
inference(definition_unfolding,[],[f19,f11,f20,f11]) ).
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 = or(sF0,q),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f31,plain,
or(sF0,q) = sF1,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF2 = not(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f33,plain,
not(sF1) = sF2,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF3 = or(sF2,q),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f35,plain,
or(sF2,q) = sF3,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF4 = not(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f37,plain,
not(sF3) = sF4,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF5 = not(q),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f39,plain,
not(q) = sF5,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF6 = or(sF5,sF1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f41,plain,
or(sF5,sF1) = sF6,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF7 = not(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f43,plain,
not(sF6) = sF7,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF8 = or(sF4,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f45,plain,
or(sF4,sF7) = sF8,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF9 = not(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f47,plain,
not(sF8) = sF9,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF10 = or(sF0,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f49,plain,
or(sF0,sF9) = sF10,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF11 = theorem(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f51,plain,
theorem(sF10) = sF11,
inference(reorient_equations,[],[f50]) ).
fof(f52,plain,
true != sF11,
inference(definition_folding,[],[f27,f51,f49,f47,f45,f43,f41,f31,f29,f39,f37,f35,f33,f31,f29,f29]) ).
fof(f54,definition,
( spl12_1
<=> theorem(sF10) = sF11 ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f56,plain,
( theorem(sF10) = sF11
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
spl12_1,
inference(avatar_split_clause,[],[f51,f54]) ).
fof(f58,plain,
( ! [X0] : true = ifeq(theorem(or(not(X0),sF10)),true,ifeq(theorem(X0),true,sF11,true),true)
| ~ spl12_1 ),
inference(superposition,[],[f26,f56]) ).
fof(f61,definition,
( spl12_2
<=> true = sF11 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f63,plain,
( true != sF11
| spl12_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
~ spl12_2,
inference(avatar_split_clause,[],[f52,f61]) ).
fof(f66,definition,
( spl12_3
<=> not(q) = sF5 ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f68,plain,
( not(q) = sF5
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
spl12_3,
inference(avatar_split_clause,[],[f39,f66]) ).
fof(f80,definition,
( spl12_5
<=> not(sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f82,plain,
( not(sF1) = sF2
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
spl12_5,
inference(avatar_split_clause,[],[f33,f80]) ).
fof(f87,definition,
( spl12_6
<=> not(sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f89,plain,
( not(sF3) = sF4
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
spl12_6,
inference(avatar_split_clause,[],[f37,f87]) ).
fof(f94,definition,
( spl12_7
<=> not(sF8) = sF9 ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f96,plain,
( not(sF8) = sF9
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
spl12_7,
inference(avatar_split_clause,[],[f47,f94]) ).
fof(f100,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true),
inference(superposition,[],[f13,f23]) ).
fof(f101,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,X0)),X0)),true),
inference(superposition,[],[f13,f21]) ).
fof(f102,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(f103,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X1,X0))),true),
inference(superposition,[],[f13,f22]) ).
fof(f105,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X1,X0))),
inference(forward_demodulation,[],[f103,f1]) ).
fof(f106,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(forward_demodulation,[],[f102,f1]) ).
fof(f107,plain,
! [X0] : true = theorem(or(not(or(X0,X0)),X0)),
inference(forward_demodulation,[],[f101,f1]) ).
fof(f108,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(forward_demodulation,[],[f100,f1]) ).
fof(f109,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),true),
inference(superposition,[],[f26,f108]) ).
fof(f115,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),
inference(forward_demodulation,[],[f109,f1]) ).
fof(f129,definition,
( spl12_8
<=> not(sF6) = sF7 ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f131,plain,
( not(sF6) = sF7
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
spl12_8,
inference(avatar_split_clause,[],[f43,f129]) ).
fof(f134,plain,
( ! [X0] : true = ifeq(theorem(or(sF7,X0)),true,ifeq(theorem(sF6),true,theorem(X0),true),true)
| ~ spl12_8 ),
inference(superposition,[],[f26,f131]) ).
fof(f136,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,f106]) ).
fof(f142,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),
inference(forward_demodulation,[],[f136,f1]) ).
fof(f169,definition,
( spl12_9
<=> or(sF5,sF1) = sF6 ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f171,plain,
( or(sF5,sF1) = sF6
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
spl12_9,
inference(avatar_split_clause,[],[f41,f169]) ).
fof(f190,definition,
( spl12_10
<=> or(sF2,q) = sF3 ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f192,plain,
( or(sF2,q) = sF3
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
spl12_10,
inference(avatar_split_clause,[],[f35,f190]) ).
fof(f205,plain,
( ! [X0] : true = ifeq(theorem(or(sF2,or(X0,q))),true,theorem(or(X0,sF3)),true)
| ~ spl12_10 ),
inference(superposition,[],[f142,f192]) ).
fof(f211,definition,
( spl12_11
<=> or(sF0,sF9) = sF10 ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f213,plain,
( or(sF0,sF9) = sF10
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
spl12_11,
inference(avatar_split_clause,[],[f49,f211]) ).
fof(f228,definition,
( spl12_12
<=> or(sF0,q) = sF1 ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f230,plain,
( or(sF0,q) = sF1
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
spl12_12,
inference(avatar_split_clause,[],[f31,f228]) ).
fof(f237,plain,
( true = theorem(or(not(q),sF1))
| ~ spl12_12 ),
inference(superposition,[],[f105,f230]) ).
fof(f245,plain,
( true = theorem(or(sF5,sF1))
| ~ spl12_3
| ~ spl12_12 ),
inference(forward_demodulation,[],[f237,f68]) ).
fof(f248,plain,
( true = theorem(sF6)
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12 ),
inference(forward_demodulation,[],[f245,f171]) ).
fof(f250,plain,
( ! [X0] : true = ifeq(theorem(or(sF7,X0)),true,ifeq(true,true,theorem(X0),true),true)
| ~ spl12_3
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12 ),
inference(backward_demodulation,[],[f134,f248]) ).
fof(f251,plain,
( ! [X0] : true = ifeq(theorem(or(sF7,X0)),true,theorem(X0),true)
| ~ spl12_3
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12 ),
inference(forward_demodulation,[],[f250,f1]) ).
fof(f253,definition,
( spl12_13
<=> or(sF4,sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f255,plain,
( or(sF4,sF7) = sF8
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
spl12_13,
inference(avatar_split_clause,[],[f45,f253]) ).
fof(f287,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(f288,plain,
! [X2,X0,X1] : true = theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(forward_demodulation,[],[f287,f1]) ).
fof(f346,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,f288]) ).
fof(f358,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,[],[f346,f1]) ).
fof(f371,plain,
( ! [X0,X1] : true = ifeq(theorem(or(sF4,X0)),true,theorem(or(not(or(X1,sF3)),or(X1,X0))),true)
| ~ spl12_6 ),
inference(superposition,[],[f358,f89]) ).
fof(f374,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f358,f108]) ).
fof(f378,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),true),
inference(superposition,[],[f358,f107]) ).
fof(f382,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF7),X0)),true,theorem(or(not(sF8),or(sF4,X0))),true)
| ~ spl12_13 ),
inference(superposition,[],[f358,f255]) ).
fof(f396,plain,
( ! [X0] : true = ifeq(theorem(or(not(sF7),X0)),true,theorem(or(sF9,or(sF4,X0))),true)
| ~ spl12_7
| ~ spl12_13 ),
inference(forward_demodulation,[],[f382,f96]) ).
fof(f399,plain,
! [X0,X1] : true = theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),
inference(forward_demodulation,[],[f378,f1]) ).
fof(f403,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f374,f1]) ).
fof(f446,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),true),
inference(superposition,[],[f26,f399]) ).
fof(f457,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),
inference(forward_demodulation,[],[f446,f1]) ).
fof(f503,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(X0),X0)),true),
inference(superposition,[],[f457,f105]) ).
fof(f529,plain,
! [X0] : true = theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f503,f1]) ).
fof(f534,plain,
( true = theorem(or(sF2,sF1))
| ~ spl12_5 ),
inference(superposition,[],[f529,f82]) ).
fof(f582,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,f403]) ).
fof(f597,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f582,f1]) ).
fof(f605,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X0,X1))),true),
inference(superposition,[],[f597,f105]) ).
fof(f638,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X0,X1))),
inference(forward_demodulation,[],[f605,f1]) ).
fof(f971,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(X0,or(not(X0),X1))),true),
inference(superposition,[],[f142,f638]) ).
fof(f988,plain,
! [X0,X1] : true = theorem(or(X0,or(not(X0),X1))),
inference(forward_demodulation,[],[f971,f1]) ).
fof(f1092,plain,
( ! [X0] : true = ifeq(true,true,theorem(or(not(sF7),X0)),true)
| ~ spl12_3
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12 ),
inference(superposition,[],[f251,f988]) ).
fof(f1113,plain,
( ! [X0] : true = theorem(or(not(sF7),X0))
| ~ spl12_3
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12 ),
inference(forward_demodulation,[],[f1092,f1]) ).
fof(f1116,plain,
( ! [X0] : true = ifeq(true,true,theorem(or(sF9,or(sF4,X0))),true)
| ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(backward_demodulation,[],[f396,f1113]) ).
fof(f1117,plain,
( ! [X0] : true = theorem(or(sF9,or(sF4,X0)))
| ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(forward_demodulation,[],[f1116,f1]) ).
fof(f1124,plain,
( true = ifeq(true,true,theorem(or(sF9,sF4)),true)
| ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(superposition,[],[f457,f1117]) ).
fof(f1141,plain,
( true = theorem(or(sF9,sF4))
| ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(forward_demodulation,[],[f1124,f1]) ).
fof(f1979,definition,
( spl12_21
<=> true = theorem(or(sF9,sF4)) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
fof(f1981,plain,
( true = theorem(or(sF9,sF4))
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f1979]) ).
fof(f1982,plain,
( spl12_21
| ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f1141,f253,f228,f169,f129,f94,f66,f1979]) ).
fof(f1984,plain,
( true = ifeq(true,true,theorem(or(sF4,sF9)),true)
| ~ spl12_21 ),
inference(superposition,[],[f115,f1981]) ).
fof(f2007,plain,
( true = theorem(or(sF4,sF9))
| ~ spl12_21 ),
inference(forward_demodulation,[],[f1984,f1]) ).
fof(f2212,plain,
( true = ifeq(theorem(or(sF4,sF9)),true,theorem(or(not(or(sF0,sF3)),sF10)),true)
| ~ spl12_6
| ~ spl12_11 ),
inference(superposition,[],[f371,f213]) ).
fof(f2229,plain,
( true = ifeq(true,true,theorem(or(not(or(sF0,sF3)),sF10)),true)
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21 ),
inference(forward_demodulation,[],[f2212,f2007]) ).
fof(f2234,plain,
( true = theorem(or(not(or(sF0,sF3)),sF10))
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21 ),
inference(forward_demodulation,[],[f2229,f1]) ).
fof(f2260,plain,
( true = ifeq(theorem(or(sF2,sF1)),true,theorem(or(sF0,sF3)),true)
| ~ spl12_10
| ~ spl12_12 ),
inference(superposition,[],[f205,f230]) ).
fof(f2270,plain,
( true = ifeq(true,true,theorem(or(sF0,sF3)),true)
| ~ spl12_5
| ~ spl12_10
| ~ spl12_12 ),
inference(forward_demodulation,[],[f2260,f534]) ).
fof(f2272,plain,
( true = theorem(or(sF0,sF3))
| ~ spl12_5
| ~ spl12_10
| ~ spl12_12 ),
inference(forward_demodulation,[],[f2270,f1]) ).
fof(f2275,definition,
( spl12_23
<=> true = theorem(or(sF0,sF3)) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
fof(f2277,plain,
( true = theorem(or(sF0,sF3))
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f2278,plain,
( spl12_23
| ~ spl12_5
| ~ spl12_10
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f2272,f228,f190,f80,f2275]) ).
fof(f2293,plain,
( true = ifeq(theorem(or(not(or(sF0,sF3)),sF10)),true,ifeq(true,true,sF11,true),true)
| ~ spl12_1
| ~ spl12_23 ),
inference(superposition,[],[f58,f2277]) ).
fof(f2301,plain,
( true = ifeq(theorem(or(not(or(sF0,sF3)),sF10)),true,sF11,true)
| ~ spl12_1
| ~ spl12_23 ),
inference(forward_demodulation,[],[f2293,f1]) ).
fof(f2309,plain,
( true = ifeq(true,true,sF11,true)
| ~ spl12_1
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21
| ~ spl12_23 ),
inference(forward_demodulation,[],[f2301,f2234]) ).
fof(f2313,plain,
( true = sF11
| ~ spl12_1
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21
| ~ spl12_23 ),
inference(forward_demodulation,[],[f2309,f1]) ).
fof(f2314,plain,
( $false
| ~ spl12_1
| spl12_2
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21
| ~ spl12_23 ),
inference(forward_subsumption_resolution,[],[f2313,f63]) ).
fof(f2315,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21
| ~ spl12_23 ),
inference(avatar_contradiction_clause,[],[f2314]) ).
cnf(s1,plain,
spl12_1,
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
spl12_3,
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
spl12_5,
inference(sat_conversion,[],[f83]) ).
cnf(s6,plain,
spl12_6,
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
spl12_7,
inference(sat_conversion,[],[f97]) ).
cnf(s8,plain,
spl12_8,
inference(sat_conversion,[],[f132]) ).
cnf(s9,plain,
spl12_9,
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
spl12_10,
inference(sat_conversion,[],[f193]) ).
cnf(s11,plain,
spl12_11,
inference(sat_conversion,[],[f214]) ).
cnf(s12,plain,
spl12_12,
inference(sat_conversion,[],[f231]) ).
cnf(s13,plain,
spl12_13,
inference(sat_conversion,[],[f256]) ).
cnf(s21,plain,
( ~ spl12_3
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13
| spl12_21 ),
inference(sat_conversion,[],[f1982]) ).
cnf(s23,plain,
( ~ spl12_5
| ~ spl12_10
| ~ spl12_12
| spl12_23 ),
inference(sat_conversion,[],[f2278]) ).
cnf(s24,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_6
| ~ spl12_11
| ~ spl12_21
| ~ spl12_23 ),
inference(sat_conversion,[],[f2315]) ).
cnf(s25,plain,
spl12_23,
inference(rat,[],[s23,s10,s12,s5]) ).
cnf(s30,plain,
spl12_21,
inference(rat,[],[s21,s7,s13,s12,s9,s8,s3]) ).
cnf(s35,plain,
~ spl12_1,
inference(rat,[],[s24,s25,s30,s11,s6,s2]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s1,s35]) ).
fof(f2316,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL341-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n003.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 15:37:26 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 8.79/2.33 % (720327)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.79/2.33 % (720332)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=3491828072:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.79/2.33 % (720334)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2034203107:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.79/2.33 % (720336)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3126704173:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.79/2.33 % (720333)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=419490921:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.79/2.33 % (720337)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3893086438:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.79/2.33 % (720335)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2774200608:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.79/2.33 % (720338)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1538106939:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.79/2.33 % (720335)Instruction limit reached!
% 8.79/2.33 % (720335)------------------------------
% 8.79/2.33 % (720335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.33 % (720335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.33 % (720335)CaDiCaL version: 2.1.3
% 8.79/2.33 % (720335)Termination reason: Instruction limit
% 8.79/2.33 % (720335)Termination phase: Saturation
% 8.79/2.33 % (720335)Time elapsed: 0.136 s
% 8.79/2.33 % (720335)Peak memory usage: 89 MB
% 8.79/2.33 % (720335)Instructions burned: 136 (million)
% 8.79/2.33 % (720336)Instruction limit reached!
% 8.79/2.33 % (720336)------------------------------
% 8.79/2.33 % (720336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.33 % (720336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.33 % (720336)CaDiCaL version: 2.1.3
% 8.79/2.33 % (720336)Termination reason: Instruction limit
% 8.79/2.33 % (720336)Termination phase: Saturation
% 8.79/2.33 % (720336)Time elapsed: 0.181 s
% 8.79/2.33 % (720336)Peak memory usage: 89 MB
% 8.79/2.33 % (720336)Instructions burned: 181 (million)
% 8.79/2.33 % (720337)Instruction limit reached!
% 8.79/2.33 % (720337)------------------------------
% 8.79/2.33 % (720337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.33 % (720337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.33 % (720337)CaDiCaL version: 2.1.3
% 8.79/2.33 % (720337)Termination reason: Instruction limit
% 8.79/2.33 % (720337)Termination phase: Saturation
% 8.79/2.33 % (720337)Time elapsed: 0.252 s
% 8.79/2.33 % (720337)Peak memory usage: 91 MB
% 8.79/2.33 % (720337)Instructions burned: 257 (million)
% 8.79/2.33 % (720346)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1049996307:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 8.79/2.33 % (720347)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3212744012:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 8.79/2.33 % (720348)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2748447424:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 8.79/2.33 % (720348)Instruction limit reached!
% 8.79/2.33 % (720348)------------------------------
% 8.79/2.33 % (720348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.33 % (720348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.33 % (720348)CaDiCaL version: 2.1.3
% 8.79/2.33 % (720348)Termination reason: Instruction limit
% 8.79/2.33 % (720348)Termination phase: Saturation
% 8.79/2.33 % (720348)Time elapsed: 0.181 s
% 8.79/2.33 % (720348)Peak memory usage: 88 MB
% 8.79/2.33 % (720348)Instructions burned: 215 (million)
% 8.79/2.33 % (720332)First to succeed.
% 8.79/2.33 % (720332)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-720327"
% 8.79/2.33 % (720352)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=387533310:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 8.79/2.33 % (720332)Refutation found. Thanks to Tanya!
% 8.79/2.33 % SZS status Unsatisfiable for theBenchmark
% 8.79/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 10.52/2.53 % (720332)------------------------------
% 10.52/2.53 % (720332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.53 % (720332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.53 % (720332)CaDiCaL version: 2.1.3
% 10.52/2.53 % (720332)Termination reason: Refutation
% 10.52/2.53 % (720332)Time elapsed: 0.905 s
% 10.52/2.53 % (720332)Peak memory usage: 135 MB
% 10.52/2.53 % (720332)Instructions burned: 1517 (million)
% 10.52/2.53 % (720332)------------------------------
% 10.52/2.53 % (720332)------------------------------
% 10.52/2.53 % (720327)Success in time 1.386 s
% 10.52/2.53 % Vampire exiting
%------------------------------------------------------------------------------