%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL400-10 : 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 11:52:17 AM UTC 2026
% Result : Unsatisfiable 13.57s 3.46s
% Output : Refutation 16.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 15
% Syntax : Number of formulae : 126 ( 107 unt; 9 def)
% Number of atoms : 163 ( 110 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 74 ( 37 ~; 32 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 237 ( 0 sgn 237 !; 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,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f3,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(f5,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(f7,plain,
! [X0] : true = is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(f9,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
is_a_theorem(implies(not(implies(x,y)),x)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_66) ).
fof(f11,plain,
true != is_a_theorem(implies(not(implies(x,y)),x)),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
sF0 = implies(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f13,plain,
implies(x,y) = sF0,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF1 = not(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f15,plain,
not(sF0) = sF1,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF2 = implies(sF1,x),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f17,plain,
implies(sF1,x) = sF2,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF3 = is_a_theorem(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f19,plain,
is_a_theorem(sF2) = sF3,
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
true != sF3,
inference(definition_folding,[],[f11,f19,f17,f15,f13]) ).
fof(f28,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)),true,ifeq(true,true,is_a_theorem(X1),true),true),
inference(superposition,[],[f3,f7]) ).
fof(f29,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f32,definition,
( spl4_1
<=> is_a_theorem(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f34,plain,
( is_a_theorem(sF2) = sF3
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
spl4_1,
inference(avatar_split_clause,[],[f19,f32]) ).
fof(f38,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f5]) ).
fof(f42,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f38,f1]) ).
fof(f43,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f42,f9]) ).
fof(f44,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),true),
inference(superposition,[],[f42,f7]) ).
fof(f45,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),true),
inference(superposition,[],[f42,f5]) ).
fof(f50,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),
inference(forward_demodulation,[],[f45,f1]) ).
fof(f51,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(forward_demodulation,[],[f44,f1]) ).
fof(f52,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f43,f1]) ).
fof(f55,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),true),
inference(superposition,[],[f3,f52]) ).
fof(f57,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(superposition,[],[f3,f52]) ).
fof(f58,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)),X3)),true,is_a_theorem(X3),true),
inference(forward_demodulation,[],[f57,f1]) ).
fof(f59,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),
inference(forward_demodulation,[],[f55,f1]) ).
fof(f63,definition,
( spl4_2
<=> true = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f65,plain,
( true != sF3
| spl4_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f20,f63]) ).
fof(f68,definition,
( spl4_3
<=> implies(x,y) = sF0 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f70,plain,
( implies(x,y) = sF0
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
spl4_3,
inference(avatar_split_clause,[],[f13,f68]) ).
fof(f81,definition,
( spl4_4
<=> not(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f83,plain,
( not(sF0) = sF1
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
spl4_4,
inference(avatar_split_clause,[],[f15,f81]) ).
fof(f86,definition,
( spl4_5
<=> implies(sF1,x) = sF2 ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f88,plain,
( implies(sF1,x) = sF2
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
spl4_5,
inference(avatar_split_clause,[],[f17,f86]) ).
fof(f135,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(superposition,[],[f3,f51]) ).
fof(f136,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)),X2)),true,is_a_theorem(X2),true),
inference(forward_demodulation,[],[f135,f1]) ).
fof(f163,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(X0,X0)),true),
inference(superposition,[],[f59,f7]) ).
fof(f180,plain,
! [X0] : true = is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f163,f1]) ).
fof(f195,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,ifeq(true,true,is_a_theorem(X1),true),true),
inference(superposition,[],[f3,f180]) ).
fof(f196,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f195,f1]) ).
fof(f235,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),true),
inference(superposition,[],[f3,f50]) ).
fof(f240,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)),X4)),true,ifeq(true,true,is_a_theorem(X4),true),true),
inference(superposition,[],[f3,f50]) ).
fof(f241,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)),X4)),true,is_a_theorem(X4),true),
inference(forward_demodulation,[],[f240,f1]) ).
fof(f242,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),
inference(forward_demodulation,[],[f235,f1]) ).
fof(f251,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f242,f52]) ).
fof(f252,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),true),
inference(superposition,[],[f242,f50]) ).
fof(f272,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),
inference(forward_demodulation,[],[f252,f1]) ).
fof(f273,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f251,f1]) ).
fof(f345,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),true),
inference(superposition,[],[f59,f273]) ).
fof(f361,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(forward_demodulation,[],[f345,f1]) ).
fof(f372,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),true),
inference(superposition,[],[f196,f361]) ).
fof(f390,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),
inference(forward_demodulation,[],[f372,f1]) ).
fof(f618,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f136,f272]) ).
fof(f625,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),true),
inference(superposition,[],[f3,f272]) ).
fof(f638,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),
inference(forward_demodulation,[],[f625,f1]) ).
fof(f643,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f618,f1]) ).
fof(f712,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f643]) ).
fof(f725,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f712,f1]) ).
fof(f1023,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f725,f390]) ).
fof(f1085,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1023,f1]) ).
fof(f1094,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),true),
inference(superposition,[],[f136,f1085]) ).
fof(f1135,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),
inference(forward_demodulation,[],[f1094,f1]) ).
fof(f1200,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f638,f1135]) ).
fof(f1259,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f1200,f1]) ).
fof(f1653,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),true),
inference(superposition,[],[f242,f1259]) ).
fof(f1689,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),
inference(forward_demodulation,[],[f1653,f1]) ).
fof(f1701,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f59,f1689]) ).
fof(f1738,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f1701,f1]) ).
fof(f1743,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X0),X0),X2),implies(X0,X2))),true),
inference(superposition,[],[f725,f1738]) ).
fof(f1799,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X0),X0),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1743,f1]) ).
fof(f1853,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X0,X1))),true),
inference(superposition,[],[f58,f1799]) ).
fof(f1893,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(X0,X1))),
inference(forward_demodulation,[],[f1853,f1]) ).
fof(f1909,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),true),
inference(superposition,[],[f42,f1893]) ).
fof(f1953,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1909,f1]) ).
fof(f1989,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),true),
inference(superposition,[],[f3,f1953]) ).
fof(f2006,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),
inference(forward_demodulation,[],[f1989,f1]) ).
fof(f2189,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f2006,f1689]) ).
fof(f2248,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f2189,f1]) ).
fof(f2269,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f725,f2248]) ).
fof(f2326,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f2269,f1]) ).
fof(f2553,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true),
inference(superposition,[],[f58,f2326]) ).
fof(f2556,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),true),
inference(superposition,[],[f241,f2326]) ).
fof(f2589,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[],[f2556,f1]) ).
fof(f2592,plain,
! [X0,X1] : true = is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(forward_demodulation,[],[f2553,f1]) ).
fof(f2608,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),true),
inference(superposition,[],[f42,f2592]) ).
fof(f2631,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(forward_demodulation,[],[f2608,f1]) ).
fof(f2657,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(not(X0),X2)),true),true),
inference(superposition,[],[f3,f2631]) ).
fof(f2682,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(not(X0),X2)),true),
inference(forward_demodulation,[],[f2657,f1]) ).
fof(f3087,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(implies(X0,X1)),implies(not(X0),X2))),true),
inference(superposition,[],[f2682,f2631]) ).
fof(f3157,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(not(implies(X0,X1)),implies(not(X0),X2))),
inference(forward_demodulation,[],[f3087,f1]) ).
fof(f3210,plain,
( ! [X0] : true = is_a_theorem(implies(not(sF0),implies(not(x),X0)))
| ~ spl4_3 ),
inference(superposition,[],[f3157,f70]) ).
fof(f3251,plain,
( ! [X0] : true = is_a_theorem(implies(sF1,implies(not(x),X0)))
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f3210,f83]) ).
fof(f4215,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(not(X0),X0)),implies(X1,X0))),true),
inference(superposition,[],[f29,f2589]) ).
fof(f4278,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,implies(not(X0),X0)),implies(X1,X0))),
inference(forward_demodulation,[],[f4215,f1]) ).
fof(f4303,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X0,X1)),true),true),
inference(superposition,[],[f3,f4278]) ).
fof(f4332,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f4303,f1]) ).
fof(f4387,plain,
( true = ifeq(is_a_theorem(implies(sF1,implies(not(x),x))),true,is_a_theorem(sF2),true)
| ~ spl4_5 ),
inference(superposition,[],[f4332,f88]) ).
fof(f4448,plain,
( true = ifeq(is_a_theorem(implies(sF1,implies(not(x),x))),true,sF3,true)
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f4387,f34]) ).
fof(f4488,plain,
( true = ifeq(true,true,sF3,true)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f4448,f3251]) ).
fof(f4489,plain,
( true = sF3
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f4488,f1]) ).
fof(f4490,plain,
( $false
| ~ spl4_1
| spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f4489,f65]) ).
fof(f4491,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f4490]) ).
cnf(s1,plain,
spl4_1,
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f66]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f89]) ).
cnf(s11,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f4491]) ).
cnf(s16,plain,
~ spl4_1,
inference(rat,[],[s11,s5,s4,s3,s2]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s16]) ).
fof(f4492,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n018.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 15:42:23 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 13.57/3.46 % (2531627)Detected a unit-equality problem, will run specialized UEQ schedule.
% 13.57/3.46 % (2531632)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=2639899051:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 13.57/3.46 % (2531633)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=1580709309:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 13.57/3.46 % (2531634)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2100876056:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 13.57/3.46 % (2531636)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1634071035:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 13.57/3.46 % (2531637)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=416937937:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 13.57/3.46 % (2531635)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2461133733:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 13.57/3.46 % (2531638)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3677649121:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 13.57/3.46 % (2531635)Instruction limit reached!
% 13.57/3.46 % (2531635)------------------------------
% 13.57/3.46 % (2531635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531635)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531635)Termination reason: Instruction limit
% 13.57/3.46 % (2531635)Termination phase: Saturation
% 13.57/3.46 % (2531635)Time elapsed: 0.128 s
% 13.57/3.46 % (2531635)Peak memory usage: 89 MB
% 13.57/3.46 % (2531635)Instructions burned: 136 (million)
% 13.57/3.46 % (2531636)Instruction limit reached!
% 13.57/3.46 % (2531636)------------------------------
% 13.57/3.46 % (2531636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531636)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531636)Termination reason: Instruction limit
% 13.57/3.46 % (2531636)Termination phase: Saturation
% 13.57/3.46 % (2531636)Time elapsed: 0.174 s
% 13.57/3.46 % (2531636)Peak memory usage: 90 MB
% 13.57/3.46 % (2531636)Instructions burned: 181 (million)
% 13.57/3.46 % (2531637)Instruction limit reached!
% 13.57/3.46 % (2531637)------------------------------
% 13.57/3.46 % (2531637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531637)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531637)Termination reason: Instruction limit
% 13.57/3.46 % (2531637)Termination phase: Saturation
% 13.57/3.46 % (2531637)Time elapsed: 0.257 s
% 13.57/3.46 % (2531637)Peak memory usage: 91 MB
% 13.57/3.46 % (2531637)Instructions burned: 258 (million)
% 13.57/3.46 % (2531646)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2054311209:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 13.57/3.46 % (2531647)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1399156152:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 13.57/3.46 % (2531648)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3725315836:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 13.57/3.46 % (2531648)Instruction limit reached!
% 13.57/3.46 % (2531648)------------------------------
% 13.57/3.46 % (2531648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531648)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531648)Termination reason: Instruction limit
% 13.57/3.46 % (2531648)Termination phase: Saturation
% 13.57/3.46 % (2531648)Time elapsed: 0.186 s
% 13.57/3.46 % (2531648)Peak memory usage: 88 MB
% 13.57/3.46 % (2531648)Instructions burned: 215 (million)
% 13.57/3.46 % (2531652)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=1849136266: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)
% 13.57/3.46 % (2531638)Instruction limit reached!
% 13.57/3.46 % (2531638)------------------------------
% 13.57/3.46 % (2531638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531638)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531638)Termination reason: Instruction limit
% 13.57/3.46 % (2531638)Termination phase: Saturation
% 13.57/3.46 % (2531638)Time elapsed: 1.070 s
% 13.57/3.46 % (2531638)Peak memory usage: 98 MB
% 13.57/3.46 % (2531638)Instructions burned: 1187 (million)
% 13.57/3.46 % (2531652)Instruction limit reached!
% 13.57/3.46 % (2531652)------------------------------
% 13.57/3.46 % (2531652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.57/3.46 % (2531652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.57/3.46 % (2531652)CaDiCaL version: 2.1.3
% 13.57/3.46 % (2531652)Termination reason: Instruction limit
% 13.57/3.46 % (2531652)Termination phase: Saturation
% 13.57/3.46 % (2531652)Time elapsed: 0.298 s
% 13.57/3.46 % (2531652)Peak memory usage: 93 MB
% 13.57/3.46 % (2531652)Instructions burned: 317 (million)
% 13.57/3.46 % (2531654)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=1109473433:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 13.57/3.46 % (2531632)First to succeed.
% 13.57/3.46 % (2531632)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2531627"
% 13.57/3.46 % (2531656)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1470241021:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2983 on theBenchmark for (2983ds/2836Mi)
% 13.57/3.46 % (2531633)Also succeeded, but the first one will report.
% 13.57/3.46 % (2531634)Also succeeded, but the first one will report.
% 13.57/3.46 % (2531646)Also succeeded, but the first one will report.
% 13.57/3.46 % (2531632)Refutation found. Thanks to Tanya!
% 13.57/3.46 % SZS status Unsatisfiable for theBenchmark
% 13.57/3.46 % SZS output start Proof for theBenchmark
% See solution above
% 16.25/3.72 % (2531632)------------------------------
% 16.25/3.72 % (2531632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.25/3.72 % (2531632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.25/3.72 % (2531632)CaDiCaL version: 2.1.3
% 16.25/3.72 % (2531632)Termination reason: Refutation
% 16.25/3.72 % (2531632)Time elapsed: 1.511 s
% 16.25/3.72 % (2531632)Peak memory usage: 137 MB
% 16.25/3.72 % (2531632)Instructions burned: 1786 (million)
% 16.25/3.72 % (2531632)------------------------------
% 16.25/3.72 % (2531632)------------------------------
% 16.25/3.72 % (2531627)Success in time 2.188 s
% 16.25/3.72 % Vampire exiting
%------------------------------------------------------------------------------