%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:17:17 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 31
% Syntax : Number of formulae : 191 ( 19 unt; 14 def)
% Number of atoms : 548 ( 175 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 678 ( 321 ~; 343 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c5) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f44,definition,
( spl0_1
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( sk_c6 != inverse(sk_c5)
| spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f49,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f52,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c5)
| sk_c6 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f55,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f48,f54,f51,f48,f44]) ).
fof(f58,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c3,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f58,f44]) ).
fof(f63,definition,
( spl0_6
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f65,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f68,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f70,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f73,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f75,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f34,f73,f44]) ).
fof(f80,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f28,f80,f44]) ).
fof(f84,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f26,f80,f63]) ).
fof(f85,plain,
( spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f24,f80,f68]) ).
fof(f87,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f89,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f20,f87,f63]) ).
fof(f92,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f18,f87,f68]) ).
fof(f94,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_1
| spl0_11 ),
inference(avatar_split_clause,[],[f16,f94,f44]) ).
fof(f98,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f14,f94,f63]) ).
fof(f99,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f12,f94,f68]) ).
fof(f101,definition,
( spl0_12
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f103,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f10,f101,f44]) ).
fof(f105,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f8,f101,f63]) ).
fof(f106,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f6,f101,f68]) ).
fof(f107,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f75]) ).
fof(f108,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f82]) ).
fof(f112,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f113,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f103]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f112,f1]) ).
fof(f119,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f107]) ).
fof(f120,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f119,f1]) ).
fof(f129,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f120,f60]) ).
fof(f155,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f116,f3]) ).
fof(f156,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f116,f116]) ).
fof(f157,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f116,f103]) ).
fof(f163,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_9 ),
inference(superposition,[],[f116,f108]) ).
fof(f164,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f116,f107]) ).
fof(f177,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f157,f96]) ).
fof(f178,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f155,f156]) ).
fof(f179,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f113,f177]) ).
fof(f180,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f116,f177]) ).
fof(f182,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f180,f3]) ).
fof(f183,plain,
( multiply(sk_c1,sk_c7) = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f179,f129]) ).
fof(f184,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f183,f103]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f182]) ).
fof(f192,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f182]) ).
fof(f197,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f192,f3]) ).
fof(f198,plain,
( sk_c6 = sk_c2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f197,f182]) ).
fof(f201,plain,
( sk_c6 != inverse(sk_c6)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f46,f184]) ).
fof(f209,plain,
( sk_c2 = sk_c3
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f163,f164]) ).
fof(f214,plain,
( sk_c6 = sk_c3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f209,f198]) ).
fof(f223,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f75,f214]) ).
fof(f224,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f223,f201]) ).
fof(f225,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f232,plain,
( identity != sk_c6
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f49,f3]) ).
fof(f233,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f49,f103]) ).
fof(f234,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f235,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f234,f96]) ).
fof(f236,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f245,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f89,f198]) ).
fof(f246,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f82,f198]) ).
fof(f314,plain,
( sk_c6 = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f190]) ).
fof(f322,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_1 ),
inference(superposition,[],[f3,f45]) ).
fof(f327,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f65]) ).
fof(f349,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c5))
| ~ spl0_3 ),
inference(superposition,[],[f52,f3]) ).
fof(f352,plain,
( sk_c6 != inverse(inverse(sk_c5))
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f349,f182]) ).
fof(f355,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f352,f45]) ).
fof(f357,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f355,f246]) ).
fof(f358,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f361,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f55,f314]) ).
fof(f368,plain,
( identity != sk_c6
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f361,f3]) ).
fof(f376,plain,
( sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f368,f182]) ).
fof(f385,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f376,f246]) ).
fof(f388,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f385,f246]) ).
fof(f389,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f396,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_4 ),
inference(superposition,[],[f55,f1]) ).
fof(f409,definition,
( spl0_18
<=> sk_c6 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f410,plain,
( sk_c6 = inverse(identity)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( sk_c6 != inverse(identity)
| spl0_18 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f413,definition,
( spl0_19
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f414,plain,
( sk_c6 = sk_c5
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f415,plain,
( sk_c6 != sk_c5
| spl0_19 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f416,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f396,f54,f413,f409]) ).
fof(f426,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_6 ),
inference(superposition,[],[f116,f327]) ).
fof(f429,plain,
( sk_c4 = inverse(sk_c7)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f426,f178]) ).
fof(f432,plain,
( identity = multiply(sk_c4,sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f3,f429]) ).
fof(f433,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f432,f70]) ).
fof(f435,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f1,f433]) ).
fof(f441,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_6
| ~ spl0_7
| spl0_18 ),
inference(forward_demodulation,[],[f411,f433]) ).
fof(f443,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_19 ),
inference(superposition,[],[f45,f414]) ).
fof(f447,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f443,f441]) ).
fof(f448,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f452,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f232,f433]) ).
fof(f453,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f410,f433]) ).
fof(f456,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f452,f429]) ).
fof(f458,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f456,f65]) ).
fof(f459,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f462,plain,
( sk_c6 != inverse(inverse(sk_c5))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f349,f433]) ).
fof(f464,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f462,f45]) ).
fof(f470,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f464,f453]) ).
fof(f471,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f470]) ).
fof(f576,plain,
( identity = sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f435,f322]) ).
fof(f587,plain,
( sk_c6 = sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f576,f433]) ).
fof(f590,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f587,f415]) ).
fof(f591,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f590]) ).
cnf(s1,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f76]) ).
cnf(s9,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s10,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s11,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f85]) ).
cnf(s13,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f91]) ).
cnf(s14,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s15,plain,
( spl0_1
| spl0_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s18,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f225]) ).
cnf(s22,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f236]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f358]) ).
cnf(s39,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f389]) ).
cnf(s42,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f416]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f448]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f459]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(sat_conversion,[],[f471]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_19 ),
inference(sat_conversion,[],[f591]) ).
cnf(s55,plain,
spl0_1,
inference(rat,[],[s21,s3,s6,s9,s15,s18]) ).
cnf(s57,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s39,s10,s13,s16,s19]) ).
cnf(s58,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s42,s44,s54,s57,s55]) ).
cnf(s59,plain,
~ spl0_4,
inference(rat,[],[s39,s11,s14,s17,s20,s58]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s49,s44,s54,s55]) ).
cnf(s61,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s11,s33,s17,s20,s55]) ).
cnf(s62,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s33,s10,s16,s19,s60,s55]) ).
cnf(s63,plain,
~ spl0_3,
inference(rat,[],[s62,s61]) ).
cnf(s64,plain,
spl0_2,
inference(rat,[],[s2,s59,s55,s63]) ).
cnf(s65,plain,
spl0_7,
inference(rat,[],[s22,s17,s20,s64]) ).
cnf(s66,plain,
~ spl0_6,
inference(rat,[],[s46,s64,s65]) ).
cnf(s67,plain,
spl0_12,
inference(rat,[],[s19,s66]) ).
cnf(s68,plain,
spl0_11,
inference(rat,[],[s16,s66]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s22,s64,s68,s67]) ).
fof(f592,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 % Computer : n018.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 09:45:09 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.41 Running first-order model finding
% 0.08/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47 % (2084904)Will run a generic schedule for satisfiability detection.
% 0.13/0.47 % (2084915)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1325660493:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.47 % (2084910)% WARNING: option uhcvi not known.
% 0.13/0.47 % (2084909)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3496513882_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.47 % (2084910)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=338608202:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.47 % (2084911)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1223439686:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.47 % (2084912)dis+10_1_sil=32000:sp=arity:random_seed=2276599445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.47 % (2084914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4167882674:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.47 % (2084913)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2780463557:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.47 % TRYING [1]
% 0.13/0.47 % TRYING [2]
% 0.13/0.47 % TRYING [3]
% 0.13/0.47 % TRYING [4]
% 0.13/0.47 % (2084912) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2084904-2084912"...
% 0.13/0.47 % (2084913) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2084904-2084913"...
% 0.13/0.47 % (2084914) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2084904-2084914"...
% 0.13/0.47 % (2084912)...printing done.
% 0.13/0.47 % TRYING [5]
% 0.13/0.47 % (2084913)...printing done.
% 0.13/0.47 % (2084914)...printing done.
% 0.13/0.47 % (2084913)Refutation found. Thanks to Tanya!
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.47 % (2084913)------------------------------
% 0.13/0.47 % (2084913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.47 % (2084913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.47 % (2084913)CaDiCaL version: 2.1.3
% 0.13/0.47 % (2084913)Termination reason: Refutation
% 0.13/0.47 % (2084913)Time elapsed: 0.014 s
% 0.13/0.47 % (2084913)Peak memory usage: 12 MB
% 0.13/0.47 % (2084913)Instructions burned: 19 (million)
% 0.13/0.47 % (2084904)Success in time 0.056 s
% 0.13/0.47 % Vampire exiting
%------------------------------------------------------------------------------