%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:13:37 AM UTC 2026
% Result : Unsatisfiable 2.11s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 40
% Syntax : Number of formulae : 191 ( 19 unt; 19 def)
% Number of atoms : 496 ( 181 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 551 ( 246 ~; 286 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',associativity) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f97,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(X5,sk_c7) != sk_c9
| inverse(X5) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c7,sk_c9)
| sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) ),
inference(reorient_equations,[],[f103]) ).
fof(f106,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f107,plain,
( ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_2
<=> sk_c8 = multiply(sk_c7,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( sk_c8 != multiply(sk_c7,sk_c9)
| spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_3
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f114,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,definition,
( spl0_4
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f117,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_5
<=> ! [X2] :
( sk_c9 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f120,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_6
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f123,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3
| spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f104,f122,f116,f113,f119,f116,f113,f109,f106]) ).
fof(f127,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f129,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f131,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f133,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f102,f131,f127]) ).
fof(f136,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f138,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f100,f131,f136]) ).
fof(f140,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f98,f131,f109]) ).
fof(f142,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f147,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f149,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f152,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f157,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f159,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f162,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f164,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f88,f162,f127]) ).
fof(f166,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f86,f162,f136]) ).
fof(f167,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f84,f162,f109]) ).
fof(f173,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f175,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f179,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f68,f173,f142]) ).
fof(f180,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f66,f173,f147]) ).
fof(f184,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f190,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f184,f142]) ).
fof(f191,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f184,f147]) ).
fof(f195,definition,
( spl0_17
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f197,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f203,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f36,f195,f152]) ).
fof(f204,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f195,f157]) ).
fof(f206,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f214,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f206,f152]) ).
fof(f215,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f206,f157]) ).
fof(f216,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f122,f127]) ).
fof(f217,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f122,f136]) ).
fof(f218,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f122,f109]) ).
fof(f223,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f3,f129]) ).
fof(f228,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f230,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f223]) ).
fof(f234,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f230,f1]) ).
fof(f235,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f228,f1]) ).
fof(f242,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f234,f138]) ).
fof(f245,plain,
( sk_c8 = sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f242,f110]) ).
fof(f253,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f138,f245]) ).
fof(f254,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f110,f245]) ).
fof(f265,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f124,f254]) ).
fof(f267,plain,
( $false
| ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f265,f245]) ).
fof(f268,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f272,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f117,f154]) ).
fof(f273,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f272]) ).
fof(f274,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f273,f159]) ).
fof(f275,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f296,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f117,f197]) ).
fof(f298,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f296]) ).
fof(f299,plain,
( ~ spl0_18
| ~ spl0_4
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f298,f195,f116,f206]) ).
fof(f306,plain,
( sk_c8 != sk_c7
| sk_c9 != multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f120,f129]) ).
fof(f309,plain,
( sk_c8 != sk_c8
| sk_c9 != multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f120,f133]) ).
fof(f310,plain,
( sk_c9 != multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f309]) ).
fof(f313,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f310,f164]) ).
fof(f314,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f316,plain,
( sk_c9 != multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f306,f245]) ).
fof(f318,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f316,f253]) ).
fof(f319,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f342,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f114,f144]) ).
fof(f345,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f114,f175]) ).
fof(f348,plain,
( sk_c7 != multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f345]) ).
fof(f349,plain,
( sk_c7 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f342]) ).
fof(f351,plain,
( $false
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f348,f186]) ).
fof(f352,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f358,definition,
( spl0_23
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f359,plain,
( sk_c8 = sk_c7
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f362,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f349,f149]) ).
fof(f363,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f517,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f235,f164]) ).
fof(f523,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f517,f133]) ).
fof(f537,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f123,f523]) ).
fof(f547,plain,
( spl0_23
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f537,f162,f131,f122,f358]) ).
fof(f553,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_1
| ~ spl0_23 ),
inference(superposition,[],[f107,f359]) ).
fof(f567,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f553,f358,f106,f119]) ).
fof(f569,plain,
( sk_c8 != multiply(sk_c8,sk_c9)
| spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f111,f359]) ).
fof(f576,plain,
( $false
| spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f569,f523]) ).
fof(f577,plain,
( spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f583,plain,
( spl0_23
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f245,f136,f127,f109,f358]) ).
cnf(s1,plain,
( spl0_3
| spl0_4
| spl0_1
| spl0_3
| ~ spl0_2
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f134]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f139]) ).
cnf(s5,plain,
( spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f140]) ).
cnf(s10,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s11,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f166]) ).
cnf(s12,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f180]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f190]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f191]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s45,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f216]) ).
cnf(s46,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f217]) ).
cnf(s47,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f218]) ).
cnf(s52,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f268]) ).
cnf(s53,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f275]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f299]) ).
cnf(s57,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_14 ),
inference(sat_conversion,[],[f314]) ).
cnf(s58,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f319]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f352]) ).
cnf(s63,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f363]) ).
cnf(s67,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_23 ),
inference(sat_conversion,[],[f547]) ).
cnf(s72,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_23 ),
inference(sat_conversion,[],[f567]) ).
cnf(s73,plain,
( spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_23 ),
inference(sat_conversion,[],[f577]) ).
cnf(s74,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| spl0_23 ),
inference(sat_conversion,[],[f583]) ).
cnf(s75,plain,
spl0_2,
inference(rat,[],[s67,s73,s5,s12,s47]) ).
cnf(s76,plain,
spl0_6,
inference(rat,[],[s52,s45,s46,s75]) ).
cnf(s77,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s57,s4,s11]) ).
cnf(s78,plain,
( ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s57,s3,s10,s58,s75]) ).
cnf(s79,plain,
~ spl0_5,
inference(rat,[],[s78,s77]) ).
cnf(s81,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s53,s43,s44]) ).
cnf(s82,plain,
( ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s53,s36,s37,s56]) ).
cnf(s83,plain,
~ spl0_4,
inference(rat,[],[s82,s81]) ).
cnf(s85,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s61,s21,s28]) ).
cnf(s86,plain,
( ~ spl0_11
| ~ spl0_3 ),
inference(rat,[],[s61,s20,s27,s63]) ).
cnf(s87,plain,
~ spl0_3,
inference(rat,[],[s86,s85]) ).
cnf(s88,plain,
spl0_1,
inference(rat,[],[s2,s75,s79,s76,s83,s87]) ).
cnf(s89,plain,
~ spl0_23,
inference(rat,[],[s72,s79,s88]) ).
cnf(s91,plain,
spl0_7,
inference(rat,[],[s67,s3,s10,s76,s89]) ).
cnf(s92,plain,
~ spl0_9,
inference(rat,[],[s74,s89,s75,s91]) ).
cnf(s96,plain,
spl0_14,
inference(rat,[],[s11,s92]) ).
cnf(s97,plain,
spl0_8,
inference(rat,[],[s4,s92]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s67,s89,s76,s97,s96]) ).
fof(f585,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:49:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.11/1.30 % (4165189)Input is clausal, will run a generic CNF schedule.
% 2.11/1.30 % (4165194)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=80976131:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.11/1.30 % (4165197)lrs+10_1_sil=8000:sp=occurrence:random_seed=2264328879:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.11/1.30 % (4165195)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1798112796:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.11/1.30 % (4165200)dis-21_1_sil=8000:lcm=predicate:random_seed=2832526106:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.11/1.30 % (4165198)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2233220321:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.11/1.30 % (4165196)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=798425707:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.11/1.30 % (4165199)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1634902487:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.11/1.30 % (4165200)Refutation not found, incomplete strategy
% 2.11/1.30 % (4165200)------------------------------
% 2.11/1.30 % (4165200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.30 % (4165200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.30 % (4165200)CaDiCaL version: 2.1.3
% 2.11/1.30 % (4165200)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.30 % (4165200)Time elapsed: 0.002 s
% 2.11/1.30 % (4165200)Peak memory usage: 88 MB
% 2.11/1.30 % (4165200)Instructions burned: 2 (million)
% 2.11/1.30 % (4165197)Refutation not found, incomplete strategy
% 2.11/1.30 % (4165197)------------------------------
% 2.11/1.30 % (4165197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.30 % (4165197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.30 % (4165197)CaDiCaL version: 2.1.3
% 2.11/1.30 % (4165197)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.30 % (4165197)Time elapsed: 0.003 s
% 2.11/1.30 % (4165197)Peak memory usage: 88 MB
% 2.11/1.30 % (4165197)Instructions burned: 4 (million)
% 2.11/1.30 % (4165199)First to succeed.
% 2.11/1.30 % (4165199)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4165189"
% 2.11/1.30 % (4165198)Instruction limit reached!
% 2.11/1.30 % (4165198)------------------------------
% 2.11/1.30 % (4165198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.30 % (4165198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.30 % (4165198)CaDiCaL version: 2.1.3
% 2.11/1.30 % (4165198)Termination reason: Instruction limit
% 2.11/1.30 % (4165198)Termination phase: Saturation
% 2.11/1.30 % (4165198)Time elapsed: 0.066 s
% 2.11/1.30 % (4165198)Peak memory usage: 89 MB
% 2.11/1.30 % (4165198)Instructions burned: 115 (million)
% 2.11/1.30 % (4165208)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2148546536:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.11/1.30 % (4165208)Refutation not found, incomplete strategy
% 2.11/1.30 % (4165208)------------------------------
% 2.11/1.30 % (4165208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.30 % (4165208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.30 % (4165208)CaDiCaL version: 2.1.3
% 2.11/1.30 % (4165208)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.30 % (4165208)Time elapsed: 0.004 s
% 2.11/1.30 % (4165208)Peak memory usage: 88 MB
% 2.11/1.30 % (4165208)Instructions burned: 4 (million)
% 2.11/1.30 % (4165197)------------------------------
% 2.11/1.30 % (4165197)------------------------------
% 2.11/1.30 % (4165200)------------------------------
% 2.11/1.30 % (4165200)------------------------------
% 2.11/1.30 % (4165199)Refutation found. Thanks to Tanya!
% 2.11/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.11/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.51 % (4165199)------------------------------
% 0.17/1.51 % (4165199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (4165199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (4165199)CaDiCaL version: 2.1.3
% 0.17/1.51 % (4165199)Termination reason: Refutation
% 0.17/1.51 % (4165199)Time elapsed: 0.014 s
% 0.17/1.51 % (4165199)Peak memory usage: 89 MB
% 0.17/1.51 % (4165199)Instructions burned: 19 (million)
% 0.17/1.51 % (4165199)------------------------------
% 0.17/1.51 % (4165199)------------------------------
% 0.17/1.51 % (4165189)Success in time 0.452 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------