%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP234-1 : 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 : n007.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 10:13:24 AM UTC 2026
% Result : Unsatisfiable 2.29s 1.10s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 32
% Syntax : Number of formulae : 200 ( 16 unt; 13 def)
% Number of atoms : 611 ( 191 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 799 ( 388 ~; 398 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 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(f5,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c7) = sk_c6
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f25,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c7) != sk_c6
| multiply(X0,sk_c7) != sk_c6
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(sk_c7,X3) != sk_c6
| multiply(X4,sk_c7) != X3
| inverse(X4) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c7) != sk_c6
| sk_c6 != multiply(X0,sk_c7)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,X3)
| multiply(X4,sk_c7) != X3
| sk_c7 != inverse(X4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( inverse(sk_c7) != sk_c6
| sk_c6 != multiply(X0,sk_c7)
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl0_4
<=> ! [X0] : sk_c6 != multiply(X0,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f59,plain,
( ! [X0] : sk_c6 != multiply(X0,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_5
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f62,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( inverse(sk_c7) != sk_c6
| spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f47,f61,f58,f55,f52,f49]) ).
fof(f66,definition,
( spl0_6
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f72,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f44,f70,f66]) ).
fof(f75,definition,
( spl0_8
<=> sk_c5 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f77,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f42,f70,f75]) ).
fof(f80,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f40,f70,f80]) ).
fof(f85,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f87,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f38,f70,f85]) ).
fof(f90,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f36,f70,f90]) ).
fof(f95,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f97,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f95,f66]) ).
fof(f99,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f32,f95,f75]) ).
fof(f100,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f30,f95,f80]) ).
fof(f101,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f28,f95,f85]) ).
fof(f102,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f26,f95,f90]) ).
fof(f112,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f61,f66]) ).
fof(f113,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f61,f75]) ).
fof(f114,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f61,f80]) ).
fof(f115,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f61,f85]) ).
fof(f116,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f61,f90]) ).
fof(f117,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_6 ),
inference(superposition,[],[f3,f68]) ).
fof(f118,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f92]) ).
fof(f121,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f123,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f117]) ).
fof(f126,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f123,f1]) ).
fof(f127,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f121,f1]) ).
fof(f135,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f126,f77]) ).
fof(f141,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f135,f82]) ).
fof(f165,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f127,f118]) ).
fof(f167,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f127,f82]) ).
fof(f169,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f127,f87]) ).
fof(f178,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f169,f92]) ).
fof(f179,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f167,f141]) ).
fof(f183,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f178,f141]) ).
fof(f184,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f179,f3]) ).
fof(f188,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f127,f183]) ).
fof(f190,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f188,f3]) ).
fof(f192,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f190,f184]) ).
fof(f198,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f165,f184]) ).
fof(f206,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f198,f192]) ).
fof(f207,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f3]) ).
fof(f208,plain,
( sk_c7 = sk_c3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f207,f190]) ).
fof(f212,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f92,f208]) ).
fof(f233,plain,
( sk_c7 != sk_c6
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f63,f212]) ).
fof(f237,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f233,f141]) ).
fof(f238,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f239,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f56,f141]) ).
fof(f241,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f239,f68]) ).
fof(f246,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f241]) ).
fof(f250,plain,
( sk_c7 != sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f246,f77]) ).
fof(f253,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f250,f192]) ).
fof(f254,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f253]) ).
fof(f293,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f53,f141]) ).
fof(f302,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f293,f68]) ).
fof(f307,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f302]) ).
fof(f310,plain,
( sk_c7 != sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f307,f77]) ).
fof(f311,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(sk_c7,multiply(X4,sk_c7)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f50,f141]) ).
fof(f315,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c7,multiply(sk_c4,sk_c7))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f311,f68]) ).
fof(f320,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c4,sk_c7))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f315]) ).
fof(f322,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f320,f126]) ).
fof(f323,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f325,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f3,f62]) ).
fof(f326,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f127,f97]) ).
fof(f328,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f326,f72]) ).
fof(f336,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c7,multiply(sk_c2,sk_c7))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f50,f72]) ).
fof(f338,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c2,sk_c7))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f336]) ).
fof(f344,definition,
( spl0_15
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f345,plain,
( sk_c7 = sk_c6
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f346,plain,
( sk_c7 != sk_c6
| spl0_15 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f348,plain,
( sk_c6 != multiply(sk_c7,sk_c6)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f338,f97]) ).
fof(f350,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_5 ),
inference(superposition,[],[f127,f325]) ).
fof(f361,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f348,f328]) ).
fof(f364,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f127,f328]) ).
fof(f366,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f364,f3]) ).
fof(f369,plain,
( ~ spl0_15
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f361,f95,f70,f49,f344]) ).
fof(f417,plain,
( sk_c6 != sk_c6
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f59,f169]) ).
fof(f421,plain,
( sk_c6 != sk_c6
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f59,f97]) ).
fof(f422,plain,
( $false
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f421]) ).
fof(f423,plain,
( ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f422]) ).
fof(f426,plain,
( $false
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f417]) ).
fof(f427,plain,
( ~ spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f426]) ).
fof(f448,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c7) )
| ~ spl0_2
| ~ spl0_15 ),
inference(forward_demodulation,[],[f53,f345]) ).
fof(f450,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[],[f448,f72]) ).
fof(f452,plain,
( sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f450]) ).
fof(f454,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f452,f97]) ).
fof(f455,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f454,f345]) ).
fof(f456,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f499,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f190,f184]) ).
fof(f504,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f499,f310]) ).
fof(f505,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f537,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f56,f72]) ).
fof(f538,plain,
( sk_c6 != multiply(sk_c2,sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f537]) ).
fof(f541,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f538,f97]) ).
fof(f542,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f634,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f350,f366]) ).
fof(f635,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f634,f3]) ).
fof(f636,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f635,f366]) ).
fof(f641,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f636,f346]) ).
fof(f642,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f641]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f93]) ).
cnf(s7,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f98]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f99]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f100]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f101]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f102]) ).
cnf(s17,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f112]) ).
cnf(s18,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s19,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f114]) ).
cnf(s20,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f115]) ).
cnf(s21,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s22,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f238]) ).
cnf(s25,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f254]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f323]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f369]) ).
cnf(s39,plain,
( ~ spl0_4
| ~ spl0_12 ),
inference(sat_conversion,[],[f423]) ).
cnf(s41,plain,
( ~ spl0_4
| ~ spl0_10 ),
inference(sat_conversion,[],[f427]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f456]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f505]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f542]) ).
cnf(s52,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f642]) ).
cnf(s53,plain,
spl0_5,
inference(rat,[],[s22,s17,s18,s19,s20,s21]) ).
cnf(s54,plain,
~ spl0_4,
inference(rat,[],[s10,s39,s41]) ).
cnf(s55,plain,
( spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s25,s3,s4,s5,s6]) ).
cnf(s56,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s25,s8,s9,s10,s11,s50,s55]) ).
cnf(s57,plain,
~ spl0_3,
inference(rat,[],[s50,s2,s7,s56]) ).
cnf(s58,plain,
( spl0_7
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s48,s3,s4,s5,s6]) ).
cnf(s60,plain,
( ~ spl0_12
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s46,s52,s53]) ).
cnf(s61,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s48,s8,s9,s10,s11,s60,s58]) ).
cnf(s62,plain,
~ spl0_2,
inference(rat,[],[s46,s52,s2,s7,s61,s53]) ).
cnf(s63,plain,
spl0_1,
inference(rat,[],[s1,s53,s54,s57,s62]) ).
cnf(s64,plain,
( ~ spl0_12
| ~ spl0_7 ),
inference(rat,[],[s34,s52,s53,s63]) ).
cnf(s65,plain,
( spl0_12
| ~ spl0_6 ),
inference(rat,[],[s32,s8,s9,s63]) ).
cnf(s66,plain,
~ spl0_6,
inference(rat,[],[s32,s3,s4,s64,s65,s63]) ).
cnf(s68,plain,
spl0_12,
inference(rat,[],[s7,s66]) ).
cnf(s69,plain,
spl0_7,
inference(rat,[],[s2,s66]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s64,s69,s68]) ).
fof(f643,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP234-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:36:10 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.29/1.10 % (1160574)Input is clausal, will run a generic CNF schedule.
% 2.29/1.10 % (1160618)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2444051524:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.29/1.10 % (1160614)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1683844831:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.29/1.10 % (1160616)lrs+10_1_sil=8000:sp=occurrence:random_seed=1674806051:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.29/1.10 % (1160612)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=776107599:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.29/1.10 % (1160617)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3708259486:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.29/1.10 % (1160613)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2751684101:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.29/1.10 % (1160619)dis-21_1_sil=8000:lcm=predicate:random_seed=1382297534: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)
% 2.29/1.10 % (1160619)Refutation not found, incomplete strategy
% 2.29/1.10 % (1160619)------------------------------
% 2.29/1.10 % (1160619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.10 % (1160619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.10 % (1160619)CaDiCaL version: 2.1.3
% 2.29/1.10 % (1160619)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.10 % (1160619)Time elapsed: 0.001 s
% 2.29/1.10 % (1160619)Peak memory usage: 88 MB
% 2.29/1.10 % (1160619)Instructions burned: 1 (million)
% 2.29/1.10 % (1160616)Refutation not found, incomplete strategy
% 2.29/1.10 % (1160616)------------------------------
% 2.29/1.10 % (1160616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.10 % (1160616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.10 % (1160616)CaDiCaL version: 2.1.3
% 2.29/1.10 % (1160616)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.10 % (1160616)Time elapsed: 0.002 s
% 2.29/1.10 % (1160616)Peak memory usage: 88 MB
% 2.29/1.10 % (1160616)Instructions burned: 2 (million)
% 2.29/1.10 % (1160618)First to succeed.
% 2.29/1.10 % (1160618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1160574"
% 2.29/1.10 % (1160617)Instruction limit reached!
% 2.29/1.10 % (1160617)------------------------------
% 2.29/1.10 % (1160617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.10 % (1160617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.10 % (1160617)CaDiCaL version: 2.1.3
% 2.29/1.10 % (1160617)Termination reason: Instruction limit
% 2.29/1.10 % (1160617)Termination phase: Saturation
% 2.29/1.10 % (1160617)Time elapsed: 0.066 s
% 2.29/1.10 % (1160617)Peak memory usage: 89 MB
% 2.29/1.10 % (1160617)Instructions burned: 115 (million)
% 2.29/1.10 % (1160692)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=3654786007:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.29/1.10 % (1160692)Refutation not found, incomplete strategy
% 2.29/1.10 % (1160692)------------------------------
% 2.29/1.10 % (1160692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.10 % (1160692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.10 % (1160692)CaDiCaL version: 2.1.3
% 2.29/1.10 % (1160692)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.10 % (1160692)Time elapsed: 0.003 s
% 2.29/1.10 % (1160692)Peak memory usage: 88 MB
% 2.29/1.10 % (1160692)Instructions burned: 7 (million)
% 2.29/1.10 % (1160619)------------------------------
% 2.29/1.10 % (1160619)------------------------------
% 2.29/1.10 % (1160616)------------------------------
% 2.29/1.10 % (1160616)------------------------------
% 2.29/1.10 % (1160618)Refutation found. Thanks to Tanya!
% 2.29/1.10 % SZS status Unsatisfiable for theBenchmark
% 2.29/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.30 % (1160618)------------------------------
% 0.18/1.30 % (1160618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (1160618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (1160618)CaDiCaL version: 2.1.3
% 0.18/1.30 % (1160618)Termination reason: Refutation
% 0.18/1.30 % (1160618)Time elapsed: 0.015 s
% 0.18/1.30 % (1160618)Peak memory usage: 89 MB
% 0.18/1.30 % (1160618)Instructions burned: 23 (million)
% 0.18/1.30 % (1160618)------------------------------
% 0.18/1.30 % (1160618)------------------------------
% 0.18/1.30 % (1160574)Success in time 0.452 s
% 0.18/1.30 % Vampire exiting
%------------------------------------------------------------------------------