%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 10:13:21 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.28s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of formulae : 158 ( 14 unt; 12 def)
% Number of atoms : 437 ( 162 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 544 ( 265 ~; 267 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = inverse(sk_c1)
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c2) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(sk_c7,X1) != sk_c6
| multiply(X2,sk_c7) != X3
| inverse(X2) != sk_c7
| multiply(X4,X3) != sk_c6
| inverse(X4) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,X1)
| multiply(X2,sk_c7) != X3
| sk_c7 != inverse(X2)
| sk_c6 != multiply(X4,X3)
| inverse(X4) != X3 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,X1)
| sk_c7 != inverse(X2)
| sk_c6 != multiply(X4,multiply(X2,sk_c7))
| multiply(X2,sk_c7) != inverse(X4) ),
inference(equality_resolution,[],[f29]) ).
fof(f32,definition,
( spl0_1
<=> ! [X2,X4] :
( sk_c7 != inverse(X2)
| multiply(X2,sk_c7) != inverse(X4)
| sk_c6 != multiply(X4,multiply(X2,sk_c7)) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f33,plain,
( ! [X2,X4] :
( sk_c7 != inverse(X2)
| multiply(X2,sk_c7) != inverse(X4)
| sk_c6 != multiply(X4,multiply(X2,sk_c7)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,definition,
( spl0_2
<=> ! [X1] : sk_c6 != multiply(sk_c7,X1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f36,plain,
( ! [X1] : sk_c6 != multiply(sk_c7,X1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,definition,
( spl0_3
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f30,f38,f35,f32]) ).
fof(f42,definition,
( spl0_4
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f44,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f46,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f27,f46,f42]) ).
fof(f51,definition,
( spl0_6
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f25,f46,f51]) ).
fof(f56,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f23,f46,f56]) ).
fof(f61,definition,
( spl0_8
<=> multiply(sk_c3,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f66,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f68,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f19,f66,f42]) ).
fof(f70,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f17,f66,f51]) ).
fof(f71,plain,
( spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f15,f66,f56]) ).
fof(f72,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f13,f66,f61]) ).
fof(f74,definition,
( spl0_10
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f76,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f11,f74,f42]) ).
fof(f78,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f9,f74,f51]) ).
fof(f79,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f7,f74,f56]) ).
fof(f80,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f5,f74,f61]) ).
fof(f81,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_4 ),
inference(superposition,[],[f3,f44]) ).
fof(f82,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f58]) ).
fof(f85,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f88,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f85,f1]) ).
fof(f91,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f81]) ).
fof(f92,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c4,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f91,f1]) ).
fof(f93,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f36,f82]) ).
fof(f100,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f92,f53]) ).
fof(f119,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f88,f63]) ).
fof(f123,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f88,f100]) ).
fof(f130,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f123,f3]) ).
fof(f133,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f130,f93]) ).
fof(f134,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f135,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f48,f36]) ).
fof(f136,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f138,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c1,X0)) = X0
| ~ spl0_9 ),
inference(superposition,[],[f88,f68]) ).
fof(f139,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f68]) ).
fof(f144,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f88,f76]) ).
fof(f145,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f76]) ).
fof(f146,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f144,f68]) ).
fof(f148,plain,
( ! [X0] :
( sk_c7 != sk_c7
| inverse(X0) != multiply(sk_c1,sk_c7)
| sk_c6 != multiply(X0,multiply(sk_c1,sk_c7)) )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f33,f68]) ).
fof(f149,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c1,sk_c7)
| sk_c6 != multiply(X0,multiply(sk_c1,sk_c7)) )
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f148]) ).
fof(f150,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,multiply(sk_c1,sk_c7)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f149,f76]) ).
fof(f159,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f150,f76]) ).
fof(f172,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f176,definition,
( spl0_16
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f177,plain,
( sk_c6 = sk_c5
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f189,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f88,f146]) ).
fof(f191,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f189,f3]) ).
fof(f195,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f145,f146]) ).
fof(f201,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f195,f76]) ).
fof(f206,plain,
( sk_c5 = multiply(inverse(inverse(sk_c3)),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f88,f119]) ).
fof(f353,plain,
( sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f39,f68]) ).
fof(f355,plain,
( multiply(sk_c1,sk_c7) != sk_c6
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f353]) ).
fof(f358,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f355,f76]) ).
fof(f359,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f373,plain,
( sk_c6 = multiply(sk_c7,sk_c1)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f139,f191]) ).
fof(f379,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c1,X0))
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f4,f373]) ).
fof(f380,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f379,f138]) ).
fof(f381,plain,
( ! [X0] : multiply(inverse(sk_c6),X0) = X0
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f88,f380]) ).
fof(f418,plain,
( ! [X0] : multiply(inverse(inverse(sk_c6)),X0) = X0
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f88,f381]) ).
fof(f473,plain,
( identity = inverse(sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f3,f418]) ).
fof(f477,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f473,f191]) ).
fof(f482,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f159,f477]) ).
fof(f486,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f482]) ).
fof(f490,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f486,f201]) ).
fof(f491,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f496,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f206,f58]) ).
fof(f500,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f496,f3]) ).
fof(f506,plain,
( sk_c6 = sk_c5
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f500,f130]) ).
fof(f509,plain,
( spl0_16
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f506,f61,f56,f51,f42,f176]) ).
fof(f511,plain,
( sk_c7 != sk_c7
| sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f39,f58]) ).
fof(f512,plain,
( sk_c6 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f511]) ).
fof(f513,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f512,f63]) ).
fof(f514,plain,
( ~ spl0_16
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f513,f61,f56,f38,f176]) ).
fof(f515,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f53,f177]) ).
fof(f524,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f515,f176,f51,f172]) ).
fof(f526,plain,
( ! [X0] :
( sk_c7 != sk_c7
| inverse(X0) != multiply(sk_c3,sk_c7)
| sk_c6 != multiply(X0,multiply(sk_c3,sk_c7)) )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f33,f58]) ).
fof(f527,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c3,sk_c7)
| sk_c6 != multiply(X0,multiply(sk_c3,sk_c7)) )
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f526]) ).
fof(f528,plain,
( ! [X0] :
( inverse(X0) != sk_c5
| sk_c6 != multiply(X0,multiply(sk_c3,sk_c7)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f527,f63]) ).
fof(f529,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,multiply(sk_c3,sk_c7)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f528,f177]) ).
fof(f530,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c5)
| inverse(X0) != sk_c6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f529,f63]) ).
fof(f531,plain,
( ! [X0] :
( inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c6) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f530,f177]) ).
fof(f536,plain,
( sk_c6 != sk_c5
| sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f531,f44]) ).
fof(f540,plain,
( sk_c6 != multiply(sk_c4,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f536,f177]) ).
fof(f541,plain,
( ~ spl0_15
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f540,f176,f61,f56,f42,f32,f172]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f59]) ).
cnf(s6,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f69]) ).
cnf(s7,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f70]) ).
cnf(s8,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f72]) ).
cnf(s10,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f77]) ).
cnf(s11,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f78]) ).
cnf(s12,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f79]) ).
cnf(s13,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f80]) ).
cnf(s14,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f134]) ).
cnf(s15,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f136]) ).
cnf(s21,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f359]) ).
cnf(s23,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f491]) ).
cnf(s28,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f509]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16 ),
inference(sat_conversion,[],[f514]) ).
cnf(s30,plain,
( ~ spl0_6
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f524]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f541]) ).
cnf(s32,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s21,s6,s10]) ).
cnf(s33,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s28,s29,s11,s12,s13,s32]) ).
cnf(s34,plain,
~ spl0_3,
inference(rat,[],[s28,s29,s7,s8,s9,s21,s33,s32]) ).
cnf(s35,plain,
~ spl0_2,
inference(rat,[],[s14,s2,s3,s4,s15]) ).
cnf(s36,plain,
spl0_1,
inference(rat,[],[s1,s34,s35]) ).
cnf(s37,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_4
| ~ spl0_8 ),
inference(rat,[],[s31,s30,s28,s36]) ).
cnf(s38,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s37,s11,s12,s13]) ).
cnf(s39,plain,
~ spl0_4,
inference(rat,[],[s37,s7,s8,s9,s23,s38,s36]) ).
cnf(s40,plain,
spl0_10,
inference(rat,[],[s10,s39]) ).
cnf(s41,plain,
spl0_9,
inference(rat,[],[s6,s39]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s23,s36,s40,s41]) ).
fof(f542,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:37:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.77/1.28 % (1779845)Input is clausal, will run a generic CNF schedule.
% 2.77/1.28 % (1779853)lrs+10_1_sil=8000:sp=occurrence:random_seed=2707940793:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.28 % (1779853)Refutation not found, incomplete strategy
% 2.77/1.28 % (1779853)------------------------------
% 2.77/1.28 % (1779853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (1779853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (1779853)CaDiCaL version: 2.1.3
% 2.77/1.28 % (1779853)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.28 % (1779853)Time elapsed: 0.001 s
% 2.77/1.28 % (1779853)Peak memory usage: 88 MB
% 2.77/1.28 % (1779853)Instructions burned: 1 (million)
% 2.77/1.28 % (1779854)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3434446578:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.28 % (1779851)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=161310070:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.28 % (1779852)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1184803115:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.28 % (1779850)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=434416393:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.28 % (1779855)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4032916758:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.28 % (1779855)First to succeed.
% 2.77/1.28 % (1779855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1779845"
% 2.77/1.28 % (1779856)dis-21_1_sil=8000:lcm=predicate:random_seed=929069675: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)
% 2.77/1.28 % (1779856)Refutation not found, incomplete strategy
% 2.77/1.28 % (1779856)------------------------------
% 2.77/1.28 % (1779856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (1779856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (1779856)CaDiCaL version: 2.1.3
% 2.77/1.28 % (1779856)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.28 % (1779856)Time elapsed: 0.002 s
% 2.77/1.28 % (1779856)Peak memory usage: 88 MB
% 2.77/1.28 % (1779856)Instructions burned: 1 (million)
% 2.77/1.28 % (1779854)Instruction limit reached!
% 2.77/1.28 % (1779854)------------------------------
% 2.77/1.28 % (1779854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (1779854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (1779854)CaDiCaL version: 2.1.3
% 2.77/1.28 % (1779854)Termination reason: Instruction limit
% 2.77/1.28 % (1779854)Termination phase: Saturation
% 2.77/1.28 % (1779854)Time elapsed: 0.068 s
% 2.77/1.28 % (1779854)Peak memory usage: 89 MB
% 2.77/1.28 % (1779854)Instructions burned: 114 (million)
% 2.77/1.28 % (1779853)------------------------------
% 2.77/1.28 % (1779853)------------------------------
% 2.77/1.28 % (1779864)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=1013472589:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.77/1.28 % (1779865)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3870252118:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.77/1.28 % (1779865)Refutation not found, incomplete strategy
% 2.77/1.28 % (1779865)------------------------------
% 2.77/1.28 % (1779865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.28 % (1779865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.28 % (1779865)CaDiCaL version: 2.1.3
% 2.77/1.28 % (1779865)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.28 % (1779865)Time elapsed: 0.001 s
% 2.77/1.28 % (1779865)Peak memory usage: 88 MB
% 2.77/1.28 % (1779865)Instructions burned: 2 (million)
% 2.77/1.28 % (1779856)------------------------------
% 2.77/1.28 % (1779856)------------------------------
% 2.77/1.28 % (1779855)Refutation found. Thanks to Tanya!
% 2.77/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.49 % (1779855)------------------------------
% 3.71/1.49 % (1779855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.49 % (1779855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.49 % (1779855)CaDiCaL version: 2.1.3
% 3.71/1.49 % (1779855)Termination reason: Refutation
% 3.71/1.49 % (1779855)Time elapsed: 0.016 s
% 3.71/1.49 % (1779855)Peak memory usage: 89 MB
% 3.71/1.49 % (1779855)Instructions burned: 22 (million)
% 3.71/1.49 % (1779855)------------------------------
% 3.71/1.49 % (1779855)------------------------------
% 3.71/1.49 % (1779845)Success in time 0.446 s
% 3.71/1.49 % Vampire exiting
%------------------------------------------------------------------------------