%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP229-1 : 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 : n016.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 10:13:23 AM UTC 2026
% Result : Unsatisfiable 2.69s 1.28s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 41
% Syntax : Number of formulae : 202 ( 17 unt; 13 def)
% Number of atoms : 560 ( 214 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 631 ( 273 ~; 345 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 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,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c1) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c1) = sk_c8
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f20]) ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,X4,X5] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X5] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( inverse(sk_c8) != sk_c7
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f67,f72,f69,f75,f72,f69]) ).
fof(f80,definition,
( spl0_4
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_5
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f63,f84,f80]) ).
fof(f89,definition,
( spl0_6
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f91,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f61,f84,f89]) ).
fof(f94,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f59,f84,f94]) ).
fof(f99,definition,
( spl0_8
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f101,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f57,f84,f99]) ).
fof(f104,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f106,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f55,f84,f104]) ).
fof(f108,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f53,f84,f75]) ).
fof(f110,definition,
( spl0_10
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f51,f110,f80]) ).
fof(f114,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f49,f110,f89]) ).
fof(f115,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f47,f110,f94]) ).
fof(f116,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f45,f110,f99]) ).
fof(f117,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f43,f110,f104]) ).
fof(f118,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f41,f110,f75]) ).
fof(f120,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f39,f120,f80]) ).
fof(f124,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f37,f120,f89]) ).
fof(f125,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f35,f120,f94]) ).
fof(f126,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f33,f120,f99]) ).
fof(f127,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f31,f120,f104]) ).
fof(f128,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f29,f120,f75]) ).
fof(f130,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f136,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f21,f130,f99]) ).
fof(f137,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f19,f130,f104]) ).
fof(f138,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f17,f130,f75]) ).
fof(f140,definition,
( spl0_13
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f142,plain,
( inverse(sk_c1) = sk_c8
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f146,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f9,f140,f99]) ).
fof(f147,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f7,f140,f104]) ).
fof(f148,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f5,f140,f75]) ).
fof(f149,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f73,f101]) ).
fof(f150,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f149]) ).
fof(f151,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f150,f106]) ).
fof(f152,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f153,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| sk_c8 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f70,f91]) ).
fof(f154,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f153,f96]) ).
fof(f155,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f154,f82]) ).
fof(f156,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f142]) ).
fof(f160,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_5 ),
inference(superposition,[],[f3,f86]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f170,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c8,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f112]) ).
fof(f172,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f163,f1]) ).
fof(f238,plain,
( multiply(sk_c2,identity) = multiply(sk_c3,sk_c2)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f170,f160]) ).
fof(f262,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_13 ),
inference(superposition,[],[f172,f157]) ).
fof(f268,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f172,f122]) ).
fof(f269,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_5 ),
inference(superposition,[],[f172,f160]) ).
fof(f274,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f172,f112]) ).
fof(f279,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f274,f86]) ).
fof(f304,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f279,f122]) ).
fof(f429,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f132,f304]) ).
fof(f438,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f268,f304]) ).
fof(f439,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f438,f3]) ).
fof(f443,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f439]) ).
fof(f444,plain,
( sk_c1 = sk_c2
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f269,f262]) ).
fof(f447,plain,
( sk_c3 = multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f112,f444]) ).
fof(f500,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f238,f443]) ).
fof(f516,plain,
( sk_c8 = sk_c3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f429,f447]) ).
fof(f729,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c8 != multiply(sk_c8,multiply(X5,sk_c8)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f70,f304]) ).
fof(f733,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f729,f86]) ).
fof(f734,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f733]) ).
fof(f737,plain,
( sk_c8 != multiply(sk_c8,sk_c3)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f734,f112]) ).
fof(f741,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f737,f279]) ).
fof(f742,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f746,plain,
( sk_c8 != inverse(sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f77,f304]) ).
fof(f749,plain,
( sk_c2 = multiply(sk_c2,sk_c3)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f500,f439]) ).
fof(f755,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f749,f516]) ).
fof(f761,plain,
( sk_c3 = sk_c2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f755,f112]) ).
fof(f765,plain,
( sk_c1 = sk_c3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f761,f444]) ).
fof(f766,plain,
( sk_c1 = sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f765,f516]) ).
fof(f768,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f142,f766]) ).
fof(f786,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f768,f746]) ).
fof(f787,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f786]) ).
fof(f789,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f73,f304]) ).
fof(f801,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f789,f86]) ).
fof(f802,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f801]) ).
fof(f805,plain,
( sk_c8 != sk_c3
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f802,f112]) ).
fof(f809,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f805,f516]) ).
fof(f810,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f809]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f78]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s10,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s11,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f115]) ).
cnf(s12,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s13,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s18,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f126]) ).
cnf(s19,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s20,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f128]) ).
cnf(s24,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f136]) ).
cnf(s25,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s26,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s30,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s31,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s32,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f156]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f742]) ).
cnf(s42,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f787]) ).
cnf(s44,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f810]) ).
cnf(s46,plain,
spl0_3,
inference(rat,[],[s42,s8,s14,s20,s26,s32]) ).
cnf(s48,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s33,s30,s31]) ).
cnf(s49,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s33,s24,s25]) ).
cnf(s50,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s33,s18,s19]) ).
cnf(s51,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s33,s12,s13]) ).
cnf(s52,plain,
( ~ spl0_10
| ~ spl0_13
| ~ spl0_12
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s33,s6,s7,s44]) ).
cnf(s53,plain,
~ spl0_2,
inference(rat,[],[s52,s51,s50,s49,s48]) ).
cnf(s54,plain,
spl0_1,
inference(rat,[],[s2,s46,s53]) ).
cnf(s55,plain,
spl0_11,
inference(rat,[],[s34,s15,s16,s17,s54]) ).
cnf(s56,plain,
spl0_10,
inference(rat,[],[s34,s9,s10,s11,s54]) ).
cnf(s57,plain,
~ spl0_5,
inference(rat,[],[s40,s54,s55,s56]) ).
cnf(s60,plain,
spl0_7,
inference(rat,[],[s5,s57]) ).
cnf(s61,plain,
spl0_6,
inference(rat,[],[s4,s57]) ).
cnf(s62,plain,
spl0_4,
inference(rat,[],[s3,s57]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s34,s54,s60,s61,s62]) ).
fof(f813,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP229-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n016.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 09:43:17 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 2.69/1.28 % (2377644)Input is clausal, will run a generic CNF schedule.
% 2.69/1.28 % (2377762)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=528922776:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.69/1.28 % (2377764)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1132420815:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.69/1.28 % (2377763)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3989157539:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.69/1.28 % (2377766)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2703229442:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.69/1.28 % (2377765)lrs+10_1_sil=8000:sp=occurrence:random_seed=1913102433:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.69/1.28 % (2377768)dis-21_1_sil=8000:lcm=predicate:random_seed=3274731109: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)
% 2.69/1.28 % (2377765)Refutation not found, incomplete strategy
% 2.69/1.28 % (2377765)------------------------------
% 2.69/1.28 % (2377765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.28 % (2377765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.28 % (2377765)CaDiCaL version: 2.1.3
% 2.69/1.28 % (2377765)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.28 % (2377765)Time elapsed: 0.005 s
% 2.69/1.28 % (2377765)Peak memory usage: 88 MB
% 2.69/1.28 % (2377765)Instructions burned: 8 (million)
% 2.69/1.28 % (2377768)Refutation not found, incomplete strategy
% 2.69/1.28 % (2377768)------------------------------
% 2.69/1.28 % (2377768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.28 % (2377768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.28 % (2377768)CaDiCaL version: 2.1.3
% 2.69/1.28 % (2377768)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.28 % (2377768)Time elapsed: 0.002 s
% 2.69/1.28 % (2377768)Peak memory usage: 88 MB
% 2.69/1.28 % (2377768)Instructions burned: 2 (million)
% 2.69/1.28 % (2377767)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=667396014:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.69/1.28 % (2377767)First to succeed.
% 2.69/1.28 % (2377767)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2377644"
% 2.69/1.28 % (2377766)Instruction limit reached!
% 2.69/1.28 % (2377766)------------------------------
% 2.69/1.28 % (2377766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.28 % (2377766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.28 % (2377766)CaDiCaL version: 2.1.3
% 2.69/1.28 % (2377766)Termination reason: Instruction limit
% 2.69/1.28 % (2377766)Termination phase: Saturation
% 2.69/1.28 % (2377766)Time elapsed: 0.066 s
% 2.69/1.28 % (2377766)Peak memory usage: 89 MB
% 2.69/1.28 % (2377766)Instructions burned: 115 (million)
% 2.69/1.28 % (2377776)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=341545661:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.69/1.28 % (2377776)Refutation not found, incomplete strategy
% 2.69/1.28 % (2377776)------------------------------
% 2.69/1.28 % (2377776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.28 % (2377776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.28 % (2377776)CaDiCaL version: 2.1.3
% 2.69/1.28 % (2377776)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.28 % (2377776)Time elapsed: 0.005 s
% 2.69/1.28 % (2377776)Peak memory usage: 88 MB
% 2.69/1.28 % (2377776)Instructions burned: 7 (million)
% 2.69/1.28 % (2377765)------------------------------
% 2.69/1.28 % (2377765)------------------------------
% 2.69/1.28 % (2377768)------------------------------
% 2.69/1.28 % (2377768)------------------------------
% 2.69/1.28 % (2377767)Refutation found. Thanks to Tanya!
% 2.69/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.47 % (2377767)------------------------------
% 3.57/1.47 % (2377767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.47 % (2377767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.47 % (2377767)CaDiCaL version: 2.1.3
% 3.57/1.47 % (2377767)Termination reason: Refutation
% 3.57/1.47 % (2377767)Time elapsed: 0.016 s
% 3.57/1.47 % (2377767)Peak memory usage: 89 MB
% 3.57/1.47 % (2377767)Instructions burned: 25 (million)
% 3.57/1.47 % (2377767)------------------------------
% 3.57/1.47 % (2377767)------------------------------
% 3.57/1.47 % (2377644)Success in time 0.42 s
% 3.57/1.47 % Vampire exiting
%------------------------------------------------------------------------------