%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 10:17:20 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of formulae : 190 ( 16 unt; 15 def)
% Number of atoms : 615 ( 196 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 839 ( 414 ~; 410 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f27,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c4) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c6,sk_c4)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(sk_c6,X2) != sk_c7
| multiply(X3,sk_c6) != X2
| inverse(X3) != sk_c6
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| inverse(sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(sk_c6,X2)
| multiply(X3,sk_c6) != X2
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != inverse(sk_c6) ),
inference(equality_resolution,[],[f48]) ).
fof(f51,definition,
( spl0_1
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( sk_c7 != inverse(sk_c6)
| spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_2
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f56,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f59,plain,
( ! [X3] :
( sk_c7 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f62,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f55,f61,f58,f55,f51]) ).
fof(f65,definition,
( spl0_5
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f67,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f65,f51]) ).
fof(f70,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f75,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f77,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f80,definition,
( spl0_8
<=> sk_c4 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f82,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f40,f80,f51]) ).
fof(f87,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c6,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f89,plain,
( sk_c7 = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f87,f51]) ).
fof(f94,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f96,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_1
| spl0_10 ),
inference(avatar_split_clause,[],[f28,f94,f51]) ).
fof(f108,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f108,f51]) ).
fof(f112,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f14,f108,f70]) ).
fof(f113,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f12,f108,f75]) ).
fof(f115,definition,
( spl0_13
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f117,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f10,f115,f51]) ).
fof(f119,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f8,f115,f70]) ).
fof(f120,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f6,f115,f75]) ).
fof(f121,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_5 ),
inference(superposition,[],[f3,f67]) ).
fof(f122,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f96]) ).
fof(f126,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f129,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f132,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f129,f1]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f126,f1]) ).
fof(f140,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f132,f82]) ).
fof(f143,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f140,f89]) ).
fof(f148,plain,
( sk_c7 != inverse(sk_c7)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f53,f143]) ).
fof(f153,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f122,f143]) ).
fof(f193,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f133,f117]) ).
fof(f225,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f193,f110]) ).
fof(f239,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f133,f225]) ).
fof(f241,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f243,plain,
( identity != inverse(identity)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f148,f241]) ).
fof(f248,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f153,f241]) ).
fof(f256,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f248,f1]) ).
fof(f263,plain,
( sk_c6 = inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f96,f256]) ).
fof(f272,plain,
( sk_c7 = inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f263,f143]) ).
fof(f274,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f241]) ).
fof(f307,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f274,f243]) ).
fof(f308,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f355,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f56,f241]) ).
fof(f360,plain,
( identity != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f355,f117]) ).
fof(f362,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f360,f241]) ).
fof(f365,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f362,f110]) ).
fof(f366,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f367,plain,
( ! [X3] :
( identity != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f59,f241]) ).
fof(f373,plain,
( identity = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f52,f241]) ).
fof(f379,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f373]) ).
fof(f380,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f387,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f373,f380]) ).
fof(f415,plain,
( ! [X3] :
( identity != multiply(identity,multiply(X3,identity))
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f367,f380]) ).
fof(f416,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f415,f1]) ).
fof(f417,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f416,f380]) ).
fof(f430,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f417,f3]) ).
fof(f432,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f430]) ).
fof(f435,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f432,f387]) ).
fof(f438,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f435,f387]) ).
fof(f439,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f440,plain,
( ! [X1] :
( sk_c7 != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f62,f380]) ).
fof(f441,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c6 != inverse(X1) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f440,f241]) ).
fof(f442,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f441,f380]) ).
fof(f452,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f442,f3]) ).
fof(f454,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f452]) ).
fof(f457,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f454,f387]) ).
fof(f460,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f457,f387]) ).
fof(f461,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f463,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_1 ),
inference(superposition,[],[f3,f52]) ).
fof(f464,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f133,f77]) ).
fof(f466,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f464,f72]) ).
fof(f469,plain,
( identity != sk_c7
| sk_c6 != inverse(inverse(sk_c6))
| ~ spl0_4 ),
inference(superposition,[],[f62,f3]) ).
fof(f474,plain,
( sk_c6 != inverse(sk_c7)
| identity != sk_c7
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f469,f52]) ).
fof(f476,definition,
( spl0_16
<=> sk_c6 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f477,plain,
( sk_c6 = inverse(identity)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f478,plain,
( sk_c6 != inverse(identity)
| spl0_16 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f485,definition,
( spl0_18
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f486,plain,
( identity = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f489,definition,
( spl0_19
<=> sk_c6 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f491,plain,
( sk_c6 != inverse(sk_c7)
| spl0_19 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f492,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f474,f61,f51,f489,f485]) ).
fof(f498,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f133,f466]) ).
fof(f500,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f498,f3]) ).
fof(f502,plain,
( spl0_18
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f500,f75,f70,f485]) ).
fof(f504,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_1
| ~ spl0_18 ),
inference(superposition,[],[f463,f486]) ).
fof(f505,plain,
( sk_c6 != inverse(identity)
| ~ spl0_18
| spl0_19 ),
inference(superposition,[],[f491,f486]) ).
fof(f506,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_18 ),
inference(forward_demodulation,[],[f504,f1]) ).
fof(f507,plain,
( sk_c7 = inverse(identity)
| ~ spl0_1
| ~ spl0_18 ),
inference(superposition,[],[f52,f506]) ).
fof(f519,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_18 ),
inference(forward_demodulation,[],[f507,f486]) ).
fof(f537,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_18
| spl0_19 ),
inference(forward_demodulation,[],[f505,f506]) ).
fof(f540,plain,
( identity != inverse(identity)
| ~ spl0_1
| spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f478,f506]) ).
fof(f546,plain,
( $false
| ~ spl0_1
| spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f519,f540]) ).
fof(f547,plain,
( ~ spl0_1
| spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f548,plain,
( ! [X3] :
( sk_c7 != multiply(identity,multiply(X3,identity))
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f59,f506]) ).
fof(f550,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f477,f506]) ).
fof(f551,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f548,f1]) ).
fof(f552,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f551,f486]) ).
fof(f553,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f552,f506]) ).
fof(f559,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f553,f3]) ).
fof(f560,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f559]) ).
fof(f562,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f560,f550]) ).
fof(f565,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f562,f550]) ).
fof(f566,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f567,plain,
( ! [X4] :
( identity != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_demodulation,[],[f56,f486]) ).
fof(f568,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f537,f550]) ).
fof(f569,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f575,plain,
( identity != sk_c7
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f567,f77]) ).
fof(f577,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f575,f486]) ).
fof(f580,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f577,f72]) ).
fof(f581,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f580]) ).
cnf(s1,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f68]) ).
cnf(s6,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f83]) ).
cnf(s9,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f90]) ).
cnf(s12,plain,
( spl0_1
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s18,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s21,plain,
( spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f118]) ).
cnf(s22,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s24,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f308]) ).
cnf(s31,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f366]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f439]) ).
cnf(s38,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f461]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f492]) ).
cnf(s42,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f502]) ).
cnf(s46,plain,
( ~ spl0_1
| spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f547]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f566]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f569]) ).
cnf(s50,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(sat_conversion,[],[f581]) ).
cnf(s51,plain,
spl0_1,
inference(rat,[],[s24,s3,s6,s9,s12,s18,s21]) ).
cnf(s52,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s38,s19,s22,s51]) ).
cnf(s53,plain,
( ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s49,s41,s46,s51]) ).
cnf(s54,plain,
~ spl0_4,
inference(rat,[],[s38,s20,s23,s42,s53,s52,s51]) ).
cnf(s55,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s48,s46,s51]) ).
cnf(s56,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s35,s20,s23,s51]) ).
cnf(s57,plain,
~ spl0_3,
inference(rat,[],[s35,s19,s22,s42,s56,s55,s51]) ).
cnf(s58,plain,
spl0_2,
inference(rat,[],[s2,s54,s51,s57]) ).
cnf(s59,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s50,s42,s58]) ).
cnf(s60,plain,
spl0_7,
inference(rat,[],[s31,s20,s23,s58]) ).
cnf(s61,plain,
~ spl0_6,
inference(rat,[],[s59,s60]) ).
cnf(s62,plain,
spl0_13,
inference(rat,[],[s22,s61]) ).
cnf(s63,plain,
spl0_12,
inference(rat,[],[s19,s61]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s31,s58,s62,s63]) ).
fof(f582,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n016.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 09:48:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.47 % (2380480)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2380485)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2842905593_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (2380486)% WARNING: option uhcvi not known.
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (2380487)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3138645179:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2380488)dis+10_1_sil=32000:sp=arity:random_seed=3207408121:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2380490)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3649947479:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2380486)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3504548917:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2380491)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2805489678:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (2380489)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=582807472:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2380488) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2380480-2380488"...
% 0.16/0.47 % (2380489) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2380480-2380489"...
% 0.16/0.47 % (2380488)...printing done.
% 0.16/0.47 % (2380488)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2380488)------------------------------
% 0.16/0.47 % (2380488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2380488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2380488)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2380488)Termination reason: Refutation
% 0.16/0.47 % (2380488)Time elapsed: 0.013 s
% 0.16/0.47 % (2380488)Peak memory usage: 12 MB
% 0.16/0.47 % (2380488)Instructions burned: 20 (million)
% 0.16/0.47 % (2380480)Success in time 0.053 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------