%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 10:17:13 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 38
% Syntax : Number of formulae : 181 ( 14 unt; 14 def)
% Number of atoms : 450 ( 179 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 474 ( 205 ~; 255 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| multiply(sk_c7,X1) != sk_c6
| multiply(X2,sk_c7) != X1
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != multiply(sk_c7,X1)
| multiply(X2,sk_c7) != X1
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X3,X0,X4] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2)
| sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ! [X2] :
( sk_c6 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f47,f52,f55,f52,f49]) ).
fof(f59,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_5
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f63,f59]) ).
fof(f68,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f70,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f63,f68]) ).
fof(f73,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f75,plain,
( sk_c7 = multiply(sk_c4,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f63,f73]) ).
fof(f78,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f80,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f63,f78]) ).
fof(f83,definition,
( spl0_9
<=> sk_c3 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f85,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f36,f83,f59]) ).
fof(f87,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f83,f68]) ).
fof(f88,plain,
( spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f32,f83,f73]) ).
fof(f89,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f30,f83,f78]) ).
fof(f91,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f93,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f28,f91,f59]) ).
fof(f95,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f26,f91,f68]) ).
fof(f96,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f24,f91,f73]) ).
fof(f97,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f22,f91,f78]) ).
fof(f99,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f20,f99,f59]) ).
fof(f103,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f18,f99,f68]) ).
fof(f104,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f16,f99,f73]) ).
fof(f105,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f14,f99,f78]) ).
fof(f107,definition,
( spl0_12
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f109,plain,
( inverse(sk_c1) = sk_c7
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f12,f107,f59]) ).
fof(f111,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f10,f107,f68]) ).
fof(f112,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f8,f107,f73]) ).
fof(f113,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f6,f107,f78]) ).
fof(f115,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f53,f75]) ).
fof(f116,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f115]) ).
fof(f118,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f116,f80]) ).
fof(f119,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f121,plain,
( sk_c7 != sk_c7
| inverse(sk_c1) != sk_c7
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f53,f101]) ).
fof(f122,plain,
( inverse(sk_c1) != sk_c7
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f123,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f122,f109]) ).
fof(f124,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f123]) ).
fof(f125,plain,
( sk_c6 != multiply(sk_c7,sk_c3)
| sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f56,f85]) ).
fof(f126,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f125,f93]) ).
fof(f129,plain,
( sk_c7 != sk_c7
| inverse(sk_c1) != sk_c6
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f50,f101]) ).
fof(f130,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f50,f70]) ).
fof(f131,plain,
( sk_c6 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f130]) ).
fof(f132,plain,
( inverse(sk_c1) != sk_c6
| ~ spl0_1
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f129]) ).
fof(f135,plain,
( sk_c7 != sk_c6
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f132,f109]) ).
fof(f136,plain,
( ~ spl0_4
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f131,f68,f49,f59]) ).
fof(f139,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f80]) ).
fof(f153,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f70]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f153,f1]) ).
fof(f164,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f139]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f231,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_6 ),
inference(superposition,[],[f159,f70]) ).
fof(f233,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_9 ),
inference(superposition,[],[f159,f85]) ).
fof(f239,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f233,f65]) ).
fof(f242,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f239,f93]) ).
fof(f250,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f242,f135]) ).
fof(f251,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f253,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f126,f91,f83,f55,f63]) ).
fof(f256,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f159,f75]) ).
fof(f258,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f256,f80]) ).
fof(f276,definition,
( spl0_17
<=> sk_c6 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f277,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f350,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f231,f61]) ).
fof(f351,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f350,f68,f59,f276]) ).
fof(f355,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f156,f277]) ).
fof(f381,definition,
( spl0_24
<=> sk_c6 = multiply(sk_c7,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f382,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f389,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f355,f70]) ).
fof(f399,plain,
( spl0_24
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f258,f78,f73,f381]) ).
fof(f415,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f56,f165]) ).
fof(f421,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f415,f80]) ).
fof(f470,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_17
| ~ spl0_24 ),
inference(superposition,[],[f389,f382]) ).
fof(f480,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f470,f421]) ).
fof(f481,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f480]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s11,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s12,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s14,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s15,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s19,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s20,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s21,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f112]) ).
cnf(s22,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f119]) ).
cnf(s24,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f124]) ).
cnf(s27,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f136]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f251]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f253]) ).
cnf(s40,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f351]) ).
cnf(s49,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_24 ),
inference(sat_conversion,[],[f399]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17
| ~ spl0_24 ),
inference(sat_conversion,[],[f481]) ).
cnf(s57,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s32,s3,s7,s11]) ).
cnf(s58,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s40,s56,s49,s12,s13,s14,s57]) ).
cnf(s59,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s40,s56,s49,s8,s9,s10,s57]) ).
cnf(s60,plain,
~ spl0_3,
inference(rat,[],[s40,s56,s49,s4,s5,s6,s32,s59,s58,s57]) ).
cnf(s62,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s24,s18,s22]) ).
cnf(s63,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s24,s17,s21,s23]) ).
cnf(s64,plain,
~ spl0_2,
inference(rat,[],[s63,s62]) ).
cnf(s65,plain,
spl0_1,
inference(rat,[],[s2,s60,s64]) ).
cnf(s67,plain,
( spl0_6
| ~ spl0_10 ),
inference(rat,[],[s31,s4,s8,s16,s20,s65]) ).
cnf(s68,plain,
~ spl0_10,
inference(rat,[],[s31,s3,s7,s15,s19,s27,s67,s65]) ).
cnf(s69,plain,
spl0_6,
inference(rat,[],[s12,s68]) ).
cnf(s70,plain,
spl0_4,
inference(rat,[],[s11,s68]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s27,s65,s69,s70]) ).
fof(f482,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n001.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 09:44:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % (3306602)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3306608)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3306608)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=94909309:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % (3306609)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4009551356:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (3306608) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3306602-3306608"...
% 0.10/0.46 % (3306607)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3417320518_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (3306612)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1406654273:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (3306610)dis+10_1_sil=32000:sp=arity:random_seed=2816096358:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3306611)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=723633057:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (3306613)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3907677895:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (3306608)...printing done.
% 0.10/0.46 % (3306608)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.46 % (3306608)------------------------------
% 0.33/0.46 % (3306608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (3306608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (3306608)CaDiCaL version: 2.1.3
% 0.33/0.46 % (3306608)Termination reason: Refutation
% 0.33/0.46 % (3306608)Time elapsed: 0.008 s
% 0.33/0.46 % (3306608)Peak memory usage: 12 MB
% 0.33/0.46 % (3306608)Instructions burned: 19 (million)
% 0.33/0.46 % (3306602)Success in time 0.041 s
% 0.33/0.46 % Vampire exiting
%------------------------------------------------------------------------------