%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP304-1 : 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 : n015.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 10:17:26 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 38
% Syntax : Number of formulae : 222 ( 23 unt; 15 def)
% Number of atoms : 661 ( 215 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 824 ( 385 ~; 424 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 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_c7,sk_c6) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c5 = inverse(sk_c7)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c5 = inverse(sk_c7)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = inverse(sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,X2) != sk_c6
| multiply(X3,sk_c7) != X2
| inverse(X3) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,X2)
| multiply(X3,sk_c7) != X2
| sk_c7 != inverse(X3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c5 != inverse(sk_c7)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ),
inference(equality_resolution,[],[f47]) ).
fof(f50,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f51,plain,
( ! [X3] :
( sk_c6 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_2
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f54,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,definition,
( spl0_3
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f57,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl0_4
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( sk_c5 != inverse(sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_5
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f48,f67,f63,f59,f56,f53,f50]) ).
fof(f72,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f45,f76,f72]) ).
fof(f81,definition,
( spl0_9
<=> sk_c4 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( sk_c4 = multiply(sk_c3,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f43,f76,f81]) ).
fof(f86,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c7,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f88,plain,
( sk_c6 = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f41,f76,f86]) ).
fof(f91,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f39,f76,f91]) ).
fof(f96,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f37,f76,f96]) ).
fof(f101,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f35,f101,f72]) ).
fof(f105,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f33,f101,f81]) ).
fof(f106,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f31,f101,f86]) ).
fof(f107,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f29,f101,f91]) ).
fof(f108,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f27,f101,f96]) ).
fof(f109,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f25,f59,f72]) ).
fof(f110,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f23,f59,f81]) ).
fof(f111,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f21,f59,f86]) ).
fof(f112,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f19,f59,f91]) ).
fof(f113,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f17,f59,f96]) ).
fof(f114,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f15,f63,f72]) ).
fof(f115,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f13,f63,f81]) ).
fof(f116,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f11,f63,f86]) ).
fof(f119,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f67]) ).
fof(f120,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f74]) ).
fof(f124,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f129,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f124,f1]) ).
fof(f132,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f120]) ).
fof(f133,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f132,f1]) ).
fof(f136,plain,
( sk_c7 = multiply(sk_c7,sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f133,f83]) ).
fof(f143,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f88,f136]) ).
fof(f149,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f68,f143]) ).
fof(f150,plain,
( sk_c5 != multiply(sk_c7,sk_c7)
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f65,f143]) ).
fof(f151,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f149,f150]) ).
fof(f152,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f211,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f129,f3]) ).
fof(f212,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f129,f129]) ).
fof(f219,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f129,f136]) ).
fof(f224,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f129,f98]) ).
fof(f233,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f224,f143]) ).
fof(f237,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f241,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f211,f212]) ).
fof(f242,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f233,f93]) ).
fof(f247,plain,
( ! [X0] : multiply(X0,sk_c4) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f241,f237]) ).
fof(f251,plain,
( sk_c7 = sk_c5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f149,f242]) ).
fof(f254,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f129,f242]) ).
fof(f256,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f3]) ).
fof(f261,plain,
( sk_c7 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f237,f256]) ).
fof(f287,plain,
( identity = inverse(sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f3,f247]) ).
fof(f299,plain,
( identity = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f287,f261]) ).
fof(f303,plain,
( sk_c4 = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f299,f237]) ).
fof(f305,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f303,f261]) ).
fof(f387,plain,
( sk_c7 != sk_c5
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f61,f305]) ).
fof(f392,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f387,f251]) ).
fof(f393,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f392]) ).
fof(f418,plain,
( sk_c4 = inverse(sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f287,f237]) ).
fof(f421,plain,
( ! [X3] :
( sk_c7 != multiply(sk_c7,multiply(X3,sk_c7))
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f51,f143]) ).
fof(f431,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f3,f60]) ).
fof(f467,plain,
( sk_c7 != multiply(sk_c7,sk_c4)
| sk_c7 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f421,f83]) ).
fof(f482,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f467,f136]) ).
fof(f490,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f482,f74]) ).
fof(f491,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f500,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f54,f143]) ).
fof(f504,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f500,f1]) ).
fof(f522,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c6 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f57,f143]) ).
fof(f523,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f522,f143]) ).
fof(f534,plain,
( sk_c7 != sk_c4
| sk_c7 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f523,f83]) ).
fof(f563,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f534,f261]) ).
fof(f578,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f563,f74]) ).
fof(f579,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f599,plain,
( sk_c7 != inverse(identity)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f504]) ).
fof(f605,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f599,f237]) ).
fof(f630,plain,
( sk_c7 != sk_c4
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f605,f418]) ).
fof(f636,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f630,f261]) ).
fof(f637,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f652,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f78]) ).
fof(f663,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f129,f103]) ).
fof(f665,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f663,f78]) ).
fof(f691,definition,
( spl0_14
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f692,plain,
( sk_c6 = sk_c5
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f693,plain,
( sk_c6 != sk_c5
| spl0_14 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f837,plain,
( sk_c7 != sk_c7
| sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f57,f103]) ).
fof(f838,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f837]) ).
fof(f839,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f838,f78]) ).
fof(f840,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f847,definition,
( spl0_20
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f848,plain,
( identity = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f865,plain,
( sk_c7 = multiply(inverse(sk_c5),identity)
| ~ spl0_4 ),
inference(superposition,[],[f129,f431]) ).
fof(f868,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f865,f241]) ).
fof(f873,plain,
( identity != sk_c6
| sk_c7 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f54,f431]) ).
fof(f875,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f873,f868]) ).
fof(f888,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f129,f652]) ).
fof(f891,plain,
( sk_c1 = inverse(sk_c6)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f888,f241]) ).
fof(f917,plain,
( identity = multiply(sk_c1,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f891]) ).
fof(f918,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f917,f103]) ).
fof(f919,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f918,f101,f76,f847]) ).
fof(f922,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f848]) ).
fof(f952,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f665,f64]) ).
fof(f967,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f952,f693]) ).
fof(f968,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f967]) ).
fof(f988,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f431,f692]) ).
fof(f989,plain,
( identity = sk_c5
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f988,f64]) ).
fof(f991,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f989,f692]) ).
fof(f992,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f991,f875]) ).
fof(f993,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f992]) ).
fof(f994,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f51,f922]) ).
fof(f1000,plain,
( spl0_2
| ~ spl0_1
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f994,f847,f50,f53]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f99]) ).
cnf(s7,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f104]) ).
cnf(s8,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f105]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f106]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f107]) ).
cnf(s11,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f108]) ).
cnf(s12,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f109]) ).
cnf(s13,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s15,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s17,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f114]) ).
cnf(s18,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s19,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s22,plain,
spl0_6,
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s24,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f393]) ).
cnf(s31,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f491]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f579]) ).
cnf(s60,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f637]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f840]) ).
cnf(s81,plain,
( ~ spl0_8
| ~ spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f919]) ).
cnf(s84,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f968]) ).
cnf(s89,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14 ),
inference(sat_conversion,[],[f993]) ).
cnf(s90,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_20 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s92,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1,s22]) ).
cnf(s93,plain,
spl0_4,
inference(rat,[],[s24,s12,s13,s14,s15,s16,s22]) ).
cnf(s94,plain,
spl0_5,
inference(rat,[],[s23,s17,s18,s19,s22]) ).
cnf(s95,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s39,s3,s4,s5,s6]) ).
cnf(s96,plain,
( ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s39,s8,s9,s10,s11,s74,s95]) ).
cnf(s97,plain,
~ spl0_3,
inference(rat,[],[s74,s2,s7,s96]) ).
cnf(s98,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s60,s3,s4,s5,s6]) ).
cnf(s99,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s60,s8,s9,s10,s11,s84,s98,s89,s94,s93]) ).
cnf(s100,plain,
~ spl0_2,
inference(rat,[],[s84,s2,s7,s99,s89,s94,s93]) ).
cnf(s101,plain,
spl0_1,
inference(rat,[],[s92,s93,s94,s97,s100]) ).
cnf(s102,plain,
~ spl0_20,
inference(rat,[],[s90,s100,s101]) ).
cnf(s103,plain,
( spl0_8
| ~ spl0_7 ),
inference(rat,[],[s31,s3,s4,s101]) ).
cnf(s104,plain,
~ spl0_7,
inference(rat,[],[s31,s8,s9,s81,s103,s101,s102]) ).
cnf(s105,plain,
spl0_13,
inference(rat,[],[s7,s104]) ).
cnf(s106,plain,
spl0_8,
inference(rat,[],[s2,s104]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s81,s102,s106,s105]) ).
fof(f1008,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n015.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 09:52:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.47 % (1414844)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (1414851)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3097189923:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (1414850)% WARNING: option uhcvi not known.
% 0.15/0.47 % (1414852)dis+10_1_sil=32000:sp=arity:random_seed=304576847:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (1414849)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1193965567_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (1414850)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=775865746:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (1414854)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=427517930:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (1414853)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3959277415:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (1414855)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1998425827:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % TRYING [4]
% 0.15/0.47 % TRYING [5]
% 0.15/0.47 % (1414852) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1414844-1414852"...
% 0.15/0.47 % (1414853) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1414844-1414853"...
% 0.15/0.47 % (1414853)...printing done.
% 0.15/0.47 % (1414852)...printing done.
% 0.15/0.47 % (1414850) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1414844-1414850"...
% 0.15/0.47 % (1414853)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (1414853)------------------------------
% 0.15/0.47 % (1414853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (1414853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (1414853)CaDiCaL version: 2.1.3
% 0.15/0.47 % (1414853)Termination reason: Refutation
% 0.15/0.47 % (1414853)Time elapsed: 0.020 s
% 0.15/0.47 % (1414853)Peak memory usage: 12 MB
% 0.15/0.47 % (1414853)Instructions burned: 30 (million)
% 0.15/0.47 % (1414844)Success in time 0.056 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------