%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP292-1 : 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 10:17:24 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 36
% Syntax : Number of formulae : 205 ( 20 unt; 12 def)
% Number of atoms : 552 ( 199 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 628 ( 281 ~; 335 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 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,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = inverse(sk_c2)
| sk_c4 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X2,X3) != sk_c6
| inverse(X2) != X3
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(X2,X3)
| inverse(X2) != X3
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
! [X2,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1)
| sk_c7 != multiply(sk_c5,sk_c6)
| sk_c6 != multiply(X2,inverse(X2))
| sk_c6 != multiply(inverse(X2),sk_c5) ),
inference(equality_resolution,[],[f46]) ).
fof(f49,definition,
( spl0_1
<=> ! [X2] :
( sk_c6 != multiply(X2,inverse(X2))
| sk_c6 != multiply(inverse(X2),sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X2] :
( sk_c6 != multiply(X2,inverse(X2))
| sk_c6 != multiply(inverse(X2),sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_2
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( sk_c7 != multiply(sk_c5,sk_c6)
| spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f56,definition,
( spl0_3
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f57,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl0_4
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,definition,
( spl0_5
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f47,f62,f59,f56,f52,f49]) ).
fof(f67,definition,
( spl0_6
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f69,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_7
<=> sk_c5 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f73,plain,
( sk_c5 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f44,f71,f67]) ).
fof(f76,definition,
( spl0_8
<=> sk_c4 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c4 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f42,f71,f76]) ).
fof(f81,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c3,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( sk_c6 = multiply(sk_c3,sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f40,f71,f81]) ).
fof(f85,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f38,f71,f52]) ).
fof(f87,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f89,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f36,f87,f67]) ).
fof(f91,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f34,f87,f76]) ).
fof(f92,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f32,f87,f81]) ).
fof(f93,plain,
( spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f30,f87,f52]) ).
fof(f95,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f97,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f28,f95,f67]) ).
fof(f99,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f26,f95,f76]) ).
fof(f100,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f24,f95,f81]) ).
fof(f101,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f22,f95,f52]) ).
fof(f103,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f20,f103,f67]) ).
fof(f107,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f18,f103,f76]) ).
fof(f108,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f16,f103,f81]) ).
fof(f109,plain,
( spl0_2
| spl0_12 ),
inference(avatar_split_clause,[],[f14,f103,f52]) ).
fof(f110,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f62,f67]) ).
fof(f111,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f62,f76]) ).
fof(f112,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f62,f81]) ).
fof(f113,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f62,f52]) ).
fof(f114,plain,
( identity = multiply(sk_c4,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f78]) ).
fof(f117,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f119,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c3,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f83]) ).
fof(f120,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f69]) ).
fof(f121,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f117,f1]) ).
fof(f124,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c4,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f114]) ).
fof(f125,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f124,f1]) ).
fof(f129,plain,
( sk_c4 = multiply(sk_c4,sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f125,f83]) ).
fof(f139,plain,
( multiply(sk_c3,sk_c4) = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f119,f129]) ).
fof(f141,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f139,f83]) ).
fof(f142,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f120,f53]) ).
fof(f147,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f142,f141]) ).
fof(f155,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f121,f3]) ).
fof(f156,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f121,f121]) ).
fof(f163,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f121,f147]) ).
fof(f164,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c4)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f121,f129]) ).
fof(f165,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f121,f69]) ).
fof(f169,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f164,f3]) ).
fof(f170,plain,
( sk_c7 = sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f163,f165]) ).
fof(f173,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f155,f156]) ).
fof(f174,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f173,f169]) ).
fof(f176,plain,
( sk_c5 != multiply(sk_c5,sk_c6)
| ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f64,f170]) ).
fof(f177,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f176,f174]) ).
fof(f178,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f179,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c5)
| inverse(X0) != sk_c7 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f60,f170]) ).
fof(f181,plain,
( ! [X0] :
( inverse(X0) != sk_c5
| sk_c6 != multiply(X0,sk_c5) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f179,f170]) ).
fof(f182,plain,
( spl0_3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f181,f81,f76,f67,f59,f52,f56]) ).
fof(f183,plain,
( sk_c6 != multiply(sk_c3,sk_c4)
| sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f50,f78]) ).
fof(f186,plain,
( identity != sk_c6
| sk_c6 != multiply(sk_c5,inverse(sk_c5))
| ~ spl0_1 ),
inference(superposition,[],[f50,f3]) ).
fof(f189,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f183,f83]) ).
fof(f192,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f189,f69]) ).
fof(f193,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f197,plain,
( identity != sk_c6
| sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_3 ),
inference(superposition,[],[f57,f3]) ).
fof(f198,plain,
( sk_c6 != sk_c6
| sk_c5 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f57,f69]) ).
fof(f199,plain,
( sk_c5 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f198]) ).
fof(f263,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f165,f174]) ).
fof(f270,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f263,f199]) ).
fof(f271,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f276,plain,
( identity = multiply(sk_c5,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f73]) ).
fof(f281,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f121,f89]) ).
fof(f283,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f281,f73]) ).
fof(f284,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f121,f105]) ).
fof(f286,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f284,f97]) ).
fof(f287,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f286,f63]) ).
fof(f289,plain,
( sk_c2 = multiply(inverse(sk_c5),identity)
| ~ spl0_7 ),
inference(superposition,[],[f121,f276]) ).
fof(f292,plain,
( sk_c2 = inverse(sk_c5)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f289,f173]) ).
fof(f303,plain,
( identity = multiply(sk_c2,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f3,f292]) ).
fof(f304,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f303,f89]) ).
fof(f344,plain,
( sk_c7 != sk_c5
| spl0_2
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f54,f283]) ).
fof(f352,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f344,f287]) ).
fof(f353,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f356,plain,
( sk_c5 != inverse(inverse(sk_c5))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f197,f304]) ).
fof(f357,plain,
( sk_c5 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f356,f292]) ).
fof(f358,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f357,f73]) ).
fof(f359,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f360,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c5)
| inverse(X0) != sk_c7 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f60,f287]) ).
fof(f361,plain,
( ! [X0] :
( inverse(X0) != sk_c5
| sk_c6 != multiply(X0,sk_c5) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f360,f287]) ).
fof(f362,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f361,f103,f95,f62,f59,f56]) ).
fof(f363,plain,
( sk_c6 != multiply(sk_c5,inverse(sk_c5))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f186,f304]) ).
fof(f364,plain,
( sk_c6 != multiply(sk_c5,sk_c2)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f363,f292]) ).
fof(f365,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f364,f276]) ).
fof(f366,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f365,f304]) ).
fof(f367,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f74]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f91]) ).
cnf(s8,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s9,plain,
( spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f93]) ).
cnf(s10,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s11,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s12,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s13,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f101]) ).
cnf(s14,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s15,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s16,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s17,plain,
( spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f109]) ).
cnf(s18,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f110]) ).
cnf(s19,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f111]) ).
cnf(s20,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s21,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f113]) ).
cnf(s22,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f178]) ).
cnf(s23,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f182]) ).
cnf(s25,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f271]) ).
cnf(s30,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f353]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f359]) ).
cnf(s32,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f362]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f367]) ).
cnf(s34,plain,
spl0_2,
inference(rat,[],[s30,s5,s9,s13,s17,s21]) ).
cnf(s35,plain,
spl0_5,
inference(rat,[],[s22,s18,s19,s20,s34]) ).
cnf(s36,plain,
( spl0_9
| ~ spl0_4
| spl0_3 ),
inference(rat,[],[s32,s12,s16,s35]) ).
cnf(s37,plain,
( spl0_8
| ~ spl0_4
| spl0_3 ),
inference(rat,[],[s32,s11,s15,s35]) ).
cnf(s38,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s32,s10,s14,s23,s34,s35]) ).
cnf(s39,plain,
( ~ spl0_4
| spl0_3 ),
inference(rat,[],[s38,s37,s36]) ).
cnf(s40,plain,
( spl0_3
| spl0_1 ),
inference(rat,[],[s39,s1,s35,s34]) ).
cnf(s41,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s31,s4,s8]) ).
cnf(s42,plain,
( spl0_6
| ~ spl0_3 ),
inference(rat,[],[s31,s2,s6]) ).
cnf(s43,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s31,s3,s7,s28]) ).
cnf(s44,plain,
~ spl0_3,
inference(rat,[],[s43,s42,s41]) ).
cnf(s45,plain,
spl0_1,
inference(rat,[],[s40,s44]) ).
cnf(s47,plain,
spl0_9,
inference(rat,[],[s33,s4,s8,s45]) ).
cnf(s48,plain,
spl0_6,
inference(rat,[],[s33,s2,s6,s45]) ).
cnf(s49,plain,
~ spl0_8,
inference(rat,[],[s25,s45,s47,s48]) ).
cnf(s52,plain,
spl0_10,
inference(rat,[],[s7,s49]) ).
cnf(s53,plain,
spl0_7,
inference(rat,[],[s3,s49]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s33,s45,s52,s53]) ).
fof(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP292-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:51:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.15/0.48 % (3310698)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (3310705)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3949985798:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (3310704)% WARNING: option uhcvi not known.
% 0.15/0.48 % (3310703)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3840742503_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (3310704)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3878602481:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (3310708)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3999941516:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (3310706)dis+10_1_sil=32000:sp=arity:random_seed=4293127725:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (3310707)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=700164789:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (3310709)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2482519169:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (3310707) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3310698-3310707"...
% 0.15/0.48 % (3310707)...printing done.
% 0.15/0.48 % (3310707)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (3310707)------------------------------
% 0.15/0.48 % (3310707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (3310707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (3310707)CaDiCaL version: 2.1.3
% 0.15/0.48 % (3310707)Termination reason: Refutation
% 0.15/0.48 % (3310707)Time elapsed: 0.010 s
% 0.15/0.48 % (3310707)Peak memory usage: 12 MB
% 0.15/0.48 % (3310707)Instructions burned: 14 (million)
% 0.15/0.48 % (3310698)Success in time 0.055 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------