%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:27 AM UTC 2026
% Result : Unsatisfiable 0.55s 1.01s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 176 ( 16 unt; 12 def)
% Number of atoms : 530 ( 167 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 680 ( 326 ~; 342 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 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 : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c5) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(sk_c5) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f44,definition,
( spl0_1
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( sk_c6 != inverse(sk_c5)
| spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f49,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f52,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f55,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c5 != multiply(X1,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f48,f54,f51,f48,f44]) ).
fof(f58,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c3,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f58,f44]) ).
fof(f63,definition,
( spl0_6
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f65,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f68,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f70,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f73,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f75,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f34,f73,f44]) ).
fof(f80,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f28,f80,f44]) ).
fof(f87,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f89,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_1
| spl0_10 ),
inference(avatar_split_clause,[],[f22,f87,f44]) ).
fof(f91,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f20,f87,f63]) ).
fof(f92,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f18,f87,f68]) ).
fof(f94,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_1
| spl0_11 ),
inference(avatar_split_clause,[],[f16,f94,f44]) ).
fof(f98,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f14,f94,f63]) ).
fof(f99,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f12,f94,f68]) ).
fof(f101,definition,
( spl0_12
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f103,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f10,f101,f44]) ).
fof(f105,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f8,f101,f63]) ).
fof(f106,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f6,f101,f68]) ).
fof(f107,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f75]) ).
fof(f112,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f113,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f103]) ).
fof(f114,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c6,X0)) = multiply(sk_c5,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f89]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f112,f1]) ).
fof(f119,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c3,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f107]) ).
fof(f120,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f119,f1]) ).
fof(f129,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f120,f60]) ).
fof(f156,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f116,f103]) ).
fof(f163,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f116,f107]) ).
fof(f164,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f116,f89]) ).
fof(f173,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f164,f82]) ).
fof(f175,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f156,f96]) ).
fof(f177,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f116,f173]) ).
fof(f179,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f177,f3]) ).
fof(f181,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f113,f175]) ).
fof(f182,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f116,f175]) ).
fof(f184,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f182,f3]) ).
fof(f185,plain,
( multiply(sk_c1,sk_c7) = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f181,f129]) ).
fof(f186,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f185,f103]) ).
fof(f196,plain,
( sk_c6 != inverse(sk_c6)
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f46,f186]) ).
fof(f197,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f163,f179]) ).
fof(f198,plain,
( sk_c3 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f197,f186]) ).
fof(f199,plain,
( identity = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f198,f3]) ).
fof(f200,plain,
( sk_c5 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f199,f179]) ).
fof(f201,plain,
( sk_c6 = sk_c3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f200,f186]) ).
fof(f206,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f75,f201]) ).
fof(f238,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f196,f206]) ).
fof(f239,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f271,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f49,f103]) ).
fof(f272,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f271]) ).
fof(f273,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f272,f96]) ).
fof(f274,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f314,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f116,f70]) ).
fof(f316,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f314,f65]) ).
fof(f360,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_1 ),
inference(superposition,[],[f3,f45]) ).
fof(f361,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f360,f184]) ).
fof(f379,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c5,sk_c5)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f114,f361]) ).
fof(f380,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f116,f361]) ).
fof(f382,plain,
( identity = sk_c5
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f380,f3]) ).
fof(f383,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f379,f89]) ).
fof(f384,plain,
( sk_c6 = sk_c5
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f382,f184]) ).
fof(f398,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f45,f384]) ).
fof(f401,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f383,f384]) ).
fof(f402,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f52,f398]) ).
fof(f405,plain,
( sk_c6 != multiply(sk_c6,sk_c5)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f402]) ).
fof(f407,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f405,f361]) ).
fof(f408,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f409,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f55,f384]) ).
fof(f413,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f409,f45]) ).
fof(f414,plain,
( sk_c6 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f413]) ).
fof(f416,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f414,f384]) ).
fof(f417,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f401,f416]) ).
fof(f418,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f420,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f55,f45]) ).
fof(f433,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f116,f316]) ).
fof(f435,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f433,f3]) ).
fof(f438,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f1,f435]) ).
fof(f450,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c5,sk_c5)
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f52,f45]) ).
fof(f458,plain,
( identity = sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f360,f438]) ).
fof(f461,plain,
( sk_c6 = sk_c5
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f458,f435]) ).
fof(f481,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f49,f70]) ).
fof(f482,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f481]) ).
fof(f484,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f482,f65]) ).
fof(f485,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f487,plain,
( sk_c5 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f420]) ).
fof(f497,plain,
( sk_c6 != multiply(sk_c5,sk_c5)
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f450]) ).
fof(f503,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f497,f461]) ).
fof(f509,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f503,f438]) ).
fof(f510,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f515,plain,
( sk_c6 != multiply(sk_c6,sk_c6)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f487,f461]) ).
fof(f524,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f515,f438]) ).
fof(f525,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f524]) ).
cnf(s1,plain,
( spl0_2
| ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f76]) ).
cnf(s9,plain,
( spl0_1
| spl0_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s12,plain,
( spl0_1
| spl0_10 ),
inference(sat_conversion,[],[f90]) ).
cnf(s13,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f91]) ).
cnf(s14,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s15,plain,
( spl0_1
| spl0_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s16,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f98]) ).
cnf(s17,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s18,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f239]) ).
cnf(s26,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f274]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f408]) ).
cnf(s42,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f418]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f485]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f510]) ).
cnf(s56,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f525]) ).
cnf(s57,plain,
spl0_1,
inference(rat,[],[s21,s3,s6,s9,s12,s15,s18]) ).
cnf(s58,plain,
( spl0_6
| ~ spl0_4 ),
inference(rat,[],[s42,s13,s16,s19,s57]) ).
cnf(s59,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s42,s14,s17,s20,s56,s57]) ).
cnf(s60,plain,
~ spl0_4,
inference(rat,[],[s59,s58]) ).
cnf(s61,plain,
( spl0_6
| ~ spl0_3 ),
inference(rat,[],[s41,s16,s19,s57]) ).
cnf(s62,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s41,s17,s20,s51,s57]) ).
cnf(s63,plain,
~ spl0_3,
inference(rat,[],[s62,s61]) ).
cnf(s64,plain,
spl0_2,
inference(rat,[],[s2,s57,s60,s63]) ).
cnf(s65,plain,
spl0_6,
inference(rat,[],[s26,s16,s19,s64]) ).
cnf(s66,plain,
~ spl0_7,
inference(rat,[],[s45,s64,s65]) ).
cnf(s67,plain,
spl0_12,
inference(rat,[],[s20,s66]) ).
cnf(s68,plain,
spl0_11,
inference(rat,[],[s17,s66]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s26,s64,s67,s68]) ).
fof(f526,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:45:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/1.01 % (3299902)Input is clausal, will run a generic CNF schedule.
% 0.55/1.01 % (3299912)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2827209103:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.55/1.01 % (3299910)lrs+10_1_sil=8000:sp=occurrence:random_seed=4133799959:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.55/1.01 % (3299913)dis-21_1_sil=8000:lcm=predicate:random_seed=597870432:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.55/1.01 % (3299909)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1076422209:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.55/1.01 % (3299907)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1583940679:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.55/1.01 % (3299911)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=43674392:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.55/1.01 % (3299908)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=921358108:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.55/1.01 % (3299913)Refutation not found, incomplete strategy
% 0.55/1.01 % (3299913)------------------------------
% 0.55/1.01 % (3299913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.55/1.01 % (3299913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/1.01 % (3299913)CaDiCaL version: 2.1.3
% 0.55/1.01 % (3299913)Termination reason: Refutation not found, incomplete strategy
% 0.55/1.01 % (3299913)Time elapsed: 0.001 s
% 0.55/1.01 % (3299913)Peak memory usage: 88 MB
% 0.55/1.01 % (3299913)Instructions burned: 1 (million)
% 0.55/1.01 % (3299910)Refutation not found, incomplete strategy
% 0.55/1.01 % (3299910)------------------------------
% 0.55/1.01 % (3299910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.55/1.01 % (3299910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/1.01 % (3299910)CaDiCaL version: 2.1.3
% 0.55/1.01 % (3299910)Termination reason: Refutation not found, incomplete strategy
% 0.55/1.01 % (3299910)Time elapsed: 0.002 s
% 0.55/1.01 % (3299910)Peak memory usage: 88 MB
% 0.55/1.01 % (3299910)Instructions burned: 2 (million)
% 0.55/1.01 % (3299912)First to succeed.
% 0.55/1.01 % (3299912)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3299902"
% 0.55/1.01 % (3299911)Instruction limit reached!
% 0.55/1.01 % (3299911)------------------------------
% 0.55/1.01 % (3299911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.55/1.01 % (3299911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/1.01 % (3299911)CaDiCaL version: 2.1.3
% 0.55/1.01 % (3299911)Termination reason: Instruction limit
% 0.55/1.01 % (3299911)Termination phase: Saturation
% 0.55/1.01 % (3299911)Time elapsed: 0.065 s
% 0.55/1.01 % (3299911)Peak memory usage: 89 MB
% 0.55/1.01 % (3299911)Instructions burned: 114 (million)
% 0.55/1.01 % (3299913)------------------------------
% 0.55/1.01 % (3299913)------------------------------
% 0.55/1.01 % (3299910)------------------------------
% 0.55/1.01 % (3299910)------------------------------
% 0.55/1.01 % (3299921)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2502035460:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.55/1.01 % (3299921)Refutation not found, incomplete strategy
% 0.55/1.01 % (3299921)------------------------------
% 0.55/1.01 % (3299921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.55/1.01 % (3299921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/1.01 % (3299921)CaDiCaL version: 2.1.3
% 0.55/1.01 % (3299921)Termination reason: Refutation not found, incomplete strategy
% 0.55/1.01 % (3299921)Time elapsed: 0.005 s
% 0.55/1.01 % (3299921)Peak memory usage: 88 MB
% 0.55/1.01 % (3299921)Instructions burned: 7 (million)
% 0.55/1.01 % (3299912)Refutation found. Thanks to Tanya!
% 0.55/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.55/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 3.23/1.11 % (3299912)------------------------------
% 3.23/1.11 % (3299912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.11 % (3299912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.11 % (3299912)CaDiCaL version: 2.1.3
% 3.23/1.11 % (3299912)Termination reason: Refutation
% 3.23/1.11 % (3299912)Time elapsed: 0.013 s
% 3.23/1.11 % (3299912)Peak memory usage: 89 MB
% 3.23/1.11 % (3299912)Instructions burned: 18 (million)
% 3.23/1.11 % (3299912)------------------------------
% 3.23/1.11 % (3299912)------------------------------
% 3.23/1.11 % (3299902)Success in time 0.424 s
% 3.23/1.11 % Vampire exiting
%------------------------------------------------------------------------------