%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP334-1 : 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 : n010.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 10:13:40 AM UTC 2026
% Result : Unsatisfiable 2.76s 1.31s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 34
% Syntax : Number of formulae : 204 ( 22 unt; 17 def)
% Number of atoms : 575 ( 183 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 703 ( 332 ~; 354 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 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_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c6,sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c4 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f14]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f34]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,X2) != sk_c5
| multiply(X3,sk_c6) != X2
| inverse(X3) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(sk_c6)
| sk_c5 != inverse(sk_c7)
| sk_c5 != multiply(sk_c6,X2)
| multiply(X3,sk_c6) != X2
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c5 != inverse(sk_c6)
| sk_c5 != inverse(sk_c7)
| sk_c5 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) ),
inference(equality_resolution,[],[f47]) ).
fof(f50,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(sk_c6,multiply(X3,sk_c6))
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f51,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c5 != multiply(sk_c6,multiply(X3,sk_c6)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,definition,
( spl0_2
<=> sk_c5 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f54,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( sk_c5 != inverse(sk_c7)
| spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl0_3
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f58,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( sk_c5 != inverse(sk_c6)
| spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f62,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl0_5
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c6 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,definition,
( spl0_6
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) = 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,f64,f61,f57,f53,f50]) ).
fof(f72,definition,
( spl0_7
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ 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_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( sk_c4 = multiply(sk_c3,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f86,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c6,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f88,plain,
( sk_c5 = multiply(sk_c6,sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f39,f76,f53]) ).
fof(f93,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f35,f93,f72]) ).
fof(f99,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f29,f93,f53]) ).
fof(f102,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f104,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f25,f102,f72]) ).
fof(f106,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f23,f102,f81]) ).
fof(f107,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f21,f102,f86]) ).
fof(f108,plain,
( spl0_2
| spl0_12 ),
inference(avatar_split_clause,[],[f19,f102,f53]) ).
fof(f111,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f15,f111,f72]) ).
fof(f115,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f13,f111,f81]) ).
fof(f116,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f11,f111,f86]) ).
fof(f117,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f9,f111,f53]) ).
fof(f119,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f67]) ).
fof(f120,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_4 ),
inference(superposition,[],[f62,f1]) ).
fof(f122,definition,
( spl0_14
<=> sk_c6 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f123,plain,
( sk_c6 = inverse(identity)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( sk_c6 != inverse(identity)
| spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl0_15
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f127,plain,
( sk_c6 = sk_c5
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f120,f61,f126,f122]) ).
fof(f130,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_2 ),
inference(superposition,[],[f3,f54]) ).
fof(f131,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f3,f58]) ).
fof(f139,definition,
( spl0_17
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f140,plain,
( identity = sk_c6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f145,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f152,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f145,f1]) ).
fof(f155,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f131]) ).
fof(f156,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f155,f1]) ).
fof(f169,plain,
( sk_c7 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f156,f68]) ).
fof(f189,definition,
( spl0_19
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f190,plain,
( sk_c6 = sk_c7
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f229,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f152,f68]) ).
fof(f237,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f152,f83]) ).
fof(f244,plain,
( sk_c6 = multiply(sk_c6,sk_c4)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f237,f74]) ).
fof(f269,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f130,f127]) ).
fof(f275,plain,
( sk_c7 = multiply(sk_c6,sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f169,f127]) ).
fof(f280,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f269,f68]) ).
fof(f283,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f280,f127]) ).
fof(f289,plain,
( spl0_17
| ~ spl0_2
| ~ spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f283,f126,f67,f53,f139]) ).
fof(f297,plain,
( sk_c6 != inverse(sk_c6)
| spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f124,f140]) ).
fof(f299,plain,
( sk_c6 != sk_c5
| ~ spl0_3
| spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f297,f58]) ).
fof(f301,plain,
( $false
| ~ spl0_3
| spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f299,f127]) ).
fof(f302,plain,
( ~ spl0_3
| spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f303,plain,
( sk_c6 != inverse(sk_c6)
| spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f59,f127]) ).
fof(f304,plain,
( sk_c6 = multiply(sk_c2,sk_c6)
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f78,f127]) ).
fof(f307,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f229,f127]) ).
fof(f312,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_15 ),
inference(forward_demodulation,[],[f307,f3]) ).
fof(f317,plain,
( sk_c6 = sk_c7
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f312,f140]) ).
fof(f318,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f317,f139,f126,f67,f189]) ).
fof(f320,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_11 ),
inference(superposition,[],[f3,f95]) ).
fof(f321,plain,
( sk_c6 = multiply(sk_c6,sk_c2)
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f320,f140]) ).
fof(f338,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f54,f190]) ).
fof(f349,plain,
( spl0_3
| ~ spl0_2
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f338,f189,f53,f57]) ).
fof(f354,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f152,f113]) ).
fof(f356,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f354,f104]) ).
fof(f358,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c6,multiply(sk_c1,sk_c6))
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f51,f104]) ).
fof(f359,plain,
( sk_c6 != sk_c6
| sk_c5 != multiply(sk_c6,multiply(sk_c3,sk_c6))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f51,f74]) ).
fof(f362,plain,
( sk_c5 != multiply(sk_c6,multiply(sk_c3,sk_c6))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f359]) ).
fof(f363,plain,
( sk_c5 != multiply(sk_c6,multiply(sk_c1,sk_c6))
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f364,plain,
( sk_c5 != multiply(sk_c6,sk_c4)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f362,f83]) ).
fof(f365,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f363,f113]) ).
fof(f366,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f364,f88]) ).
fof(f367,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f368,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f365,f68]) ).
fof(f369,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f385,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f152,f321]) ).
fof(f387,plain,
( identity = sk_c2
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f385,f3]) ).
fof(f389,plain,
( sk_c6 = sk_c2
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f140]) ).
fof(f392,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f95,f389]) ).
fof(f403,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f244,f88]) ).
fof(f504,plain,
( $false
| spl0_3
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f392,f303]) ).
fof(f505,plain,
( spl0_3
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f515,plain,
( sk_c6 != inverse(sk_c7)
| spl0_2
| ~ spl0_15 ),
inference(forward_demodulation,[],[f55,f127]) ).
fof(f516,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f152,f304]) ).
fof(f518,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f516,f95]) ).
fof(f585,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f68,f356]) ).
fof(f598,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(superposition,[],[f152,f518]) ).
fof(f600,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f598,f3]) ).
fof(f606,plain,
( sk_c6 = inverse(sk_c6)
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f58,f127]) ).
fof(f610,plain,
( sk_c6 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_demodulation,[],[f275,f518]) ).
fof(f630,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f600,f126,f93,f76,f139]) ).
fof(f634,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f610,f126,f93,f76,f67,f57,f189]) ).
fof(f646,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f123,f312]) ).
fof(f647,plain,
( $false
| spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f646,f515]) ).
fof(f648,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f650,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f585,f111,f102,f67,f126]) ).
fof(f652,plain,
( spl0_15
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f403,f86,f81,f72,f126]) ).
fof(f679,plain,
( sk_c6 != sk_c7
| sk_c6 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f65,f1]) ).
fof(f683,plain,
( sk_c6 != sk_c7
| sk_c6 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f65,f304]) ).
fof(f684,plain,
( sk_c6 != sk_c7
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f683,f95]) ).
fof(f687,plain,
( sk_c6 != inverse(sk_c6)
| sk_c6 != sk_c7
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f679,f140]) ).
fof(f688,plain,
( ~ spl0_19
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f684,f126,f93,f76,f64,f189]) ).
fof(f692,plain,
( sk_c6 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f687,f606]) ).
fof(f694,plain,
( ~ spl0_19
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f692,f139,f126,f64,f57,f189]) ).
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(s5,plain,
( spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f96]) ).
cnf(s10,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s12,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f105]) ).
cnf(s13,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s14,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s15,plain,
( spl0_2
| spl0_12 ),
inference(sat_conversion,[],[f108]) ).
cnf(s17,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f116]) ).
cnf(s20,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f117]) ).
cnf(s22,plain,
spl0_6,
inference(sat_conversion,[],[f119]) ).
cnf(s23,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f129]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f289]) ).
cnf(s35,plain,
( ~ spl0_3
| spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f302]) ).
cnf(s36,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f318]) ).
cnf(s38,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_19 ),
inference(sat_conversion,[],[f349]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f367]) ).
cnf(s40,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f369]) ).
cnf(s51,plain,
( spl0_3
| ~ spl0_11
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f505]) ).
cnf(s58,plain,
( ~ spl0_8
| ~ spl0_11
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f630]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f634]) ).
cnf(s64,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f648]) ).
cnf(s66,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f650]) ).
cnf(s71,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f652]) ).
cnf(s89,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_11
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f688]) ).
cnf(s91,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_15
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f694]) ).
cnf(s93,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1,s22]) ).
cnf(s94,plain,
spl0_2,
inference(rat,[],[s35,s51,s64,s58,s66,s5,s10,s15,s20,s22]) ).
cnf(s95,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s59,s89,s66,s2,s7,s12,s17,s22]) ).
cnf(s97,plain,
( spl0_13
| spl0_15
| ~ spl0_7 ),
inference(rat,[],[s71,s18,s19]) ).
cnf(s98,plain,
( spl0_15
| ~ spl0_7 ),
inference(rat,[],[s71,s13,s14,s66,s97,s22]) ).
cnf(s99,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s91,s36,s33,s98,s95,s94,s22]) ).
cnf(s100,plain,
( ~ spl0_15
| ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s23,s35,s33,s22,s94]) ).
cnf(s101,plain,
spl0_15,
inference(rat,[],[s66,s12,s17,s98,s22]) ).
cnf(s102,plain,
spl0_17,
inference(rat,[],[s33,s94,s22,s101]) ).
cnf(s103,plain,
spl0_19,
inference(rat,[],[s36,s101,s22,s102]) ).
cnf(s104,plain,
spl0_3,
inference(rat,[],[s38,s94,s103]) ).
cnf(s105,plain,
~ spl0_5,
inference(rat,[],[s99,s104]) ).
cnf(s109,plain,
~ spl0_4,
inference(rat,[],[s100,s101,s104]) ).
cnf(s110,plain,
spl0_1,
inference(rat,[],[s93,s94,s109,s104,s105]) ).
cnf(s111,plain,
( spl0_13
| ~ spl0_7 ),
inference(rat,[],[s39,s18,s19,s110]) ).
cnf(s112,plain,
~ spl0_7,
inference(rat,[],[s39,s13,s14,s40,s111,s110,s22]) ).
cnf(s113,plain,
spl0_13,
inference(rat,[],[s17,s112]) ).
cnf(s114,plain,
spl0_12,
inference(rat,[],[s12,s112]) ).
cnf(s117,plain,
$false,
inference(rat,[],[s40,s110,s22,s113,s114]) ).
fof(f695,plain,
$false,
inference(avatar_sat_refutation,[],[s117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP334-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:53:52 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.76/1.31 % (713487)Input is clausal, will run a generic CNF schedule.
% 2.76/1.31 % (713495)lrs+10_1_sil=8000:sp=occurrence:random_seed=4954142:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.76/1.31 % (713495)Instruction limit reached!
% 2.76/1.31 % (713495)------------------------------
% 2.76/1.31 % (713495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.31 % (713495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.31 % (713495)CaDiCaL version: 2.1.3
% 2.76/1.31 % (713495)Termination reason: Instruction limit
% 2.76/1.31 % (713495)Termination phase: Saturation
% 2.76/1.31 % (713495)Time elapsed: 0.031 s
% 2.76/1.31 % (713495)Peak memory usage: 89 MB
% 2.76/1.31 % (713495)Instructions burned: 111 (million)
% 2.76/1.31 % (713493)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3565961820:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.76/1.31 % (713492)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=479194630:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.76/1.31 % (713498)dis-21_1_sil=8000:lcm=predicate:random_seed=155000832: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)
% 2.76/1.31 % (713494)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3822510241:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.76/1.31 % (713496)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1390237245:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.76/1.31 % (713497)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2736375136:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.76/1.31 % (713498)Refutation not found, incomplete strategy
% 2.76/1.31 % (713498)------------------------------
% 2.76/1.31 % (713498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.31 % (713498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.31 % (713498)CaDiCaL version: 2.1.3
% 2.76/1.31 % (713498)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.31 % (713498)Time elapsed: 0.002 s
% 2.76/1.31 % (713498)Peak memory usage: 88 MB
% 2.76/1.31 % (713498)Instructions burned: 1 (million)
% 2.76/1.31 % (713497)First to succeed.
% 2.76/1.31 % (713497)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-713487"
% 2.76/1.31 % (713496)Instruction limit reached!
% 2.76/1.31 % (713496)------------------------------
% 2.76/1.31 % (713496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.31 % (713496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.31 % (713496)CaDiCaL version: 2.1.3
% 2.76/1.31 % (713496)Termination reason: Instruction limit
% 2.76/1.31 % (713496)Termination phase: Saturation
% 2.76/1.31 % (713496)Time elapsed: 0.066 s
% 2.76/1.31 % (713496)Peak memory usage: 89 MB
% 2.76/1.31 % (713496)Instructions burned: 114 (million)
% 2.76/1.31 % (713500)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=1275262318:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.76/1.31 % (713500)Instruction limit reached!
% 2.76/1.31 % (713500)------------------------------
% 2.76/1.31 % (713500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.31 % (713500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.31 % (713500)CaDiCaL version: 2.1.3
% 2.76/1.31 % (713500)Termination reason: Instruction limit
% 2.76/1.31 % (713500)Termination phase: Saturation
% 2.76/1.31 % (713500)Time elapsed: 0.037 s
% 2.76/1.31 % (713500)Peak memory usage: 90 MB
% 2.76/1.31 % (713500)Instructions burned: 144 (million)
% 2.76/1.31 % (713507)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3616192088:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.76/1.31 % (713498)------------------------------
% 2.76/1.31 % (713498)------------------------------
% 2.76/1.31 % (713497)Refutation found. Thanks to Tanya!
% 2.76/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.76/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.51 % (713497)------------------------------
% 0.15/1.51 % (713497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (713497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (713497)CaDiCaL version: 2.1.3
% 0.15/1.51 % (713497)Termination reason: Refutation
% 0.15/1.51 % (713497)Time elapsed: 0.017 s
% 0.15/1.51 % (713497)Peak memory usage: 89 MB
% 0.15/1.51 % (713497)Instructions burned: 25 (million)
% 0.15/1.51 % (713497)------------------------------
% 0.15/1.51 % (713497)------------------------------
% 0.15/1.51 % (713487)Success in time 0.443 s
% 0.15/1.51 % Vampire exiting
%------------------------------------------------------------------------------