%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP355-1 : 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 : n017.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 10:17:34 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 36
% Syntax : Number of formulae : 213 ( 20 unt; 15 def)
% Number of atoms : 635 ( 202 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 804 ( 382 ~; 407 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 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(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c6
| multiply(sk_c8,X3) != sk_c6
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f48]) ).
fof(f51,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f52,plain,
( ! [X4] :
( sk_c6 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,definition,
( spl0_3
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f58,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_4
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f61,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| spl0_4 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f49,f60,f57,f57,f54,f51]) ).
fof(f65,definition,
( spl0_5
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f67,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f71,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f46,f69,f65]) ).
fof(f74,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f76,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f44,f69,f74]) ).
fof(f79,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = multiply(sk_c8,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f42,f69,f79]) ).
fof(f84,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f86,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f40,f69,f84]) ).
fof(f89,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f91,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f38,f69,f89]) ).
fof(f94,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f36,f69,f94]) ).
fof(f99,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f34,f69,f99]) ).
fof(f104,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f32,f104,f65]) ).
fof(f110,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f26,f104,f84]) ).
fof(f111,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f24,f104,f89]) ).
fof(f112,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f22,f104,f94]) ).
fof(f113,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f20,f104,f99]) ).
fof(f114,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f18,f60,f65]) ).
fof(f115,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f16,f60,f74]) ).
fof(f116,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f14,f60,f79]) ).
fof(f117,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f60,f84]) ).
fof(f118,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f10,f60,f89]) ).
fof(f121,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_5 ),
inference(superposition,[],[f3,f67]) ).
fof(f126,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f128,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f132,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f128,f1]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f126,f1]) ).
fof(f140,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f132,f76]) ).
fof(f143,plain,
( sk_c6 = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f140,f81]) ).
fof(f149,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f101,f143]) ).
fof(f205,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f133,f101]) ).
fof(f208,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f133,f91]) ).
fof(f219,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f208,f86]) ).
fof(f222,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f205,f96]) ).
fof(f244,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f133,f219]) ).
fof(f246,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f244,f3]) ).
fof(f252,plain,
( sk_c8 != multiply(identity,sk_c6)
| spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f62,f246]) ).
fof(f253,plain,
( sk_c6 != sk_c8
| spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f252,f1]) ).
fof(f254,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f253,f143]) ).
fof(f255,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f254]) ).
fof(f288,plain,
( ! [X4] :
( sk_c6 != multiply(sk_c6,multiply(X4,sk_c6))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f52,f143]) ).
fof(f289,plain,
( ! [X4] :
( sk_c6 != multiply(sk_c6,multiply(X4,sk_c6))
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f288,f143]) ).
fof(f293,plain,
( sk_c6 != multiply(sk_c6,sk_c7)
| sk_c6 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f289,f149]) ).
fof(f298,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f293,f219]) ).
fof(f304,definition,
( spl0_17
<=> sk_c6 = multiply(sk_c6,identity) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f305,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f316,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f298,f96]) ).
fof(f319,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f316,f143]) ).
fof(f320,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f321,plain,
( ! [X2] :
( identity != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f55,f246]) ).
fof(f326,plain,
( identity != sk_c7
| sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f321,f91]) ).
fof(f330,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f326,f246]) ).
fof(f335,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f330,f86]) ).
fof(f336,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f391,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f133,f106]) ).
fof(f392,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f106]) ).
fof(f393,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f391,f71]) ).
fof(f397,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f58,f101]) ).
fof(f398,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f58,f106]) ).
fof(f399,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f398]) ).
fof(f400,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f397]) ).
fof(f401,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f399,f71]) ).
fof(f402,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f401]) ).
fof(f403,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f400,f96]) ).
fof(f404,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f410,definition,
( spl0_20
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f411,plain,
( identity = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f430,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f52,f106]) ).
fof(f431,plain,
( sk_c6 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f52,f132]) ).
fof(f442,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f431,f67]) ).
fof(f443,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f430,f71]) ).
fof(f468,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f133,f222]) ).
fof(f470,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f468,f3]) ).
fof(f472,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f470,f99,f94,f410]) ).
fof(f475,plain,
( sk_c8 = multiply(identity,sk_c6)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f61,f411]) ).
fof(f476,plain,
( sk_c6 = sk_c8
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f475,f1]) ).
fof(f478,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f476,f442]) ).
fof(f479,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f481,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f133,f393]) ).
fof(f483,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f481,f3]) ).
fof(f486,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f483,f104,f69,f410]) ).
fof(f499,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f393,f476]) ).
fof(f501,plain,
( sk_c6 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f443,f476]) ).
fof(f507,plain,
( sk_c6 != multiply(sk_c6,identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f501,f411]) ).
fof(f509,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f499,f411]) ).
fof(f515,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f507,f410,f104,f69,f60,f51,f304]) ).
fof(f516,plain,
( spl0_17
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f509,f410,f104,f69,f60,f304]) ).
fof(f517,plain,
( ! [X2] :
( identity != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_2
| ~ spl0_20 ),
inference(forward_demodulation,[],[f55,f411]) ).
fof(f536,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f392,f476]) ).
fof(f537,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f536,f411]) ).
fof(f538,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c6,X0)) = X0
| ~ spl0_4
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f537,f1]) ).
fof(f539,plain,
( identity = multiply(sk_c1,sk_c6)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f538,f305]) ).
fof(f544,plain,
( identity != identity
| sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f517,f539]) ).
fof(f547,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f544]) ).
fof(f550,plain,
( sk_c6 != sk_c8
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f547,f71]) ).
fof(f552,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f550,f476]) ).
fof(f553,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f552]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f72]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f92]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f102]) ).
cnf(s10,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f107]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f111]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f113]) ).
cnf(s17,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f114]) ).
cnf(s18,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f115]) ).
cnf(s19,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s20,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s21,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s24,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f255]) ).
cnf(s33,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f320]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f336]) ).
cnf(s44,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(sat_conversion,[],[f402]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f404]) ).
cnf(s51,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f472]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_20 ),
inference(sat_conversion,[],[f479]) ).
cnf(s56,plain,
( ~ spl0_6
| ~ spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f486]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f515]) ).
cnf(s64,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f516]) ).
cnf(s69,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_13
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f553]) ).
cnf(s70,plain,
spl0_4,
inference(rat,[],[s24,s17,s18,s19,s20,s21]) ).
cnf(s71,plain,
( spl0_6
| ~ spl0_3 ),
inference(rat,[],[s45,s8,s9]) ).
cnf(s72,plain,
( ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s45,s15,s16,s44]) ).
cnf(s73,plain,
~ spl0_3,
inference(rat,[],[s72,s71]) ).
cnf(s74,plain,
( spl0_6
| ~ spl0_2 ),
inference(rat,[],[s36,s6,s7]) ).
cnf(s75,plain,
( ~ spl0_13
| ~ spl0_20
| ~ spl0_2
| ~ spl0_6 ),
inference(rat,[],[s64,s69,s70]) ).
cnf(s76,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s36,s13,s14]) ).
cnf(s77,plain,
~ spl0_2,
inference(rat,[],[s75,s56,s76,s74]) ).
cnf(s78,plain,
spl0_1,
inference(rat,[],[s2,s70,s73,s77]) ).
cnf(s79,plain,
( ~ spl0_13
| ~ spl0_20
| ~ spl0_6 ),
inference(rat,[],[s63,s64,s70,s78]) ).
cnf(s80,plain,
( ~ spl0_20
| ~ spl0_6 ),
inference(rat,[],[s79,s10,s53,s78,s70]) ).
cnf(s81,plain,
( spl0_20
| ~ spl0_6 ),
inference(rat,[],[s51,s15,s16,s56]) ).
cnf(s82,plain,
~ spl0_6,
inference(rat,[],[s81,s80]) ).
cnf(s83,plain,
spl0_12,
inference(rat,[],[s9,s82]) ).
cnf(s84,plain,
spl0_11,
inference(rat,[],[s8,s82]) ).
cnf(s85,plain,
spl0_10,
inference(rat,[],[s7,s82]) ).
cnf(s86,plain,
spl0_9,
inference(rat,[],[s6,s82]) ).
cnf(s87,plain,
spl0_8,
inference(rat,[],[s5,s82]) ).
cnf(s88,plain,
spl0_7,
inference(rat,[],[s4,s82]) ).
cnf(s89,plain,
spl0_5,
inference(rat,[],[s3,s82]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s33,s83,s84,s85,s86,s89,s78,s87,s88]) ).
fof(f554,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP355-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:51:20 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.47 % (2300371)Will run a generic schedule for satisfiability detection.
% 0.11/0.47 % (2300381)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2813225603:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.47 % (2300377)% WARNING: option uhcvi not known.
% 0.11/0.47 % (2300376)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4215622452_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.47 % (2300382)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3603235937:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.47 % (2300378)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3806907048:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.47 % (2300379)dis+10_1_sil=32000:sp=arity:random_seed=3570929710:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.47 % (2300380)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2834631752:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.47 % (2300377)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3071136555:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % TRYING [4]
% 0.18/0.47 % (2300379) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2300371-2300379"...
% 0.18/0.47 % (2300380) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2300371-2300380"...
% 0.18/0.47 % (2300379)...printing done.
% 0.18/0.47 % (2300379)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (2300379)------------------------------
% 0.18/0.47 % (2300379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (2300379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (2300379)CaDiCaL version: 2.1.3
% 0.18/0.47 % (2300379)Termination reason: Refutation
% 0.18/0.47 % (2300379)Time elapsed: 0.014 s
% 0.18/0.47 % (2300379)Peak memory usage: 12 MB
% 0.18/0.47 % (2300379)Instructions burned: 20 (million)
% 0.18/0.47 % (2300371)Success in time 0.047 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------