%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP348-1 : 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 : 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 10:17:33 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 35
% Syntax : Number of formulae : 286 ( 21 unt; 11 def)
% Number of atoms : 1093 ( 288 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1562 ( 755 ~; 796 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 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_c5,sk_c6) = sk_c4
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c5 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = inverse(sk_c2)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c4) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c4) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c4) = sk_c5
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c4) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
! [X2,X0,X1] :
( multiply(sk_c5,sk_c6) != sk_c4
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c6
| inverse(X1) != sk_c5
| multiply(X1,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
! [X2,X0,X1] :
( multiply(sk_c5,sk_c6) != sk_c4
| inverse(X0) != sk_c6
| sk_c6 != multiply(X0,sk_c5)
| sk_c5 != inverse(X1)
| sk_c5 != multiply(X1,sk_c4)
| sk_c5 != inverse(sk_c4)
| sk_c6 != multiply(sk_c4,sk_c5)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) ),
inference(reorient_equations,[],[f45]) ).
fof(f48,definition,
( spl0_1
<=> ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f49,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,definition,
( spl0_2
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( sk_c6 != multiply(sk_c4,sk_c5)
| spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_3
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( sk_c5 != inverse(sk_c4)
| spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != inverse(X1)
| sk_c5 != multiply(X1,sk_c4) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( ! [X1] :
( sk_c5 != inverse(X1)
| sk_c5 != multiply(X1,sk_c4) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,definition,
( spl0_5
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f63,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c6) != sk_c4
| spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f46,f62,f48,f59,f55,f51,f48]) ).
fof(f67,definition,
( spl0_6
<=> sk_c6 = multiply(sk_c3,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f69,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_7
<=> sk_c5 = multiply(sk_c2,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f73,plain,
( sk_c5 = multiply(sk_c2,sk_c4)
| ~ 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_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f78,plain,
( sk_c6 = 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(f80,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f40,f71,f51]) ).
fof(f81,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f38,f71,f55]) ).
fof(f83,definition,
( spl0_9
<=> sk_c5 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f85,plain,
( sk_c5 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f36,f83,f67]) ).
fof(f87,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f83,f76]) ).
fof(f88,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f32,f83,f51]) ).
fof(f89,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f30,f83,f55]) ).
fof(f91,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c1,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f93,plain,
( sk_c6 = multiply(sk_c1,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f28,f91,f67]) ).
fof(f95,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f26,f91,f76]) ).
fof(f96,plain,
( spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f24,f91,f51]) ).
fof(f97,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f22,f91,f55]) ).
fof(f99,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f101,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f20,f99,f67]) ).
fof(f103,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f18,f99,f76]) ).
fof(f104,plain,
( spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f16,f99,f51]) ).
fof(f105,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f14,f99,f55]) ).
fof(f106,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f62,f67]) ).
fof(f107,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f62,f76]) ).
fof(f108,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f62,f51]) ).
fof(f109,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f62,f55]) ).
fof(f111,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_3 ),
inference(superposition,[],[f3,f56]) ).
fof(f112,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f78]) ).
fof(f113,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f114,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f113,f4]) ).
fof(f115,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(sk_c6,X0)
| ~ spl0_2 ),
inference(superposition,[],[f4,f52]) ).
fof(f123,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f111]) ).
fof(f124,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c4,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f123,f1]) ).
fof(f127,plain,
( sk_c5 = multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f124,f52]) ).
fof(f136,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f115,f127]) ).
fof(f138,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f136,f52]) ).
fof(f151,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f114,f3]) ).
fof(f156,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f114,f114]) ).
fof(f158,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f114,f69]) ).
fof(f160,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f114,f138]) ).
fof(f161,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_3 ),
inference(superposition,[],[f114,f111]) ).
fof(f162,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f114,f112]) ).
fof(f165,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f160,f3]) ).
fof(f167,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f158,f78]) ).
fof(f172,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f151,f156]) ).
fof(f173,plain,
( sk_c5 = multiply(identity,identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f167,f165]) ).
fof(f176,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f173,f1]) ).
fof(f178,plain,
( sk_c6 = multiply(sk_c4,identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f52,f176]) ).
fof(f180,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f111,f176]) ).
fof(f189,plain,
( identity = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f180,f1]) ).
fof(f191,plain,
( sk_c6 = sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f178,f172]) ).
fof(f196,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f191,f161]) ).
fof(f201,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f196,f172]) ).
fof(f206,plain,
( sk_c6 = inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f201,f176]) ).
fof(f211,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f206,f165]) ).
fof(f258,plain,
( identity != multiply(sk_c5,sk_c6)
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f64,f189]) ).
fof(f265,plain,
( identity != sk_c5
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f258,f127]) ).
fof(f270,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f265,f176]) ).
fof(f271,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f273,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c6 != multiply(X2,sk_c5) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f49,f165]) ).
fof(f274,plain,
( multiply(sk_c5,sk_c6) = multiply(inverse(sk_c5),identity)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f63,f161]) ).
fof(f275,plain,
( ! [X2] :
( sk_c6 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f273,f176]) ).
fof(f276,plain,
( multiply(sk_c5,sk_c6) = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f274,f172]) ).
fof(f277,plain,
( ! [X2] :
( sk_c6 != X2
| identity != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f275,f172]) ).
fof(f279,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f277,f165]) ).
fof(f284,plain,
( identity != sk_c6
| identity != sk_c3
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f279,f78]) ).
fof(f285,plain,
( identity != sk_c3
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f284,f165]) ).
fof(f287,plain,
( identity != multiply(inverse(sk_c6),identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f285,f162]) ).
fof(f290,plain,
( identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f287,f172]) ).
fof(f291,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f290,f165]) ).
fof(f292,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f291,f211]) ).
fof(f293,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f294,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c5 != multiply(X1,sk_c4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f60,f176]) ).
fof(f295,plain,
( ! [X1] :
( sk_c5 != multiply(X1,multiply(inverse(sk_c5),identity))
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f294,f161]) ).
fof(f296,plain,
( ! [X1] :
( sk_c5 != multiply(X1,inverse(sk_c5))
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f295,f172]) ).
fof(f297,plain,
( ! [X1] :
( identity != multiply(X1,inverse(identity))
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f296,f176]) ).
fof(f298,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f297,f211]) ).
fof(f299,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f298,f172]) ).
fof(f305,plain,
( identity != sk_c5
| identity != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f299,f56]) ).
fof(f308,plain,
( identity != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f305,f176]) ).
fof(f311,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f308,f189]) ).
fof(f312,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f313,plain,
( sk_c6 != multiply(multiply(inverse(sk_c5),identity),sk_c5)
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f53,f161]) ).
fof(f314,plain,
( sk_c5 = multiply(sk_c2,multiply(inverse(sk_c5),identity))
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f73,f161]) ).
fof(f316,plain,
( sk_c6 != multiply(inverse(sk_c5),multiply(identity,sk_c5))
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f313,f4]) ).
fof(f317,plain,
( sk_c5 = multiply(sk_c2,inverse(sk_c5))
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f314,f172]) ).
fof(f319,plain,
( sk_c6 != multiply(inverse(sk_c5),sk_c5)
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f316,f1]) ).
fof(f321,plain,
( identity != sk_c6
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f319,f3]) ).
fof(f328,plain,
( identity = multiply(sk_c5,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f85]) ).
fof(f332,plain,
( identity = multiply(sk_c6,sk_c1)
| ~ spl0_11 ),
inference(superposition,[],[f3,f101]) ).
fof(f333,plain,
( sk_c5 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f114,f93]) ).
fof(f334,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f93]) ).
fof(f335,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f333,f101]) ).
fof(f337,plain,
( sk_c2 = multiply(inverse(sk_c5),identity)
| ~ spl0_9 ),
inference(superposition,[],[f114,f328]) ).
fof(f340,plain,
( sk_c2 = inverse(sk_c5)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f337,f172]) ).
fof(f345,plain,
( sk_c6 = multiply(inverse(sk_c5),inverse(sk_c5))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f114,f276]) ).
fof(f351,plain,
( identity = multiply(sk_c5,inverse(sk_c5))
| ~ spl0_9 ),
inference(superposition,[],[f328,f340]) ).
fof(f353,plain,
( sk_c5 = multiply(inverse(sk_c5),inverse(sk_c5))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f317,f340]) ).
fof(f354,plain,
( inverse(sk_c5) = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f114,f317]) ).
fof(f355,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c2,multiply(inverse(sk_c5),X0))
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f4,f317]) ).
fof(f356,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c5),multiply(inverse(sk_c5),X0))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f355,f340]) ).
fof(f357,plain,
( inverse(sk_c5) = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f354,f85]) ).
fof(f370,plain,
( multiply(sk_c6,sk_c2) = multiply(sk_c1,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f334,f328]) ).
fof(f371,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c1),multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f114,f334]) ).
fof(f374,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c1),multiply(multiply(inverse(sk_c5),inverse(sk_c5)),X0))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f371,f345]) ).
fof(f375,plain,
( sk_c1 = multiply(sk_c6,sk_c2)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f370,f172]) ).
fof(f380,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c1),multiply(inverse(sk_c5),multiply(inverse(sk_c5),X0)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f374,f4]) ).
fof(f381,plain,
( sk_c1 = multiply(sk_c6,inverse(sk_c5))
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f375,f340]) ).
fof(f385,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c1),multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f380,f356]) ).
fof(f386,plain,
( sk_c1 = multiply(sk_c6,multiply(sk_c5,sk_c5))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f381,f357]) ).
fof(f390,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f385,f101]) ).
fof(f391,plain,
( sk_c1 = multiply(multiply(inverse(sk_c5),inverse(sk_c5)),multiply(sk_c5,sk_c5))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f386,f345]) ).
fof(f395,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(multiply(inverse(sk_c5),inverse(sk_c5)),multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f390,f345]) ).
fof(f396,plain,
( sk_c1 = multiply(inverse(sk_c5),multiply(inverse(sk_c5),multiply(sk_c5,sk_c5)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f391,f4]) ).
fof(f400,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c5),multiply(inverse(sk_c5),multiply(sk_c5,X0)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f395,f4]) ).
fof(f401,plain,
( sk_c1 = multiply(sk_c5,multiply(sk_c5,sk_c5))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f396,f356]) ).
fof(f405,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c5,X0))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f400,f356]) ).
fof(f583,plain,
( sk_c5 = multiply(multiply(inverse(sk_c5),inverse(sk_c5)),multiply(inverse(sk_c5),inverse(sk_c5)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f335,f345]) ).
fof(f587,plain,
( sk_c1 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f401,f405]) ).
fof(f595,plain,
( sk_c5 = multiply(inverse(sk_c5),multiply(inverse(sk_c5),multiply(inverse(sk_c5),inverse(sk_c5))))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f583,f4]) ).
fof(f602,plain,
( sk_c5 = multiply(sk_c5,multiply(inverse(sk_c5),inverse(sk_c5)))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f595,f356]) ).
fof(f608,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f602,f353]) ).
fof(f634,plain,
( sk_c6 = inverse(multiply(sk_c5,sk_c5))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f587]) ).
fof(f635,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f634,f608]) ).
fof(f639,plain,
( sk_c6 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f635,f357]) ).
fof(f643,plain,
( sk_c5 = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f639,f608]) ).
fof(f652,plain,
( sk_c5 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f114,f608]) ).
fof(f654,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f652,f3]) ).
fof(f667,plain,
( identity != sk_c5
| spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f321,f643]) ).
fof(f668,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f667,f654]) ).
fof(f669,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f676,plain,
( sk_c5 = multiply(sk_c2,multiply(sk_c5,sk_c6))
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f73,f63]) ).
fof(f681,plain,
( sk_c5 = multiply(inverse(sk_c5),multiply(sk_c5,sk_c6))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f676,f340]) ).
fof(f683,plain,
( sk_c5 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f681,f114]) ).
fof(f684,plain,
( identity = multiply(sk_c5,sk_c1)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f332,f683]) ).
fof(f685,plain,
( identity = multiply(sk_c5,multiply(sk_c6,inverse(sk_c5)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f684,f381]) ).
fof(f686,plain,
( identity = multiply(sk_c5,multiply(sk_c5,inverse(sk_c5)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f685,f683]) ).
fof(f687,plain,
( identity = multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f686,f351]) ).
fof(f688,plain,
( identity = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f687,f172]) ).
fof(f690,plain,
( sk_c6 = multiply(sk_c1,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f93,f688]) ).
fof(f692,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f328,f688]) ).
fof(f695,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f692,f1]) ).
fof(f697,plain,
( sk_c6 = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f690,f172]) ).
fof(f701,plain,
( sk_c5 = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f697,f683]) ).
fof(f705,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f701,f688]) ).
fof(f712,plain,
( sk_c5 = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f85,f695]) ).
fof(f713,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f712,f688]) ).
fof(f720,plain,
( sk_c6 = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f705]) ).
fof(f721,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f720,f713]) ).
fof(f725,plain,
( sk_c5 != inverse(multiply(sk_c5,sk_c6))
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f57,f63]) ).
fof(f726,plain,
( sk_c5 != inverse(multiply(sk_c5,sk_c5))
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f725,f683]) ).
fof(f727,plain,
( identity != inverse(multiply(identity,identity))
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f726,f688]) ).
fof(f728,plain,
( identity != inverse(identity)
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f727,f1]) ).
fof(f729,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f728,f713]) ).
fof(f730,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f729]) ).
fof(f732,plain,
( ! [X2] :
( sk_c6 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f273,f688]) ).
fof(f743,plain,
( ! [X2] :
( sk_c6 != X2
| identity != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f732,f172]) ).
fof(f751,plain,
( ! [X2] :
( sk_c5 != X2
| identity != inverse(X2) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f743,f683]) ).
fof(f756,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f751,f688]) ).
fof(f793,plain,
( identity != sk_c6
| identity != sk_c1
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f756,f101]) ).
fof(f799,plain,
( identity != sk_c1
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f793,f721]) ).
fof(f802,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f799,f705]) ).
fof(f803,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f804,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c5 != multiply(X1,sk_c4) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f60,f688]) ).
fof(f805,plain,
( ! [X1] :
( sk_c5 != multiply(X1,multiply(sk_c5,sk_c6))
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f804,f63]) ).
fof(f806,plain,
( ! [X1] :
( sk_c5 != multiply(X1,multiply(sk_c5,sk_c5))
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f805,f683]) ).
fof(f807,plain,
( ! [X1] :
( identity != multiply(X1,multiply(identity,identity))
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f806,f688]) ).
fof(f808,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f807,f1]) ).
fof(f809,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f808,f172]) ).
fof(f822,plain,
( identity != sk_c6
| identity != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f809,f101]) ).
fof(f828,plain,
( identity != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f822,f721]) ).
fof(f831,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f828,f705]) ).
fof(f832,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f831]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f74]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f80]) ).
cnf(s6,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f86]) ).
cnf(s8,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s9,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s11,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s12,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f96]) ).
cnf(s14,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s15,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s16,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s17,plain,
( spl0_2
| spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f105]) ).
cnf(s19,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f106]) ).
cnf(s20,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f107]) ).
cnf(s21,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f108]) ).
cnf(s22,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f109]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f271]) ).
cnf(s25,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f293]) ).
cnf(s27,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f312]) ).
cnf(s31,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f669]) ).
cnf(s32,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f730]) ).
cnf(s36,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f803]) ).
cnf(s39,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f832]) ).
cnf(s40,plain,
( spl0_2
| ~ spl0_11
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(rat,[],[s32,s31]) ).
cnf(s41,plain,
spl0_2,
inference(rat,[],[s40,s5,s9,s13,s17,s21]) ).
cnf(s42,plain,
spl0_3,
inference(rat,[],[s32,s6,s10,s14,s18,s22]) ).
cnf(s43,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s27,s15,s16,s41,s42]) ).
cnf(s44,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s27,s11,s12,s41,s42]) ).
cnf(s45,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s27,s7,s8,s41,s42]) ).
cnf(s46,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_5
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s27,s3,s4,s39,s42,s41]) ).
cnf(s47,plain,
( ~ spl0_5
| spl0_1 ),
inference(rat,[],[s46,s45,s44,s43,s2,s41,s42]) ).
cnf(s48,plain,
spl0_5,
inference(rat,[],[s23,s19,s20,s41,s42]) ).
cnf(s49,plain,
spl0_1,
inference(rat,[],[s47,s48]) ).
cnf(s50,plain,
spl0_11,
inference(rat,[],[s25,s15,s16,s49,s41,s42]) ).
cnf(s51,plain,
spl0_7,
inference(rat,[],[s25,s3,s4,s49,s41,s42]) ).
cnf(s52,plain,
spl0_10,
inference(rat,[],[s25,s11,s12,s49,s41,s42]) ).
cnf(s53,plain,
~ spl0_9,
inference(rat,[],[s36,s51,s49,s41,s42,s48,s50,s52]) ).
cnf(s54,plain,
spl0_8,
inference(rat,[],[s8,s53]) ).
cnf(s55,plain,
spl0_6,
inference(rat,[],[s7,s53]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s25,s42,s41,s49,s54,s55]) ).
fof(f833,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:50:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.46 % (2297754)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (2297765)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3356898164:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (2297761)% WARNING: option uhcvi not known.
% 0.12/0.46 % (2297760)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2601641912_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.46 % (2297764)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2184216724:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % (2297761)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3619217238:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.46 % (2297762)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=554933329:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (2297763)dis+10_1_sil=32000:sp=arity:random_seed=3439594664:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (2297766)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1045266349:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (2297765) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2297754-2297765"...
% 0.12/0.46 % TRYING [1]
% 0.12/0.46 % TRYING [2]
% 0.12/0.46 % TRYING [3]
% 0.12/0.46 % (2297765)...printing done.
% 0.12/0.46 % (2297765)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (2297765)------------------------------
% 0.17/0.46 % (2297765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (2297765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (2297765)CaDiCaL version: 2.1.3
% 0.17/0.46 % (2297765)Termination reason: Refutation
% 0.17/0.46 % (2297765)Time elapsed: 0.010 s
% 0.17/0.46 % (2297765)Peak memory usage: 12 MB
% 0.17/0.46 % (2297765)Instructions burned: 25 (million)
% 0.17/0.46 % (2297754)Success in time 0.04 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------