%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP237-1 : 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 : n019.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 10:17:15 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 48
% Syntax : Number of formulae : 291 ( 21 unt; 17 def)
% Number of atoms : 938 ( 308 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1205 ( 558 ~; 630 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 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,
( inverse(sk_c9) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c9) = sk_c8
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c9) = sk_c8
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c9) = sk_c8
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| multiply(X3,X4) != sk_c9
| inverse(X3) != X4
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X6,X4,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X6,X5] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f79]) ).
fof(f81,plain,
! [X2,X3,X0,X6] :
( inverse(sk_c9) != sk_c8
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ),
inference(equality_resolution,[],[f80]) ).
fof(f83,definition,
( spl0_1
<=> ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f84,plain,
( ! [X6] :
( sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f87,plain,
( ! [X3] :
( sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl0_3
<=> ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f90,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,definition,
( spl0_4
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( inverse(sk_c9) = sk_c8
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( inverse(sk_c9) != sk_c8
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f81,f92,f89,f83,f86,f83]) ).
fof(f97,definition,
( spl0_5
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f99,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f103,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f111,definition,
( spl0_8
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f113,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f118,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f70,f101,f116]) ).
fof(f121,definition,
( spl0_10
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f123,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f68,f101,f121]) ).
fof(f126,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f128,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f66,f101,f126]) ).
fof(f131,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f133,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f137,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f58,f131,f116]) ).
fof(f138,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f56,f131,f121]) ).
fof(f139,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f131,f126]) ).
fof(f141,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f147,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f141,f116]) ).
fof(f148,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f141,f121]) ).
fof(f149,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f141,f126]) ).
fof(f151,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f151,f97]) ).
fof(f155,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f151,f106]) ).
fof(f156,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f151,f111]) ).
fof(f157,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f151,f116]) ).
fof(f158,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f151,f121]) ).
fof(f159,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f151,f126]) ).
fof(f161,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f161,f97]) ).
fof(f165,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f161,f106]) ).
fof(f166,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f161,f111]) ).
fof(f167,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f161,f116]) ).
fof(f168,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f161,f121]) ).
fof(f169,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f161,f126]) ).
fof(f170,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f16,f92,f97]) ).
fof(f171,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f14,f92,f106]) ).
fof(f172,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f92,f111]) ).
fof(f173,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f10,f92,f116]) ).
fof(f174,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f92,f121]) ).
fof(f175,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f6,f92,f126]) ).
fof(f176,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_5 ),
inference(superposition,[],[f3,f99]) ).
fof(f177,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f123]) ).
fof(f180,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f181,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_8 ),
inference(superposition,[],[f4,f113]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(sk_c9,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f128]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c9,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f108]) ).
fof(f185,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f180,f1]) ).
fof(f188,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f176]) ).
fof(f189,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f188,f1]) ).
fof(f192,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f189,f108]) ).
fof(f199,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f113,f192]) ).
fof(f202,plain,
( multiply(sk_c9,sk_c4) = multiply(sk_c4,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f182,f177]) ).
fof(f207,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f118,f199]) ).
fof(f216,plain,
( multiply(sk_c6,sk_c9) = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f184,f192]) ).
fof(f226,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f216,f108]) ).
fof(f236,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f185,f3]) ).
fof(f237,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f185,f185]) ).
fof(f241,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_5 ),
inference(superposition,[],[f185,f189]) ).
fof(f242,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c9),multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f185,f181]) ).
fof(f243,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_11 ),
inference(superposition,[],[f185,f128]) ).
fof(f246,plain,
( sk_c9 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f185,f207]) ).
fof(f248,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl0_10 ),
inference(superposition,[],[f185,f177]) ).
fof(f249,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f185,f226]) ).
fof(f256,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f249,f3]) ).
fof(f260,plain,
( sk_c5 = multiply(sk_c5,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f243,f123]) ).
fof(f261,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(inverse(sk_c9),multiply(sk_c9,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f242,f199]) ).
fof(f265,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f236,f237]) ).
fof(f267,plain,
( sk_c9 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f260,f207]) ).
fof(f268,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f261,f185]) ).
fof(f271,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f265,f256]) ).
fof(f273,plain,
( sk_c9 = multiply(sk_c4,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f128,f267]) ).
fof(f274,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f177,f267]) ).
fof(f275,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f182,f267]) ).
fof(f279,plain,
( sk_c7 = multiply(sk_c9,sk_c4)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f256]) ).
fof(f312,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f248,f267]) ).
fof(f319,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f312,f241]) ).
fof(f322,plain,
( sk_c4 = multiply(sk_c6,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f319,f256]) ).
fof(f323,plain,
( sk_c4 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f322,f271]) ).
fof(f325,plain,
( sk_c7 = multiply(sk_c4,sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f108,f323]) ).
fof(f327,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f323]) ).
fof(f330,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c9,X0)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f327,f275]) ).
fof(f332,plain,
( sk_c9 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f325,f273]) ).
fof(f333,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f330,f268]) ).
fof(f354,plain,
( ! [X0] : multiply(X0,sk_c9) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f271,f332]) ).
fof(f361,plain,
( identity = multiply(inverse(sk_c4),multiply(sk_c9,sk_c4))
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f185,f202]) ).
fof(f364,plain,
( identity = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f361,f279]) ).
fof(f368,plain,
( identity = inverse(sk_c4)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f364,f271]) ).
fof(f371,plain,
( identity = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f368,f123]) ).
fof(f372,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f371,f267]) ).
fof(f375,plain,
( sk_c4 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f248,f372]) ).
fof(f378,plain,
( sk_c9 = sk_c4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f375,f246]) ).
fof(f388,plain,
( inverse(sk_c9) = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f123,f378]) ).
fof(f399,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f388,f267]) ).
fof(f476,plain,
( sk_c9 != sk_c8
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f94,f399]) ).
fof(f481,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f476,f199]) ).
fof(f482,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f483,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f90,f199]) ).
fof(f485,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != X0 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f483,f354]) ).
fof(f488,plain,
( sk_c9 != sk_c5
| sk_c9 != sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f485,f123]) ).
fof(f500,plain,
( sk_c9 != sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f488,f267]) ).
fof(f505,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f500,f378]) ).
fof(f506,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f507,plain,
( ! [X6] :
( sk_c8 != multiply(X6,sk_c9)
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f84,f333]) ).
fof(f508,plain,
( ! [X6] :
( sk_c8 != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f507,f354]) ).
fof(f509,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != X6 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f508,f199]) ).
fof(f519,plain,
( sk_c9 != sk_c5
| sk_c9 != sk_c4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f509,f123]) ).
fof(f532,plain,
( sk_c9 != sk_c4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f519,f267]) ).
fof(f539,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f532,f378]) ).
fof(f540,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f539]) ).
fof(f602,plain,
( identity = multiply(sk_c8,sk_c9)
| ~ spl0_4 ),
inference(superposition,[],[f3,f93]) ).
fof(f607,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f185,f133]) ).
fof(f609,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f607,f103]) ).
fof(f615,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f185,f153]) ).
fof(f617,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f615,f163]) ).
fof(f619,plain,
( sk_c9 = multiply(inverse(sk_c8),identity)
| ~ spl0_4 ),
inference(superposition,[],[f185,f602]) ).
fof(f622,plain,
( sk_c9 = inverse(sk_c8)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f619,f265]) ).
fof(f629,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f90,f153]) ).
fof(f630,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f629]) ).
fof(f632,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f630,f163]) ).
fof(f633,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f641,definition,
( spl0_17
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f642,plain,
( sk_c9 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f649,definition,
( spl0_18
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f651,plain,
( identity != sk_c9
| spl0_18 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f668,plain,
( sk_c9 != multiply(sk_c4,sk_c5)
| sk_c9 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f87,f123]) ).
fof(f676,plain,
( identity != sk_c9
| sk_c9 != multiply(sk_c8,inverse(sk_c8))
| ~ spl0_2 ),
inference(superposition,[],[f87,f3]) ).
fof(f677,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| identity != sk_c9
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f676,f622]) ).
fof(f692,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f668,f128]) ).
fof(f694,plain,
( identity != sk_c9
| identity != sk_c9
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f677,f602]) ).
fof(f695,plain,
( identity != sk_c9
| ~ spl0_2
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f694]) ).
fof(f703,plain,
( ~ spl0_18
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f695,f92,f86,f649]) ).
fof(f727,plain,
( sk_c8 != multiply(sk_c9,identity)
| sk_c9 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f84,f602]) ).
fof(f732,plain,
( sk_c8 != multiply(sk_c9,identity)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f727,f622]) ).
fof(f738,plain,
( sk_c9 != sk_c8
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f732,f265]) ).
fof(f741,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f738,f92,f83,f641]) ).
fof(f758,plain,
( ~ spl0_9
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f692,f126,f121,f86,f116]) ).
fof(f850,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f182,f260]) ).
fof(f854,plain,
( sk_c8 = multiply(sk_c4,sk_c5)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f850,f617]) ).
fof(f857,plain,
( sk_c9 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f854,f128]) ).
fof(f858,plain,
( spl0_17
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f857,f161,f151,f126,f121,f641]) ).
fof(f861,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f143,f609]) ).
fof(f868,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f861,f141,f131,f101,f641]) ).
fof(f875,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f602,f642]) ).
fof(f879,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f875,f617]) ).
fof(f884,plain,
( identity = sk_c9
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f879,f642]) ).
fof(f885,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f884,f651]) ).
fof(f886,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f885]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s12,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s13,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s14,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f139]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s20,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f149]) ).
cnf(s21,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s23,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s24,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s25,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s26,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f159]) ).
cnf(s27,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s28,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s29,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s30,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s31,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s32,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s33,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f170]) ).
cnf(s34,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f171]) ).
cnf(s35,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f172]) ).
cnf(s36,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f173]) ).
cnf(s37,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f174]) ).
cnf(s38,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f175]) ).
cnf(s39,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f482]) ).
cnf(s44,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f506]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f540]) ).
cnf(s60,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f633]) ).
cnf(s70,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_18 ),
inference(sat_conversion,[],[f703]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_17 ),
inference(sat_conversion,[],[f741]) ).
cnf(s78,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f758]) ).
cnf(s83,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f858]) ).
cnf(s84,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f868]) ).
cnf(s88,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f886]) ).
cnf(s89,plain,
spl0_4,
inference(rat,[],[s39,s33,s34,s35,s36,s37,s38]) ).
cnf(s91,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s60,s26,s32]) ).
cnf(s92,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s60,s25,s31]) ).
cnf(s93,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s60,s24,s30]) ).
cnf(s94,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s60,s23,s29]) ).
cnf(s95,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s60,s22,s28]) ).
cnf(s96,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_9 ),
inference(rat,[],[s60,s21,s27,s44]) ).
cnf(s97,plain,
~ spl0_3,
inference(rat,[],[s96,s95,s94,s93,s92,s91]) ).
cnf(s98,plain,
( spl0_9
| spl0_18 ),
inference(rat,[],[s84,s88,s6,s12,s18,s24,s30,s89]) ).
cnf(s99,plain,
( spl0_11
| spl0_17 ),
inference(rat,[],[s84,s8,s14,s20]) ).
cnf(s100,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s84,s7,s13,s19,s78,s99,s98,s70,s89]) ).
cnf(s101,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s78,s31,s32,s98,s70,s89]) ).
cnf(s102,plain,
~ spl0_2,
inference(rat,[],[s78,s25,s26,s88,s101,s100,s98,s70,s89]) ).
cnf(s103,plain,
spl0_1,
inference(rat,[],[s2,s89,s97,s102]) ).
cnf(s104,plain,
~ spl0_17,
inference(rat,[],[s75,s89,s103]) ).
cnf(s105,plain,
spl0_11,
inference(rat,[],[s99,s104]) ).
cnf(s106,plain,
spl0_10,
inference(rat,[],[s84,s7,s13,s19,s104]) ).
cnf(s108,plain,
( spl0_15
| ~ spl0_9 ),
inference(rat,[],[s50,s27,s28,s29,s105,s103,s106]) ).
cnf(s109,plain,
~ spl0_9,
inference(rat,[],[s50,s21,s22,s23,s83,s108,s105,s103,s106,s104]) ).
cnf(s110,plain,
spl0_15,
inference(rat,[],[s30,s109]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s24,s109]) ).
cnf(s115,plain,
$false,
inference(rat,[],[s83,s106,s105,s104,s111,s110]) ).
fof(f887,plain,
$false,
inference(avatar_sat_refutation,[],[s115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP237-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n019.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 09:38:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.46 % (2837946)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2837955)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=383072328:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2837952)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2837953)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3733386856:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2837954)dis+10_1_sil=32000:sp=arity:random_seed=2817613572:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2837951)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3640620136_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (2837952)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3581547471:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2837957)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1070136083:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2837956)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1244417897:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (2837955) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2837946-2837955"...
% 0.15/0.46 % (2837955)...printing done.
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % (2837955)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2837955)------------------------------
% 0.15/0.46 % (2837955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2837955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2837955)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2837955)Termination reason: Refutation
% 0.15/0.46 % (2837955)Time elapsed: 0.010 s
% 0.15/0.46 % (2837955)Peak memory usage: 12 MB
% 0.15/0.46 % (2837955)Instructions burned: 27 (million)
% 0.15/0.46 % (2837946)Success in time 0.039 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------