%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP357-1 : 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 : n012.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 10:17:35 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 39
% Syntax : Number of formulae : 290 ( 23 unt; 13 def)
% Number of atoms : 1097 ( 292 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1565 ( 758 ~; 794 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 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_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c2 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c6
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| multiply(X1,sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| sk_c8 != multiply(X1,sk_c7)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X0,X4] :
( multiply(sk_c7,sk_c6) != sk_c8
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( sk_c6 != multiply(sk_c8,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_4
<=> ! [X0] :
( sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_5
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( sk_c6 != inverse(sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl0_6
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f88,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| spl0_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f68,f87,f83,f80,f76,f73,f70]) ).
fof(f92,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f94,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f101,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f103,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f111,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f113,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f122,definition,
( spl0_13
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f124,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f122,f92]) ).
fof(f126,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f122,f101]) ).
fof(f127,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f122,f106]) ).
fof(f128,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f122,f111]) ).
fof(f130,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f122,f76]) ).
fof(f132,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f134,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f132,f92]) ).
fof(f136,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f132,f101]) ).
fof(f137,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f132,f106]) ).
fof(f138,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f132,f111]) ).
fof(f140,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f132,f76]) ).
fof(f141,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f28,f83,f92]) ).
fof(f142,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f26,f83,f101]) ).
fof(f143,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f24,f83,f106]) ).
fof(f144,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f22,f83,f111]) ).
fof(f145,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f83,f116]) ).
fof(f146,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f83,f76]) ).
fof(f147,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f87,f92]) ).
fof(f148,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f87,f101]) ).
fof(f149,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f87,f106]) ).
fof(f150,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f87,f111]) ).
fof(f151,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f87,f116]) ).
fof(f152,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f87,f76]) ).
fof(f153,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f94]) ).
fof(f154,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f113]) ).
fof(f157,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f118]) ).
fof(f162,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f157,f1]) ).
fof(f165,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f153]) ).
fof(f166,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f165,f1]) ).
fof(f169,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f166,f103]) ).
fof(f176,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f108,f169]) ).
fof(f182,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f77,f176]) ).
fof(f235,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f162,f3]) ).
fof(f236,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f162,f162]) ).
fof(f241,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f162,f154]) ).
fof(f242,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f162,f169]) ).
fof(f244,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f162,f153]) ).
fof(f248,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f162,f118]) ).
fof(f255,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f248,f176]) ).
fof(f260,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f242,f3]) ).
fof(f264,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f235,f236]) ).
fof(f265,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f255,f113]) ).
fof(f271,plain,
( ! [X0] : multiply(X0,sk_c5) = X0
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f264,f260]) ).
fof(f275,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f160,f265]) ).
fof(f276,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f162,f265]) ).
fof(f278,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f276,f3]) ).
fof(f279,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f275,f176]) ).
fof(f281,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f182]) ).
fof(f282,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f281,f118]) ).
fof(f283,plain,
( sk_c6 = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f282,f176]) ).
fof(f285,plain,
( sk_c8 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f260,f278]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f1,f278]) ).
fof(f308,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f271,f285]) ).
fof(f317,plain,
( identity = inverse(sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f3,f271]) ).
fof(f329,plain,
( identity = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f285]) ).
fof(f333,plain,
( sk_c5 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f329,f260]) ).
fof(f335,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f333,f285]) ).
fof(f393,plain,
( sk_c6 != sk_c8
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f85,f335]) ).
fof(f398,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f393,f283]) ).
fof(f399,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f406,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f89,f283]) ).
fof(f407,plain,
( sk_c7 != sk_c8
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f406,f308]) ).
fof(f408,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f407,f176]) ).
fof(f409,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f411,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f88,f176]) ).
fof(f420,plain,
( sk_c6 = sk_c8
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f411,f287]) ).
fof(f425,plain,
( sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_12 ),
inference(forward_demodulation,[],[f117,f176]) ).
fof(f429,plain,
( sk_c4 = multiply(sk_c6,identity)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f244,f84]) ).
fof(f430,plain,
( sk_c3 = multiply(sk_c6,identity)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f241,f84]) ).
fof(f432,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f84]) ).
fof(f433,plain,
( sk_c5 = multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f432,f260]) ).
fof(f434,plain,
( sk_c3 = multiply(sk_c6,sk_c5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f430,f260]) ).
fof(f435,plain,
( sk_c4 = multiply(sk_c6,sk_c5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f429,f260]) ).
fof(f436,plain,
( sk_c6 = sk_c3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f434,f271]) ).
fof(f437,plain,
( sk_c6 = sk_c4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f435,f271]) ).
fof(f439,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f154,f436]) ).
fof(f440,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f439,f411]) ).
fof(f442,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f124]) ).
fof(f448,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f166,f437]) ).
fof(f451,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_14 ),
inference(superposition,[],[f162,f134]) ).
fof(f452,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f134]) ).
fof(f453,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f451,f124]) ).
fof(f458,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f4,f411]) ).
fof(f459,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f458,f448]) ).
fof(f477,plain,
( sk_c8 = sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f260,f440]) ).
fof(f486,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(superposition,[],[f425,f436]) ).
fof(f487,plain,
( sk_c8 != sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f486,f433]) ).
fof(f488,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f487,f477]) ).
fof(f489,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f505,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f88]) ).
fof(f523,plain,
( sk_c1 = multiply(inverse(sk_c2),identity)
| ~ spl0_13 ),
inference(superposition,[],[f162,f442]) ).
fof(f526,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_13 ),
inference(forward_demodulation,[],[f523,f264]) ).
fof(f536,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f526]) ).
fof(f537,plain,
( identity = sk_c8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f536,f134]) ).
fof(f538,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f505,f432]) ).
fof(f542,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f538,f264]) ).
fof(f548,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f1,f537]) ).
fof(f629,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f452,f453]) ).
fof(f633,plain,
( sk_c7 = multiply(sk_c1,sk_c2)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f629,f542]) ).
fof(f635,plain,
( sk_c7 = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f633,f134]) ).
fof(f667,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f88,f635]) ).
fof(f668,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f78,f635]) ).
fof(f669,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f668,f542]) ).
fof(f670,plain,
( sk_c6 = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f667,f548]) ).
fof(f674,plain,
( sk_c6 != sk_c8
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f669,f635]) ).
fof(f677,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f674,f670]) ).
fof(f678,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f681,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f74,f635]) ).
fof(f684,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f681,f1]) ).
fof(f689,plain,
( sk_c8 != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f684]) ).
fof(f693,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f689,f537]) ).
fof(f698,plain,
( sk_c6 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f693,f84]) ).
fof(f702,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f698,f670]) ).
fof(f703,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f706,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c8)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f81,f635]) ).
fof(f723,plain,
( identity != sk_c8
| sk_c8 != multiply(sk_c8,inverse(sk_c8))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f706,f3]) ).
fof(f731,plain,
( sk_c8 != multiply(sk_c8,inverse(sk_c8))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f723,f537]) ).
fof(f738,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f731,f548]) ).
fof(f747,plain,
( sk_c6 != sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f738,f84]) ).
fof(f754,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f747,f670]) ).
fof(f755,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f761,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f71,f548]) ).
fof(f762,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f761,f635]) ).
fof(f771,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f762,f1]) ).
fof(f776,plain,
( sk_c8 != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f771]) ).
fof(f780,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f776,f537]) ).
fof(f785,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f780,f84]) ).
fof(f790,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f785,f670]) ).
fof(f791,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f913,plain,
( sk_c8 != multiply(sk_c8,sk_c6)
| sk_c8 != multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f81,f84]) ).
fof(f926,plain,
( sk_c6 != sk_c8
| sk_c8 != multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f913,f459]) ).
fof(f932,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f926,f420]) ).
fof(f937,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f932,f176]) ).
fof(f945,plain,
( identity != sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f937,f432]) ).
fof(f948,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f945,f440]) ).
fof(f949,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f948]) ).
fof(f950,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f71,f459]) ).
fof(f951,plain,
( ! [X4] :
( sk_c7 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f950,f308]) ).
fof(f952,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != X4 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f951,f176]) ).
fof(f954,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f952,f84]) ).
fof(f957,plain,
( sk_c6 != sk_c8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f954]) ).
fof(f960,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f957,f420]) ).
fof(f961,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f962,plain,
( ! [X2] :
( sk_c7 != X2
| sk_c8 != inverse(X2) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f74,f308]) ).
fof(f963,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != X2 )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f962,f176]) ).
fof(f968,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f963,f84]) ).
fof(f971,plain,
( sk_c6 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f968]) ).
fof(f974,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f971,f420]) ).
fof(f975,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f974]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f90]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s20,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f141]) ).
cnf(s21,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s22,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s23,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f144]) ).
cnf(s24,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f145]) ).
cnf(s25,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f146]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f147]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f148]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f151]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f152]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f399]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f409]) ).
cnf(s35,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f489]) ).
cnf(s38,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f678]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f703]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f755]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f791]) ).
cnf(s60,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f949]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f961]) ).
cnf(s64,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f975]) ).
cnf(s65,plain,
spl0_3,
inference(rat,[],[s38,s13,s19,s25,s31]) ).
cnf(s66,plain,
spl0_6,
inference(rat,[],[s33,s26,s27,s28,s29,s30,s65]) ).
cnf(s67,plain,
spl0_5,
inference(rat,[],[s32,s20,s21,s22,s23,s24,s65]) ).
cnf(s68,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s60,s35,s67,s66]) ).
cnf(s69,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s47,s11,s17,s66,s67]) ).
cnf(s70,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s47,s10,s16,s66,s67]) ).
cnf(s71,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s47,s9,s15,s66,s67]) ).
cnf(s72,plain,
( ~ spl0_9
| ~ spl0_4
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s47,s8,s14,s68,s67,s66]) ).
cnf(s73,plain,
~ spl0_4,
inference(rat,[],[s72,s71,s70,s69]) ).
cnf(s74,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s35,s64,s66,s67]) ).
cnf(s75,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s41,s11,s17,s66,s67]) ).
cnf(s76,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s41,s10,s16,s66,s67]) ).
cnf(s77,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s41,s9,s15,s66,s67]) ).
cnf(s78,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s41,s8,s14,s74,s67,s66]) ).
cnf(s79,plain,
~ spl0_2,
inference(rat,[],[s78,s77,s76,s75]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s1,s66,s65,s73,s67,s79]) ).
cnf(s81,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s35,s62,s80,s66,s67]) ).
cnf(s82,plain,
spl0_11,
inference(rat,[],[s53,s11,s17,s80,s66,s67]) ).
cnf(s83,plain,
spl0_10,
inference(rat,[],[s53,s10,s16,s80,s66,s67]) ).
cnf(s84,plain,
spl0_9,
inference(rat,[],[s53,s9,s15,s80,s66,s67]) ).
cnf(s85,plain,
~ spl0_7,
inference(rat,[],[s81,s83,s82,s84]) ).
cnf(s86,plain,
spl0_14,
inference(rat,[],[s14,s85]) ).
cnf(s87,plain,
spl0_13,
inference(rat,[],[s8,s85]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s53,s67,s66,s80,s87,s86]) ).
fof(f976,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP357-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 09:55:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.37 % (2129851)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (2129857)% WARNING: option uhcvi not known.
% 0.07/0.37 % (2129858)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1640921572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (2129860)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1333557739:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (2129856)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3484874153_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (2129857)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2766428552:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (2129859)dis+10_1_sil=32000:sp=arity:random_seed=3337081807:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (2129861)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2369448253:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (2129862)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3112684928:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % TRYING [4]
% 0.07/0.37 % (2129860) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2129851-2129860"...
% 0.07/0.37 % (2129859) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2129851-2129859"...
% 0.07/0.37 % TRYING [5]
% 0.07/0.37 % (2129860)...printing done.
% 0.07/0.37 % (2129860)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (2129860)------------------------------
% 0.07/0.37 % (2129860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (2129860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (2129860)CaDiCaL version: 2.1.3
% 0.07/0.37 % (2129860)Termination reason: Refutation
% 0.07/0.37 % (2129860)Time elapsed: 0.010 s
% 0.07/0.37 % (2129860)Peak memory usage: 12 MB
% 0.07/0.37 % (2129860)Instructions burned: 29 (million)
% 0.07/0.37 % (2129851)Success in time 0.033 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------