%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP272-1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:21 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 46
% Syntax : Number of formulae : 315 ( 20 unt; 19 def)
% Number of atoms : 1001 ( 277 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1317 ( 631 ~; 667 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 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_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = inverse(sk_c1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f34]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X1) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f57,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f58,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f61,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl0_3
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f72,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| spl0_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl0_6
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f75,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f55,f74,f70,f67,f63,f60,f57]) ).
fof(f78,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f80,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f84,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f53,f82,f78]) ).
fof(f87,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f89,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f51,f82,f87]) ).
fof(f92,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f49,f82,f92]) ).
fof(f97,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f99,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f47,f82,f97]) ).
fof(f101,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f45,f82,f63]) ).
fof(f103,definition,
( spl0_12
<=> sk_c5 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f105,plain,
( sk_c5 = multiply(sk_c2,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f43,f103,f78]) ).
fof(f107,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f103,f87]) ).
fof(f110,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f35,f103,f63]) ).
fof(f111,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f33,f70,f78]) ).
fof(f112,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f31,f70,f87]) ).
fof(f113,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f29,f70,f92]) ).
fof(f114,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f27,f70,f97]) ).
fof(f115,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f25,f70,f63]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f23,f117,f78]) ).
fof(f121,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f21,f117,f87]) ).
fof(f122,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f19,f117,f92]) ).
fof(f123,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f17,f117,f97]) ).
fof(f124,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f15,f117,f63]) ).
fof(f126,definition,
( spl0_14
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f128,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f13,f126,f78]) ).
fof(f130,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f11,f126,f87]) ).
fof(f131,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f9,f126,f92]) ).
fof(f132,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f7,f126,f97]) ).
fof(f133,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f5,f126,f63]) ).
fof(f134,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f89]) ).
fof(f135,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f99]) ).
fof(f138,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f139,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f64]) ).
fof(f140,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f134]) ).
fof(f141,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f94]) ).
fof(f142,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f80]) ).
fof(f143,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f140,f1]) ).
fof(f144,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f138,f1]) ).
fof(f153,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f143,f80]) ).
fof(f156,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f141,f64]) ).
fof(f180,plain,
( sk_c3 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f144,f135]) ).
fof(f184,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c5)
| ~ spl0_3 ),
inference(superposition,[],[f144,f64]) ).
fof(f187,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f144,f94]) ).
fof(f196,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f187,f99]) ).
fof(f197,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f139,f196]) ).
fof(f200,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f197,f153]) ).
fof(f206,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f142,f200]) ).
fof(f207,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f144,f200]) ).
fof(f209,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f207,f3]) ).
fof(f210,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f206,f80]) ).
fof(f219,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f180,f209]) ).
fof(f220,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f196,f209]) ).
fof(f222,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f220,f1]) ).
fof(f223,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f256,plain,
( sk_c6 = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f156,f196]) ).
fof(f257,plain,
( identity = multiply(sk_c3,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f256,f222]) ).
fof(f259,plain,
( sk_c7 = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f99,f223]) ).
fof(f268,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f259,f209]) ).
fof(f274,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f257,f223]) ).
fof(f275,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f1]) ).
fof(f276,plain,
( sk_c6 != multiply(sk_c7,identity)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f72,f275]) ).
fof(f287,plain,
( sk_c6 != multiply(identity,identity)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f276,f209]) ).
fof(f291,plain,
( identity != sk_c6
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f1]) ).
fof(f294,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f291,f222]) ).
fof(f295,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f324,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f84]) ).
fof(f327,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f139,f71]) ).
fof(f329,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f71]) ).
fof(f330,plain,
( sk_c5 = multiply(sk_c5,sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f327,f153]) ).
fof(f331,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f144,f105]) ).
fof(f333,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f331,f84]) ).
fof(f334,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f144,f128]) ).
fof(f336,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f334,f119]) ).
fof(f340,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f68,f153]) ).
fof(f342,plain,
( sk_c5 != sk_c5
| sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f68,f105]) ).
fof(f343,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f342]) ).
fof(f345,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f343,f84]) ).
fof(f346,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f361,definition,
( spl0_20
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f362,plain,
( identity = sk_c5
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f379,plain,
( sk_c6 != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f58,f1]) ).
fof(f384,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f58,f80]) ).
fof(f385,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f384]) ).
fof(f387,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f385,f89]) ).
fof(f388,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f399,definition,
( spl0_25
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f400,plain,
( identity = sk_c6
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f410,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f75,f128]) ).
fof(f411,plain,
( sk_c6 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f75,f64]) ).
fof(f412,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f410]) ).
fof(f414,definition,
( spl0_26
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f416,plain,
( sk_c7 != inverse(sk_c6)
| spl0_26 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f418,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f412,f119]) ).
fof(f419,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f434,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f61,f1]) ).
fof(f437,plain,
( sk_c7 != sk_c5
| sk_c7 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f61,f153]) ).
fof(f438,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f61,f94]) ).
fof(f448,definition,
( spl0_30
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f449,plain,
( identity = sk_c7
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f461,plain,
( sk_c5 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f144,f330]) ).
fof(f463,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f461,f3]) ).
fof(f466,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f463,f87,f78,f70,f63,f361]) ).
fof(f495,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f144,f336]) ).
fof(f498,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f495,f3]) ).
fof(f500,plain,
( spl0_25
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f498,f126,f117,f399]) ).
fof(f511,plain,
( sk_c7 = multiply(inverse(identity),sk_c5)
| ~ spl0_3
| ~ spl0_25 ),
inference(superposition,[],[f184,f400]) ).
fof(f513,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f324,f400]) ).
fof(f519,plain,
( identity = sk_c2
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f513,f1]) ).
fof(f521,plain,
( sk_c7 = multiply(inverse(identity),identity)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f511,f362]) ).
fof(f530,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f521,f3]) ).
fof(f541,plain,
( spl0_30
| ~ spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f530,f399,f361,f63,f448]) ).
fof(f560,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f333,f400]) ).
fof(f564,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f560,f1]) ).
fof(f567,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f564,f399,f103,f82,f361]) ).
fof(f571,plain,
( identity != sk_c5
| sk_c6 != inverse(identity)
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f379,f400]) ).
fof(f588,plain,
( identity != inverse(identity)
| identity != sk_c5
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f571,f400]) ).
fof(f595,definition,
( spl0_31
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f596,plain,
( identity = inverse(identity)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f598,plain,
( ~ spl0_20
| ~ spl0_31
| ~ spl0_1
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f588,f399,f57,f595,f361]) ).
fof(f618,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(identity,X0))
| ~ spl0_5
| ~ spl0_20 ),
inference(superposition,[],[f329,f362]) ).
fof(f620,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,X0)
| ~ spl0_5
| ~ spl0_20 ),
inference(forward_demodulation,[],[f618,f1]) ).
fof(f625,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,X0)
| ~ spl0_5
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f620,f400]) ).
fof(f628,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_5
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f625,f1]) ).
fof(f632,plain,
( sk_c6 = multiply(identity,sk_c5)
| ~ spl0_5
| ~ spl0_30 ),
inference(superposition,[],[f71,f449]) ).
fof(f643,plain,
( sk_c6 = sk_c5
| ~ spl0_5
| ~ spl0_30 ),
inference(forward_demodulation,[],[f632,f1]) ).
fof(f655,plain,
( sk_c6 = inverse(identity)
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f84,f519]) ).
fof(f656,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f655,f400]) ).
fof(f659,plain,
( spl0_31
| ~ spl0_8
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f656,f399,f82,f595]) ).
fof(f662,plain,
( identity != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f65,f362]) ).
fof(f666,plain,
( identity != multiply(identity,sk_c7)
| spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f662,f400]) ).
fof(f667,plain,
( identity != sk_c7
| spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f666,f1]) ).
fof(f668,plain,
( ~ spl0_30
| spl0_3
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f667,f399,f361,f63,f448]) ).
fof(f721,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_25 ),
inference(superposition,[],[f336,f628]) ).
fof(f726,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f721,f400]) ).
fof(f735,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f438]) ).
fof(f738,plain,
( identity != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_2
| ~ spl0_25 ),
inference(forward_demodulation,[],[f434,f400]) ).
fof(f739,plain,
( identity != sk_c7
| sk_c7 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f437,f362]) ).
fof(f740,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f735,f92,f60,f97]) ).
fof(f748,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(forward_demodulation,[],[f200,f362]) ).
fof(f750,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f210,f400]) ).
fof(f770,plain,
( sk_c7 != inverse(identity)
| ~ spl0_25
| spl0_26 ),
inference(forward_demodulation,[],[f416,f400]) ).
fof(f773,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[],[f643,f362]) ).
fof(f775,plain,
( spl0_30
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f726,f399,f361,f126,f117,f70,f448]) ).
fof(f779,plain,
( identity != sk_c7
| identity != sk_c7
| ~ spl0_2
| ~ spl0_25
| ~ spl0_31 ),
inference(forward_demodulation,[],[f738,f596]) ).
fof(f780,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_25
| ~ spl0_31 ),
inference(duplicate_literal_removal,[],[f779]) ).
fof(f781,plain,
( sk_c7 != inverse(identity)
| identity != sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25 ),
inference(forward_demodulation,[],[f739,f400]) ).
fof(f791,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(forward_demodulation,[],[f748,f1]) ).
fof(f792,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f750,f1]) ).
fof(f801,plain,
( identity != sk_c7
| ~ spl0_25
| spl0_26
| ~ spl0_31 ),
inference(forward_demodulation,[],[f770,f596]) ).
fof(f805,plain,
( ~ spl0_30
| ~ spl0_2
| ~ spl0_25
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f780,f595,f399,f60,f448]) ).
fof(f806,plain,
( identity != sk_c7
| identity != sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25
| ~ spl0_31 ),
inference(forward_demodulation,[],[f781,f596]) ).
fof(f807,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25
| ~ spl0_31 ),
inference(duplicate_literal_removal,[],[f806]) ).
fof(f810,plain,
( spl0_30
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f791,f361,f97,f92,f87,f78,f63,f448]) ).
fof(f811,plain,
( spl0_30
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f792,f399,f97,f92,f87,f78,f63,f448]) ).
fof(f813,plain,
( ~ spl0_30
| ~ spl0_25
| spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f801,f595,f414,f399,f448]) ).
fof(f814,plain,
( ~ spl0_30
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f807,f595,f399,f361,f87,f78,f60,f448]) ).
fof(f816,plain,
( sk_c6 != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f340]) ).
fof(f822,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f816,f400]) ).
fof(f833,plain,
( spl0_31
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f268,f97,f92,f87,f78,f63,f595]) ).
fof(f837,plain,
( ~ spl0_31
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f822,f399,f87,f78,f67,f595]) ).
fof(f852,plain,
( identity != sk_c6
| sk_c7 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[],[f411,f362]) ).
fof(f859,plain,
( spl0_25
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f222,f97,f92,f87,f78,f63,f399]) ).
fof(f863,plain,
( spl0_25
| ~ spl0_5
| ~ spl0_20
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f773,f448,f361,f70,f399]) ).
fof(f864,plain,
( ~ spl0_26
| ~ spl0_25
| ~ spl0_3
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f852,f361,f74,f63,f399,f414]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f85]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f90]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f95]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f110]) ).
cnf(s12,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f111]) ).
cnf(s13,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s14,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s15,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f114]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f115]) ).
cnf(s17,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s19,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s20,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s21,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s22,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s23,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s24,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f131]) ).
cnf(s25,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f295]) ).
cnf(s31,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f346]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f388]) ).
cnf(s40,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f419]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_20 ),
inference(sat_conversion,[],[f466]) ).
cnf(s49,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_25 ),
inference(sat_conversion,[],[f500]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_25
| spl0_30 ),
inference(sat_conversion,[],[f541]) ).
cnf(s59,plain,
( ~ spl0_8
| ~ spl0_12
| spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f567]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_20
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f598]) ).
cnf(s71,plain,
( ~ spl0_8
| ~ spl0_25
| spl0_31 ),
inference(sat_conversion,[],[f659]) ).
cnf(s76,plain,
( spl0_3
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f668]) ).
cnf(s82,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f740]) ).
cnf(s98,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_25
| spl0_30 ),
inference(sat_conversion,[],[f775]) ).
cnf(s106,plain,
( ~ spl0_2
| ~ spl0_25
| ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f805]) ).
cnf(s107,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_20
| spl0_30 ),
inference(sat_conversion,[],[f810]) ).
cnf(s108,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25
| spl0_30 ),
inference(sat_conversion,[],[f811]) ).
cnf(s113,plain,
( ~ spl0_25
| spl0_26
| ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f813]) ).
cnf(s114,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f814]) ).
cnf(s124,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_31 ),
inference(sat_conversion,[],[f833]) ).
cnf(s126,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f837]) ).
cnf(s136,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_25 ),
inference(sat_conversion,[],[f859]) ).
cnf(s138,plain,
( ~ spl0_5
| ~ spl0_20
| spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f863]) ).
cnf(s139,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_20
| ~ spl0_25
| ~ spl0_26 ),
inference(sat_conversion,[],[f864]) ).
cnf(s141,plain,
spl0_3,
inference(rat,[],[s98,s76,s59,s49,s6,s11,s16,s21,s26]) ).
cnf(s142,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s40,s17,s22]) ).
cnf(s143,plain,
( spl0_14
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s139,s113,s47,s108,s124,s136,s23,s24,s25,s142,s141]) ).
cnf(s144,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s139,s113,s47,s108,s124,s136,s18,s19,s20,s40,s143,s142,s1,s141]) ).
cnf(s145,plain,
spl0_5,
inference(rat,[],[s27,s12,s13,s14,s15,s141]) ).
cnf(s147,plain,
( spl0_14
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s126,s124,s136,s23,s24,s25,s141]) ).
cnf(s148,plain,
( ~ spl0_9
| ~ spl0_25
| ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s124,s4,s5,s71,s126,s141]) ).
cnf(s149,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s31,s3,s8]) ).
cnf(s150,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s107,s19,s20,s138,s49,s47,s148,s147,s149,s141,s145]) ).
cnf(s151,plain,
~ spl0_4,
inference(rat,[],[s31,s2,s7,s150]) ).
cnf(s152,plain,
( ~ spl0_25
| ~ spl0_30
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20
| ~ spl0_9 ),
inference(rat,[],[s124,s4,s5,s71,s114,s141]) ).
cnf(s153,plain,
( ~ spl0_25
| ~ spl0_9
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s152,s55,s47,s141,s145]) ).
cnf(s154,plain,
( ~ spl0_9
| ~ spl0_14
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s107,s19,s20,s138,s49,s153,s47,s141,s145]) ).
cnf(s155,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s106,s55,s71,s59,s49,s3,s8,s18,s154,s141]) ).
cnf(s156,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s82,s24,s25]) ).
cnf(s157,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s106,s55,s71,s59,s49,s2,s7,s17,s155,s141]) ).
cnf(s158,plain,
~ spl0_2,
inference(rat,[],[s157,s156]) ).
cnf(s159,plain,
spl0_1,
inference(rat,[],[s144,s145,s151,s158]) ).
cnf(s160,plain,
( ~ spl0_8
| ~ spl0_25
| ~ spl0_12 ),
inference(rat,[],[s65,s71,s59,s159]) ).
cnf(s161,plain,
spl0_9,
inference(rat,[],[s160,s49,s3,s8,s18,s23]) ).
cnf(s162,plain,
~ spl0_7,
inference(rat,[],[s35,s159,s161]) ).
cnf(s163,plain,
spl0_14,
inference(rat,[],[s22,s162]) ).
cnf(s164,plain,
spl0_13,
inference(rat,[],[s17,s162]) ).
cnf(s165,plain,
spl0_12,
inference(rat,[],[s7,s162]) ).
cnf(s166,plain,
spl0_8,
inference(rat,[],[s2,s162]) ).
cnf(s168,plain,
spl0_25,
inference(rat,[],[s49,s163,s164]) ).
cnf(s169,plain,
$false,
inference(rat,[],[s160,s165,s168,s166]) ).
fof(f868,plain,
$false,
inference(avatar_sat_refutation,[],[s169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP272-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:44:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.48 % (705301)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (705307)% WARNING: option uhcvi not known.
% 0.15/0.48 % (705307)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3442587080:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (705306)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2703570540_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (705309)dis+10_1_sil=32000:sp=arity:random_seed=680210537:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (705308)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2465277474:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (705311)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1497282030:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (705310)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2564619718:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (705312)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4076032914:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (705309) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-705301-705309"...
% 0.15/0.48 % (705311) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-705301-705311"...
% 0.15/0.48 % (705310) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-705301-705310"...
% 0.15/0.48 % TRYING [5]
% 0.15/0.48 % (705309)...printing done.
% 0.15/0.48 % (705307) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-705301-705307"...
% 0.15/0.48 % (705309)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (705309)------------------------------
% 0.15/0.48 % (705309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (705309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (705309)CaDiCaL version: 2.1.3
% 0.15/0.48 % (705309)Termination reason: Refutation
% 0.15/0.48 % (705309)Time elapsed: 0.018 s
% 0.15/0.48 % (705309)Peak memory usage: 12 MB
% 0.15/0.48 % (705309)Instructions burned: 28 (million)
% 0.15/0.48 % (705301)Success in time 0.056 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------