%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP232-1 : 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 : n008.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 10:17:14 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 47
% Syntax : Number of formulae : 301 ( 22 unt; 16 def)
% Number of atoms : 910 ( 302 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1149 ( 540 ~; 593 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 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_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X3,X0,X1,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl0_4
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( inverse(sk_c8) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f68,f82,f79,f76,f73,f70]) ).
fof(f87,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f89,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f93,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f91,f87]) ).
fof(f96,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f91,f96]) ).
fof(f101,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f108,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f91,f106]) ).
fof(f111,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f113,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f91,f111]) ).
fof(f116,definition,
( spl0_12
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f118,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f116,f87]) ).
fof(f120,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f116,f96]) ).
fof(f121,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f116,f101]) ).
fof(f122,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f116,f106]) ).
fof(f123,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f116,f111]) ).
fof(f125,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f125,f87]) ).
fof(f129,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f125,f96]) ).
fof(f130,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f125,f101]) ).
fof(f131,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f125,f106]) ).
fof(f132,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f125,f111]) ).
fof(f134,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f134,f87]) ).
fof(f138,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f134,f96]) ).
fof(f140,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f134,f106]) ).
fof(f141,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f134,f111]) ).
fof(f143,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f145,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f143,f87]) ).
fof(f147,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f143,f96]) ).
fof(f149,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f143,f106]) ).
fof(f150,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f143,f111]) ).
fof(f151,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f82,f87]) ).
fof(f152,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f82,f96]) ).
fof(f153,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f82,f101]) ).
fof(f154,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f82,f106]) ).
fof(f155,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f82,f111]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f89]) ).
fof(f157,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f113]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f162,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f156]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f162,f1]) ).
fof(f166,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f160,f1]) ).
fof(f174,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f165,f98]) ).
fof(f181,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f103,f174]) ).
fof(f204,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f166,f3]) ).
fof(f205,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f166,f166]) ).
fof(f207,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_6 ),
inference(superposition,[],[f166,f165]) ).
fof(f208,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f166,f157]) ).
fof(f209,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f166,f174]) ).
fof(f211,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_6 ),
inference(superposition,[],[f166,f156]) ).
fof(f212,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f166,f108]) ).
fof(f221,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f212,f113]) ).
fof(f223,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f209,f3]) ).
fof(f225,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f204,f205]) ).
fof(f227,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f221,f181]) ).
fof(f230,plain,
( ! [X0] : multiply(X0,sk_c6) = X0
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f225,f223]) ).
fof(f233,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f166,f227]) ).
fof(f235,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f233,f3]) ).
fof(f238,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f223,f235]) ).
fof(f248,plain,
( identity = inverse(sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f3,f230]) ).
fof(f258,plain,
( identity = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f238]) ).
fof(f263,plain,
( inverse(sk_c8) = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f223]) ).
fof(f265,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f263,f238]) ).
fof(f278,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f208,f223]) ).
fof(f283,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f278,f207]) ).
fof(f286,plain,
( sk_c4 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f283,f230]) ).
fof(f312,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f230,f238]) ).
fof(f344,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f84,f265]) ).
fof(f349,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f344,f181]) ).
fof(f350,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f355,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),sk_c8)
| sk_c8 != multiply(X1,inverse(X1)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f77,f181]) ).
fof(f357,plain,
( ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != inverse(X1) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f355,f312]) ).
fof(f361,plain,
( sk_c8 != inverse(identity)
| sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f357,f1]) ).
fof(f363,plain,
( sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f361]) ).
fof(f367,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f363,f223]) ).
fof(f374,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f367,f238]) ).
fof(f375,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f374,f265]) ).
fof(f376,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f377,plain,
( sk_c8 != sk_c7
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(forward_demodulation,[],[f102,f174]) ).
fof(f382,plain,
( sk_c5 = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f211,f83]) ).
fof(f383,plain,
( sk_c4 = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f208,f83]) ).
fof(f385,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f83]) ).
fof(f387,plain,
( sk_c4 = multiply(sk_c7,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f383,f223]) ).
fof(f389,plain,
( sk_c7 = sk_c4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f387,f230]) ).
fof(f398,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl0_12 ),
inference(superposition,[],[f3,f118]) ).
fof(f399,plain,
( sk_c6 = multiply(sk_c3,sk_c2)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f398,f223]) ).
fof(f408,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f136]) ).
fof(f432,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f166,f145]) ).
fof(f434,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f432,f136]) ).
fof(f448,plain,
( sk_c8 != multiply(sk_c2,sk_c3)
| sk_c8 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f77,f118]) ).
fof(f466,plain,
( sk_c8 != multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f448,f127]) ).
fof(f482,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f466,f93]) ).
fof(f483,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f495,plain,
( sk_c2 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f166,f399]) ).
fof(f498,plain,
( sk_c2 = inverse(sk_c3)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f495,f230]) ).
fof(f501,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f74,f3]) ).
fof(f502,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f74,f108]) ).
fof(f505,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f502]) ).
fof(f507,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f505,f113]) ).
fof(f508,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f513,plain,
( identity = multiply(sk_c2,sk_c3)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f3,f498]) ).
fof(f514,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f513,f127]) ).
fof(f519,plain,
( sk_c7 != sk_c6
| sk_c8 != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f80,f98]) ).
fof(f520,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f80,f145]) ).
fof(f524,plain,
( sk_c7 != sk_c6
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f519,f89]) ).
fof(f528,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f211,f514]) ).
fof(f533,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f528,f3]) ).
fof(f535,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f533,f286]) ).
fof(f537,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f535,f389]) ).
fof(f540,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f537,f514]) ).
fof(f541,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f540,f377]) ).
fof(f542,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f545,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f382,f225]) ).
fof(f579,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_5 ),
inference(superposition,[],[f166,f385]) ).
fof(f582,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f579,f225]) ).
fof(f591,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_14 ),
inference(superposition,[],[f166,f408]) ).
fof(f690,plain,
( inverse(sk_c8) = sk_c1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f591,f225]) ).
fof(f693,plain,
( sk_c7 = sk_c1
| ~ spl0_5
| ~ spl0_14 ),
inference(forward_demodulation,[],[f690,f83]) ).
fof(f694,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f408,f693]) ).
fof(f697,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f694,f434]) ).
fof(f699,plain,
( ! [X0,X1] :
( sk_c7 != multiply(sk_c8,multiply(X0,multiply(X1,sk_c8)))
| sk_c8 != inverse(multiply(X0,X1)) )
| ~ spl0_1 ),
inference(superposition,[],[f71,f4]) ).
fof(f700,plain,
( sk_c7 != multiply(sk_c8,identity)
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1 ),
inference(superposition,[],[f71,f3]) ).
fof(f705,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f700,f225]) ).
fof(f710,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1,f697]) ).
fof(f736,plain,
( ! [X0] :
( sk_c7 != multiply(sk_c8,multiply(X0,sk_c8))
| sk_c8 != inverse(multiply(identity,X0)) )
| ~ spl0_1 ),
inference(superposition,[],[f699,f1]) ).
fof(f751,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| sk_c8 != inverse(multiply(identity,X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f736,f710]) ).
fof(f763,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f751,f1]) ).
fof(f769,plain,
( spl0_4
| ~ spl0_1
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f763,f143,f134,f82,f70,f79]) ).
fof(f776,plain,
( sk_c8 != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f501,f697]) ).
fof(f780,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f776,f582]) ).
fof(f785,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f780,f83]) ).
fof(f838,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f166,f434]) ).
fof(f842,plain,
( identity = sk_c7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f838,f3]) ).
fof(f846,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f842,f697]) ).
fof(f847,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f846,f785]) ).
fof(f848,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f847]) ).
fof(f849,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f520]) ).
fof(f851,definition,
( spl0_18
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f852,plain,
( sk_c8 = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f856,plain,
( ~ spl0_14
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f849,f143,f79,f134]) ).
fof(f859,plain,
( spl0_18
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f181,f101,f96,f87,f851]) ).
fof(f882,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f98,f312]) ).
fof(f908,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f882,f545]) ).
fof(f924,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f908,f524]) ).
fof(f925,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f924]) ).
fof(f941,plain,
( sk_c8 != inverse(sk_c7)
| sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f705,f83]) ).
fof(f983,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f941,f582]) ).
fof(f1006,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f983,f852]) ).
fof(f1007,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1006]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f99]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f109]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f123]) ).
cnf(s12,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s17,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s21,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s22,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s23,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f150]) ).
cnf(s27,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f151]) ).
cnf(s28,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f152]) ).
cnf(s29,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f153]) ).
cnf(s30,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s31,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f155]) ).
cnf(s32,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f350]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f376]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f483]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f508]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f542]) ).
cnf(s52,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f769]) ).
cnf(s56,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f848]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f856]) ).
cnf(s60,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f859]) ).
cnf(s75,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f925]) ).
cnf(s87,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_18 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s93,plain,
spl0_5,
inference(rat,[],[s32,s27,s28,s29,s30,s31]) ).
cnf(s95,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s58,s21,s26]) ).
cnf(s96,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s58,s20,s25]) ).
cnf(s97,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_4
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s44,s9,s14,s75,s93]) ).
cnf(s98,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s58,s18,s23]) ).
cnf(s99,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_4
| ~ spl0_11 ),
inference(rat,[],[s58,s17,s22,s97]) ).
cnf(s100,plain,
~ spl0_4,
inference(rat,[],[s99,s98,s96,s95]) ).
cnf(s101,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s39,s6,s11,s16]) ).
cnf(s102,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_11 ),
inference(rat,[],[s44,s9,s14,s93]) ).
cnf(s103,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s39,s5,s10,s15]) ).
cnf(s104,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s36,s102,s101,s103]) ).
cnf(s105,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s39,s3,s8,s13]) ).
cnf(s106,plain,
( ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s39,s2,s7,s12,s104]) ).
cnf(s107,plain,
~ spl0_3,
inference(rat,[],[s106,s105]) ).
cnf(s108,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s56,s21,s26,s93]) ).
cnf(s109,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s56,s20,s25,s41,s93]) ).
cnf(s110,plain,
~ spl0_2,
inference(rat,[],[s109,s108]) ).
cnf(s111,plain,
spl0_1,
inference(rat,[],[s1,s93,s100,s107,s110]) ).
cnf(s112,plain,
~ spl0_18,
inference(rat,[],[s87,s93,s111]) ).
cnf(s113,plain,
spl0_11,
inference(rat,[],[s52,s21,s26,s93,s100,s111]) ).
cnf(s114,plain,
( ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s60,s102,s113,s112]) ).
cnf(s115,plain,
spl0_8,
inference(rat,[],[s52,s18,s23,s93,s100,s111]) ).
cnf(s116,plain,
~ spl0_6,
inference(rat,[],[s114,s115]) ).
cnf(s117,plain,
spl0_15,
inference(rat,[],[s22,s116]) ).
cnf(s118,plain,
spl0_14,
inference(rat,[],[s17,s116]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s52,s111,s100,s93,s117,s118]) ).
fof(f1033,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:38:54 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.19/0.48 % (982787)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (982796)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=851279646:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48 % (982793)% WARNING: option uhcvi not known.
% 0.19/0.48 % (982792)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3132060736_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48 % (982793)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3239541093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48 % (982797)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4113293303:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48 % (982794)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2940683386:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48 % (982795)dis+10_1_sil=32000:sp=arity:random_seed=272655154:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (982798)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2599508693:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48 % (982796) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-982787-982796"...
% 0.19/0.48 % TRYING [1]
% 0.19/0.48 % TRYING [2]
% 0.19/0.48 % (982796)...printing done.
% 0.19/0.48 % TRYING [3]
% 0.19/0.48 % (982796)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (982796)------------------------------
% 0.19/0.48 % (982796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48 % (982796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48 % (982796)CaDiCaL version: 2.1.3
% 0.19/0.48 % (982796)Termination reason: Refutation
% 0.19/0.48 % (982796)Time elapsed: 0.011 s
% 0.19/0.48 % (982796)Peak memory usage: 12 MB
% 0.19/0.48 % (982796)Instructions burned: 32 (million)
% 0.19/0.48 % (982787)Success in time 0.035 s
% 0.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------