%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP235-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:17:15 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 45
% Syntax : Number of formulae : 276 ( 18 unt; 16 def)
% Number of atoms : 908 ( 281 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1200 ( 568 ~; 616 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 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 : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = 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_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = 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_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = 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_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| multiply(X2,sk_c8) != sk_c7
| 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/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| sk_c7 != multiply(X2,sk_c8)
| 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
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8)
| 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
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8)
| 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 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> ! [X1] :
( sk_c7 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ! [X1] :
( sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c7 != multiply(X1,inverse(X1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl0_4
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( inverse(sk_c8) != sk_c7
| spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f68,f79,f73,f76,f73,f70]) ).
fof(f84,definition,
( spl0_5
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f90,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f64,f88,f84]) ).
fof(f93,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f62,f88,f93]) ).
fof(f98,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f100,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f60,f88,f98]) ).
fof(f103,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f104,plain,
( sk_c8 != multiply(sk_c4,sk_c7)
| spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f58,f88,f103]) ).
fof(f108,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f56,f88,f108]) ).
fof(f113,definition,
( spl0_11
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f115,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f54,f113,f84]) ).
fof(f117,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f52,f113,f93]) ).
fof(f118,plain,
( spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f50,f113,f98]) ).
fof(f119,plain,
( spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f48,f113,f103]) ).
fof(f120,plain,
( spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f46,f113,f108]) ).
fof(f122,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f124,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_5
| spl0_12 ),
inference(avatar_split_clause,[],[f44,f122,f84]) ).
fof(f126,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f42,f122,f93]) ).
fof(f127,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f40,f122,f98]) ).
fof(f128,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f38,f122,f103]) ).
fof(f129,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f122,f108]) ).
fof(f140,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f142,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_5
| spl0_14 ),
inference(avatar_split_clause,[],[f24,f140,f84]) ).
fof(f144,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f22,f140,f93]) ).
fof(f145,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f20,f140,f98]) ).
fof(f146,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f18,f140,f103]) ).
fof(f147,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f16,f140,f108]) ).
fof(f148,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f14,f79,f84]) ).
fof(f149,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f79,f93]) ).
fof(f150,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f10,f79,f98]) ).
fof(f151,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f79,f103]) ).
fof(f152,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f6,f79,f108]) ).
fof(f153,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_5 ),
inference(superposition,[],[f3,f86]) ).
fof(f154,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f110]) ).
fof(f157,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f159,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f153]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f159,f1]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f157,f1]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f162,f95]) ).
fof(f177,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f171,f100]) ).
fof(f201,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f163,f154]) ).
fof(f205,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_9 ),
inference(superposition,[],[f163,f105]) ).
fof(f214,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f205,f110]) ).
fof(f219,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f214,f177]) ).
fof(f228,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f163,f219]) ).
fof(f230,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f228,f3]) ).
fof(f233,plain,
( sk_c7 != inverse(identity)
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f81,f230]) ).
fof(f251,plain,
( sk_c8 != inverse(identity)
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f233,f177]) ).
fof(f255,plain,
( identity != inverse(identity)
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f251,f230]) ).
fof(f259,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f201,f230]) ).
fof(f260,plain,
( identity = sk_c4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f259,f3]) ).
fof(f264,plain,
( sk_c8 = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f110,f260]) ).
fof(f265,plain,
( identity = inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f264,f230]) ).
fof(f308,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f255,f265]) ).
fof(f309,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f310,plain,
( ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f77,f177]) ).
fof(f312,plain,
( ! [X1] :
( identity != multiply(X1,inverse(X1))
| sk_c7 != multiply(inverse(X1),sk_c8) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f310,f230]) ).
fof(f314,plain,
( ! [X1] :
( sk_c7 != multiply(inverse(X1),identity)
| identity != multiply(X1,inverse(X1)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f312,f230]) ).
fof(f315,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),identity)
| identity != multiply(X1,inverse(X1)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f314,f177]) ).
fof(f316,plain,
( ! [X1] :
( identity != multiply(inverse(X1),identity)
| identity != multiply(X1,inverse(X1)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f315,f230]) ).
fof(f318,plain,
( identity != multiply(sk_c8,identity)
| identity != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f316,f110]) ).
fof(f326,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f318,f230]) ).
fof(f330,plain,
( identity != multiply(sk_c4,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f326,f1]) ).
fof(f332,plain,
( identity != multiply(sk_c4,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f330,f230]) ).
fof(f334,plain,
( identity != multiply(identity,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f332,f260]) ).
fof(f337,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f334,f1]) ).
fof(f338,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f339,plain,
( ! [X5] :
( sk_c7 != multiply(identity,multiply(X5,identity))
| sk_c8 != inverse(X5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f71,f230]) ).
fof(f340,plain,
( ! [X5] :
( sk_c7 != multiply(X5,identity)
| sk_c8 != inverse(X5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f339,f1]) ).
fof(f341,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| sk_c8 != inverse(X5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f340,f177]) ).
fof(f342,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c8 != inverse(X5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f341,f230]) ).
fof(f343,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f342,f230]) ).
fof(f347,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f343,f3]) ).
fof(f348,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f347]) ).
fof(f350,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f348,f265]) ).
fof(f353,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f350,f265]) ).
fof(f354,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f355,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f74,f230]) ).
fof(f356,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f355,f177]) ).
fof(f357,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f356,f230]) ).
fof(f362,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f357,f3]) ).
fof(f363,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f362]) ).
fof(f365,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f363,f265]) ).
fof(f368,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f365,f265]) ).
fof(f369,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f371,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f80]) ).
fof(f375,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f142]) ).
fof(f378,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f163,f124]) ).
fof(f380,plain,
( sk_c3 = multiply(sk_c3,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f378,f115]) ).
fof(f388,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| sk_c7 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f77,f115]) ).
fof(f391,plain,
( sk_c7 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f388,f90]) ).
fof(f397,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f399,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| spl0_16 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f421,definition,
( spl0_21
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f422,plain,
( identity = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f425,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f391,f124]) ).
fof(f426,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f431,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f71,f1]) ).
fof(f456,definition,
( spl0_25
<=> sk_c8 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f457,plain,
( sk_c8 = inverse(identity)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f458,plain,
( sk_c8 != inverse(identity)
| spl0_25 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f459,plain,
( ~ spl0_25
| ~ spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f431,f70,f397,f456]) ).
fof(f503,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f380]) ).
fof(f505,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f503,f3]) ).
fof(f509,plain,
( spl0_21
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f505,f122,f113,f421]) ).
fof(f513,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_4
| ~ spl0_21 ),
inference(superposition,[],[f371,f422]) ).
fof(f517,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f513,f1]) ).
fof(f525,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f154,f517]) ).
fof(f529,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f375,f517]) ).
fof(f534,plain,
( identity = sk_c1
| ~ spl0_4
| ~ spl0_14
| ~ spl0_21 ),
inference(forward_demodulation,[],[f529,f1]) ).
fof(f538,plain,
( identity = sk_c4
| ~ spl0_4
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f525,f1]) ).
fof(f556,plain,
( sk_c8 = inverse(identity)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_21 ),
inference(superposition,[],[f142,f534]) ).
fof(f557,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_21
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f556,f458]) ).
fof(f558,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_21
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f564,plain,
( sk_c8 != multiply(sk_c4,identity)
| spl0_9
| ~ spl0_21 ),
inference(forward_demodulation,[],[f104,f422]) ).
fof(f565,plain,
( sk_c7 != multiply(identity,identity)
| ~ spl0_4
| spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f399,f517]) ).
fof(f566,plain,
( identity = inverse(identity)
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_demodulation,[],[f457,f517]) ).
fof(f570,plain,
( identity != multiply(sk_c4,identity)
| ~ spl0_4
| spl0_9
| ~ spl0_21 ),
inference(forward_demodulation,[],[f564,f517]) ).
fof(f571,plain,
( identity != sk_c7
| ~ spl0_4
| spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f565,f1]) ).
fof(f572,plain,
( $false
| ~ spl0_4
| spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f571,f422]) ).
fof(f573,plain,
( ~ spl0_4
| spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f574,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f74,f517]) ).
fof(f578,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f574,f422]) ).
fof(f581,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f578,f517]) ).
fof(f586,plain,
( identity != multiply(identity,identity)
| ~ spl0_4
| spl0_9
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f570,f538]) ).
fof(f587,plain,
( $false
| ~ spl0_4
| spl0_9
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f586,f1]) ).
fof(f588,plain,
( ~ spl0_4
| spl0_9
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f587]) ).
fof(f602,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(superposition,[],[f581,f1]) ).
fof(f606,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f602]) ).
fof(f610,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f606,f566]) ).
fof(f611,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f610]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s8,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s9,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f117]) ).
cnf(s10,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s11,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f119]) ).
cnf(s12,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f120]) ).
cnf(s13,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f125]) ).
cnf(s14,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f126]) ).
cnf(s15,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s16,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s17,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s23,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s24,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s25,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s26,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s27,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s28,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f148]) ).
cnf(s29,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f149]) ).
cnf(s30,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f150]) ).
cnf(s31,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f151]) ).
cnf(s32,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s33,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f309]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f338]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f354]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f369]) ).
cnf(s47,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f426]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_25 ),
inference(sat_conversion,[],[f459]) ).
cnf(s56,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_21 ),
inference(sat_conversion,[],[f509]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_21
| spl0_25 ),
inference(sat_conversion,[],[f558]) ).
cnf(s59,plain,
( ~ spl0_4
| spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f573]) ).
cnf(s60,plain,
( ~ spl0_4
| spl0_9
| ~ spl0_10
| ~ spl0_21 ),
inference(sat_conversion,[],[f588]) ).
cnf(s61,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f611]) ).
cnf(s62,plain,
spl0_4,
inference(rat,[],[s33,s28,s29,s30,s31,s32]) ).
cnf(s63,plain,
( spl0_6
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s37,s4,s5,s6,s7]) ).
cnf(s64,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s47,s12,s17]) ).
cnf(s65,plain,
( spl0_9
| ~ spl0_10 ),
inference(rat,[],[s56,s11,s16,s60,s62]) ).
cnf(s66,plain,
( spl0_8
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s47,s10,s15]) ).
cnf(s67,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s47,s9,s14,s37,s66,s65,s64,s63]) ).
cnf(s68,plain,
~ spl0_3,
inference(rat,[],[s47,s3,s8,s13,s67]) ).
cnf(s69,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s61,s57,s56,s12,s17,s27,s62]) ).
cnf(s70,plain,
( spl0_14
| ~ spl0_9
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s41,s24,s25,s69]) ).
cnf(s71,plain,
( ~ spl0_21
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s57,s61,s62]) ).
cnf(s72,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s41,s14,s15,s69]) ).
cnf(s73,plain,
( ~ spl0_9
| ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s41,s9,s10,s56,s72,s71,s70,s69]) ).
cnf(s74,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s56,s71,s8,s13,s23,s73]) ).
cnf(s75,plain,
~ spl0_2,
inference(rat,[],[s74,s65,s69]) ).
cnf(s76,plain,
spl0_1,
inference(rat,[],[s2,s62,s68,s75]) ).
cnf(s77,plain,
( spl0_14
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s39,s24,s25,s27,s76]) ).
cnf(s78,plain,
( ~ spl0_21
| ~ spl0_14 ),
inference(rat,[],[s50,s57,s59,s76,s62]) ).
cnf(s79,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s39,s14,s15,s17,s76]) ).
cnf(s80,plain,
( ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s39,s9,s10,s12,s56,s79,s78,s77,s76]) ).
cnf(s81,plain,
spl0_9,
inference(rat,[],[s56,s78,s11,s16,s26]) ).
cnf(s82,plain,
~ spl0_5,
inference(rat,[],[s80,s81]) ).
cnf(s83,plain,
spl0_14,
inference(rat,[],[s23,s82]) ).
cnf(s85,plain,
spl0_12,
inference(rat,[],[s13,s82]) ).
cnf(s86,plain,
spl0_11,
inference(rat,[],[s8,s82]) ).
cnf(s88,plain,
~ spl0_21,
inference(rat,[],[s78,s83]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s56,s88,s86,s85]) ).
fof(f612,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP235-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:38:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.46 % (983056)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (983062)% WARNING: option uhcvi not known.
% 0.12/0.46 % (983065)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2358724599:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.12/0.46 % (983062)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3003334234:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.12/0.46 % (983064)dis+10_1_sil=32000:sp=arity:random_seed=627641880:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.12/0.46 % (983066)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3856924676:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.12/0.46 % (983067)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2694232523:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.12/0.46 % (983063)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2808196236:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.12/0.46 % (983061)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1996457479_3000 on theBenchmark for (3000ds/0Mi)
% 0.12/0.46 % (983064) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-983056-983064"...
% 0.12/0.46 % (983065) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-983056-983065"...
% 0.12/0.46 % TRYING [1]
% 0.12/0.46 % TRYING [2]
% 0.12/0.46 % TRYING [3]
% 0.12/0.46 % (983064)...printing done.
% 0.12/0.46 % TRYING [4]
% 0.12/0.46 % (983065)...printing done.
% 0.12/0.46 % (983064)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (983064)------------------------------
% 0.12/0.46 % (983064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (983064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (983064)CaDiCaL version: 2.1.3
% 0.12/0.46 % (983064)Termination reason: Refutation
% 0.12/0.46 % (983064)Time elapsed: 0.013 s
% 0.12/0.46 % (983064)Peak memory usage: 12 MB
% 0.12/0.46 % (983064)Instructions burned: 20 (million)
% 0.12/0.46 % (983056)Success in time 0.038 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------