%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP218-1 : 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 : n006.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 10:17:12 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 50
% Syntax : Number of formulae : 224 ( 17 unt; 18 def)
% Number of atoms : 576 ( 251 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 602 ( 250 ~; 334 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 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_c1) = sk_c10
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f17]) ).
fof(f25,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c9
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c2,sk_c3)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f59,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c10,sk_c5)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c9
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c10,sk_c5)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c9
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c10,sk_c5)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f63]) ).
fof(f69,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c5 = multiply(sk_c4,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c5
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c5 = multiply(sk_c4,sk_c10)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c5
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c5 = multiply(sk_c4,sk_c10)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = multiply(sk_c7,sk_c10) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c10
| multiply(X1,X2) != sk_c9
| inverse(X1) != X2
| multiply(X2,sk_c10) != sk_c9
| multiply(sk_c10,X3) != sk_c9
| multiply(X4,sk_c10) != X3
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(sk_c10,X6) != sk_c9
| multiply(X7,sk_c10) != X6
| inverse(X7) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| multiply(X1,X2) != sk_c9
| inverse(X1) != X2
| sk_c9 != multiply(X2,sk_c10)
| sk_c9 != multiply(sk_c10,X3)
| multiply(X4,sk_c10) != X3
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(sk_c10,X3)
| multiply(X4,sk_c10) != X3
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(sk_c10,multiply(X4,sk_c10))
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c10,X6)
| multiply(X7,sk_c10) != X6
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(sk_c10,multiply(X4,sk_c10))
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) ),
inference(equality_resolution,[],[f88]) ).
fof(f91,definition,
( spl0_1
<=> ! [X7] :
( sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f92,plain,
( ! [X7] :
( sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != inverse(X7) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,definition,
( spl0_2
<=> ! [X5] :
( sk_c10 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f95,plain,
( ! [X5] :
( sk_c10 != multiply(X5,sk_c9)
| sk_c10 != inverse(X5) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_3
<=> ! [X1] :
( sk_c9 != multiply(X1,inverse(X1))
| sk_c9 != multiply(inverse(X1),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f98,plain,
( ! [X1] :
( sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f89,f94,f97,f91,f94,f91]) ).
fof(f101,definition,
( spl0_4
<=> sk_c10 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( sk_c10 = inverse(sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl0_5
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f107,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f84,f105,f101]) ).
fof(f110,definition,
( spl0_6
<=> sk_c8 = multiply(sk_c7,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f82,f105,f110]) ).
fof(f115,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f117,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f80,f105,f115]) ).
fof(f120,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f122,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f125,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f127,plain,
( sk_c10 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f130,definition,
( spl0_10
<=> sk_c5 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f132,plain,
( sk_c5 = multiply(sk_c4,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f74,f130,f101]) ).
fof(f134,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f72,f130,f110]) ).
fof(f135,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f70,f130,f115]) ).
fof(f139,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c10,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f141,plain,
( sk_c9 = multiply(sk_c10,sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f64,f139,f101]) ).
fof(f143,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f62,f139,f110]) ).
fof(f144,plain,
( spl0_7
| spl0_11 ),
inference(avatar_split_clause,[],[f60,f139,f115]) ).
fof(f148,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f150,plain,
( sk_c9 = multiply(sk_c3,sk_c10)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f148,f101]) ).
fof(f152,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f148,f110]) ).
fof(f153,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f148,f115]) ).
fof(f154,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f148,f120]) ).
fof(f155,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f148,f125]) ).
fof(f157,definition,
( spl0_13
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f159,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f157,f101]) ).
fof(f161,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f157,f110]) ).
fof(f162,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f157,f115]) ).
fof(f163,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f157,f120]) ).
fof(f164,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f157,f125]) ).
fof(f166,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f169,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f166,f101]) ).
fof(f170,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f166,f110]) ).
fof(f171,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f166,f115]) ).
fof(f172,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f166,f120]) ).
fof(f173,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f166,f125]) ).
fof(f175,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f181,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f175,f120]) ).
fof(f182,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f175,f125]) ).
fof(f184,definition,
( spl0_16
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( inverse(sk_c1) = sk_c10
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f190,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f8,f184,f120]) ).
fof(f191,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f6,f184,f125]) ).
fof(f192,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f95,f122]) ).
fof(f193,plain,
( sk_c10 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f192]) ).
fof(f194,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f193,f127]) ).
fof(f195,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f196,plain,
( sk_c10 != sk_c10
| inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f95,f177]) ).
fof(f197,plain,
( inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f196]) ).
fof(f198,plain,
( $false
| ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f197,f186]) ).
fof(f199,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f198]) ).
fof(f203,plain,
( sk_c9 != multiply(sk_c3,sk_c10)
| sk_c9 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f98,f159]) ).
fof(f206,plain,
( sk_c9 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f203,f150]) ).
fof(f213,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f214,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f230,definition,
( spl0_21
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f232,plain,
( sk_c9 != sk_c8
| spl0_21 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f234,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f92,f112]) ).
fof(f236,plain,
( sk_c9 != multiply(sk_c10,sk_c5)
| sk_c10 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f92,f132]) ).
fof(f237,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f236,f141]) ).
fof(f247,plain,
( sk_c10 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f234,f117]) ).
fof(f248,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f237,f107]) ).
fof(f249,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f250,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f247,f103]) ).
fof(f251,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f261,plain,
( ~ spl0_14
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f206,f157,f148,f97,f166]) ).
fof(f266,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c9 != multiply(sk_c7,sk_c10)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f98,f103]) ).
fof(f270,plain,
( sk_c9 != sk_c8
| sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f266,f112]) ).
fof(f273,plain,
( ~ spl0_18
| ~ spl0_21
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f270,f110,f101,f97,f230,f213]) ).
fof(f275,plain,
( identity = multiply(sk_c10,sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f3,f127]) ).
fof(f276,plain,
( identity = multiply(sk_c10,sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f3,f103]) ).
fof(f291,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f298,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f291,f1]) ).
fof(f303,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c6,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f275]) ).
fof(f304,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c6,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f303,f1]) ).
fof(f305,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c7,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f276]) ).
fof(f306,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c7,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f305,f1]) ).
fof(f316,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f304,f122]) ).
fof(f321,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f316,f125,f120,f213]) ).
fof(f326,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f306,f112]) ).
fof(f332,plain,
( sk_c10 = sk_c9
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f326,f117]) ).
fof(f412,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f298,f214]) ).
fof(f440,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f412,f332]) ).
fof(f446,plain,
( identity = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f440,f3]) ).
fof(f466,plain,
( sk_c9 = multiply(identity,sk_c8)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f117,f446]) ).
fof(f507,plain,
( sk_c9 = sk_c8
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f466,f1]) ).
fof(f520,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f507,f232]) ).
fof(f521,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f520]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f108]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f113]) ).
cnf(s5,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f133]) ).
cnf(s9,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f134]) ).
cnf(s10,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f135]) ).
cnf(s13,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f142]) ).
cnf(s14,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f143]) ).
cnf(s15,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f144]) ).
cnf(s18,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f151]) ).
cnf(s19,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s20,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f153]) ).
cnf(s21,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f154]) ).
cnf(s22,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s23,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s24,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f161]) ).
cnf(s25,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s26,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s27,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f164]) ).
cnf(s28,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s29,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f170]) ).
cnf(s30,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f171]) ).
cnf(s31,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f172]) ).
cnf(s32,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f173]) ).
cnf(s36,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s37,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f182]) ).
cnf(s41,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f190]) ).
cnf(s42,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f191]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f195]) ).
cnf(s44,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f199]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f249]) ).
cnf(s52,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f251]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f261]) ).
cnf(s63,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f273]) ).
cnf(s67,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f321]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f521]) ).
cnf(s71,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s56,s18,s23,s28]) ).
cnf(s72,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s63,s69,s67,s29,s30,s31,s32,s71]) ).
cnf(s73,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s63,s69,s67,s24,s25,s26,s27,s71]) ).
cnf(s74,plain,
~ spl0_3,
inference(rat,[],[s63,s69,s67,s19,s20,s21,s22,s56,s73,s72,s71]) ).
cnf(s76,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s44,s37,s42]) ).
cnf(s77,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s44,s36,s41,s43]) ).
cnf(s78,plain,
~ spl0_2,
inference(rat,[],[s77,s76]) ).
cnf(s79,plain,
spl0_1,
inference(rat,[],[s2,s74,s78]) ).
cnf(s81,plain,
spl0_7,
inference(rat,[],[s51,s5,s10,s15,s79]) ).
cnf(s82,plain,
spl0_6,
inference(rat,[],[s51,s4,s9,s14,s79]) ).
cnf(s83,plain,
~ spl0_4,
inference(rat,[],[s52,s81,s79,s82]) ).
cnf(s89,plain,
spl0_11,
inference(rat,[],[s13,s83]) ).
cnf(s90,plain,
spl0_10,
inference(rat,[],[s8,s83]) ).
cnf(s91,plain,
spl0_5,
inference(rat,[],[s3,s83]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s51,s91,s79,s89,s90]) ).
fof(f530,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:37:41 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 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
% 0.14/0.46 % (2738478)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (2738484)% WARNING: option uhcvi not known.
% 0.14/0.46 % (2738483)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=966777008_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % (2738484)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1947957763:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.46 % (2738485)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3133988463:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.46 % (2738486)dis+10_1_sil=32000:sp=arity:random_seed=3006889227:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.46 % (2738487)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3162916067:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.46 % (2738488)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=580530454:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.46 % (2738489)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=206448141:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.46 % TRYING [1]
% 0.14/0.46 % TRYING [2]
% 0.14/0.46 % TRYING [3]
% 0.14/0.46 % (2738486) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2738478-2738486"...
% 0.14/0.46 % (2738484) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2738478-2738484"...
% 0.14/0.46 % TRYING [4]
% 0.14/0.46 % (2738486)...printing done.
% 0.14/0.46 % (2738484)...printing done.
% 0.14/0.46 % (2738486)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (2738486)------------------------------
% 0.14/0.46 % (2738486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (2738486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (2738486)CaDiCaL version: 2.1.3
% 0.14/0.46 % (2738486)Termination reason: Refutation
% 0.14/0.46 % (2738486)Time elapsed: 0.011 s
% 0.14/0.46 % (2738486)Peak memory usage: 12 MB
% 0.14/0.46 % (2738486)Instructions burned: 17 (million)
% 0.14/0.46 % (2738478)Success in time 0.046 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------