%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 : Fri Sep 25 01:32:26 PM UTC 2026
% Result : Unsatisfiable 10.53s 7.28s
% Output : CNFRefutation 10.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of formulae : 253 ( 44 unt; 0 def)
% Number of atoms : 607 ( 571 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 625 ( 271 ~; 354 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 156 !; 0 ?; 127 :)
% 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,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c11 = inverse(sk_c4)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c7)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = inverse(sk_c4)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c11 = inverse(sk_c6)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f30]) ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = inverse(sk_c7)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f38]) ).
fof(f44,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c10 = inverse(sk_c5)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f46]) ).
fof(f52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c7)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f56]) ).
fof(f60,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c11 = inverse(sk_c4)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f64]) ).
fof(f70,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c8 = inverse(sk_c7)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c11 = inverse(sk_c6)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f102,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
fof(f103,plain,
( sk_c11 = inverse(sk_c6)
| sk_c11 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f102]) ).
fof(f104,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| sk_c11 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f104]) ).
fof(f112,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X7,sk_c9)
| inverse(X6) != X7
| sk_c10 != multiply(X6,X7)
| sk_c11 != multiply(X5,sk_c10)
| sk_c11 != inverse(X5)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(X4,sk_c10)
| sk_c11 != inverse(X3)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(X1,sk_c10)
| inverse(X0) != sk_c11
| sk_c10 != multiply(X0,sk_c11) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c10 != multiply(inverse(X6),sk_c9)
| sk_c10 != multiply(X6,inverse(X6))
| sk_c11 != multiply(X5,sk_c10)
| sk_c11 != inverse(X5)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(X4,sk_c10)
| sk_c11 != inverse(X3)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(X1,sk_c10)
| inverse(X0) != sk_c11
| sk_c10 != multiply(X0,sk_c11) ),
inference(equality_resolution,[],[f113]) ).
tcf(c_107,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_108,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c4,sk_c11) = sk_c10 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c11 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c5,sk_c10) = sk_c9 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c10 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c8,sk_c9) = sk_c10 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c4,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c4) = sk_c11 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c6) = sk_c11 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_130,negated_conjecture,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ( multiply(sk_c5,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_134,negated_conjecture,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_136,negated_conjecture,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c4) = sk_c11 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c5,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_140,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_143,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_144,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_145,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_150,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( inverse(sk_c6) = sk_c11 ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_151,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c6,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_159,negated_conjecture,
( ( inverse(sk_c6) = sk_c11 )
| ( multiply(sk_c3,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_160,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c11 )
| ( multiply(sk_c6,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_164,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( inverse(X6) != sk_c10 )
| ( inverse(X5) != sk_c10 )
| ( inverse(X3) != sk_c11 )
| ( inverse(X2) != sk_c11 )
| ( inverse(X1) != sk_c11 )
| ( inverse(X0) != sk_c11 )
| ( multiply(X6,sk_c10) != sk_c9 )
| ( multiply(X5,sk_c10) != sk_c9 )
| ( multiply(X3,sk_c11) != sk_c10 )
| ( multiply(X2,sk_c10) != sk_c11 )
| ( multiply(X1,sk_c10) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 )
| ( multiply(inverse(X4),sk_c9) != sk_c10 )
| ( multiply(X4,inverse(X4)) != sk_c10 ) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_165,plain,
multiply(identity,sk_c10) = sk_c10,
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_423,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c10) != sk_c11 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_164]) ).
tcf(c_424,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_164]) ).
tcf(c_425,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_164]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X0,inverse(X0)) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_164]) ).
tcf(c_427,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_164]) ).
tcf(c_428,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_434,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_718,plain,
( ~ iPr_def_12
| ( inverse(sk_c5) != sk_c10 )
| ( multiply(sk_c5,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_425]) ).
tcf(c_720,plain,
( ~ iPr_def_10
| ( inverse(sk_c6) != sk_c11 )
| ( multiply(sk_c6,sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_754,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != inverse(X0) )
| ( inverse(X0) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_714]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_715]) ).
tcf(c_789,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_761]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(inverse(X0),sk_c9) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_761]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = multiply(inverse(X0),sk_c9) )
| ( sk_c10 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(inverse(X0),sk_c9) )
| ( sk_c10 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_800]) ).
tcf(c_862,plain,
multiply(inverse(sk_c9),sk_c9) = identity,
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_885,plain,
( ( sk_c10 = multiply(sk_c8,sk_c9) )
| ( sk_c10 != sk_c10 )
| ( multiply(sk_c8,sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_886,plain,
! [X0: $i] :
( ( sk_c10 = multiply(identity,X0) )
| ( sk_c10 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_887,plain,
( ( sk_c10 = multiply(identity,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_886]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,X2) )
| ( sk_c9 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_430]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_971,plain,
! [X0: $i] :
( ( sk_c10 = sk_c9 )
| ( sk_c9 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_978,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c9),sk_c9) != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_789]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(identity,X1) )
| ( multiply(inverse(X0),sk_c9) != multiply(identity,X1) ) ),
inference(instantiation,[status(thm)],[c_762]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c9) )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_429]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_897]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_894]) ).
tcf(c_1092,plain,
( ~ iPr_def_11
| ( inverse(sk_c1) != sk_c11 )
| ( multiply(sk_c1,sk_c11) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_424]) ).
tcf(c_1155,plain,
! [X0: $i] :
( ( multiply(sk_c2,sk_c10) = X0 )
| ( X0 != sk_c9 )
| ( multiply(sk_c2,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_1157,plain,
( ( multiply(sk_c2,sk_c10) = sk_c10 )
| ( sk_c10 != sk_c9 )
| ( multiply(sk_c2,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1155]) ).
tcf(c_1171,plain,
( ( sk_c10 = inverse(sk_c2) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c2) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_797]) ).
tcf(c_1174,plain,
( ~ iPr_def_12
| ( inverse(sk_c2) != sk_c10 )
| ( multiply(sk_c2,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_425]) ).
tcf(c_1206,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c11 )
| ( multiply(sk_c3,sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_1368,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_989]) ).
tcf(c_1519,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X1 )
| ( X1 != multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(inverse(X0),X0) ) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_1552,plain,
! [X0: $i] :
( ( X0 = multiply(inverse(sk_c9),sk_c9) )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_1563,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_1708,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_107,c_109]) ).
tcf(c_1709,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_108,c_109]) ).
tcf(c_1913,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c1,sk_c11) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c1,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_1985,plain,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(identity,sk_c10) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_117,c_1708]) ).
tcf(c_2014,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(identity,multiply(X0,multiply(X1,X2))) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_109,c_1708]) ).
tcf(c_2125,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( sk_c10 != inverse(sk_c2) )
| ( inverse(sk_c2) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_754]) ).
tcf(c_2163,plain,
! [X0: $i,X1: $i] :
( ( inverse(sk_c2) = X1 )
| ( X1 != X0 )
| ( inverse(sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_2419,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(sk_c1,sk_c11) = multiply(X0,X1) )
| ( multiply(sk_c1,sk_c11) != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_1913]) ).
tcf(c_2531,plain,
multiply(identity,sk_c9) = sk_c9,
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_2922,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_429,c_428]) ).
tcf(c_2967,plain,
! [X0: $i] :
( ( inverse(sk_c2) = identity )
| ( identity != X0 )
| ( inverse(sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_2163]) ).
tcf(c_2968,plain,
! [X0: $i,X1: $i] :
( ( inverse(sk_c2) = multiply(inverse(X0),sk_c9) )
| ( inverse(sk_c2) != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_2163]) ).
tcf(c_3160,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_3728,plain,
inverse(sk_c2) = inverse(sk_c2),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_4073,plain,
( ( identity = multiply(inverse(sk_c9),sk_c9) )
| ( identity != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_4361,plain,
( ( multiply(sk_c3,sk_c10) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c6) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_160,c_423]) ).
tcf(c_4364,plain,
( ( inverse(sk_c3) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c6) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_151,c_423]) ).
tcf(c_4374,plain,
( ( inverse(sk_c6) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c3) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_159,c_423]) ).
tcf(c_4649,plain,
( ( inverse(sk_c4) = sk_c11 )
| ~ iPr_def_11
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_111,c_424]) ).
tcf(c_4652,plain,
( ( multiply(sk_c1,sk_c11) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_110,c_424]) ).
tcf(c_4655,plain,
( ( inverse(sk_c1) = sk_c11 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_119,c_424]) ).
tcf(c_4746,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = multiply(sk_c1,sk_c11) )
| ( multiply(sk_c1,sk_c11) != multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(inverse(X0),X0) ) ),
inference(instantiation,[status(thm)],[c_1519]) ).
tcf(c_4769,plain,
( ( inverse(sk_c3) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c6) != sk_c11 ) ),
inference(resolution,[status(thm)],[c_423,c_151]) ).
tcf(c_4777,plain,
( ( multiply(sk_c6,sk_c10) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c3) != sk_c11 ) ),
inference(resolution,[status(thm)],[c_423,c_160]) ).
tcf(c_4833,plain,
( ( multiply(inverse(sk_c7),sk_c9) = multiply(sk_c8,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c7) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_4835,plain,
( ( multiply(inverse(sk_c2),sk_c9) = multiply(sk_c10,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c2) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_4856,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c2),sk_c9) = multiply(X0,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_5017,plain,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ~ iPr_def_12
| ( inverse(sk_c5) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_130,c_425]) ).
tcf(c_5020,plain,
( ( inverse(sk_c2) = sk_c10 )
| ~ iPr_def_12
| ( inverse(sk_c5) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_139,c_425]) ).
tcf(c_5031,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_12
| ( inverse(sk_c2) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_131,c_425]) ).
tcf(c_5054,plain,
( ( inverse(sk_c2) = sk_c10 )
| ~ iPr_def_13
| ( multiply(sk_c7,sk_c8) != sk_c10 )
| ( multiply(inverse(sk_c7),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_144,c_426]) ).
tcf(c_5055,plain,
( ( inverse(sk_c1) = sk_c11 )
| ~ iPr_def_13
| ( multiply(sk_c7,sk_c8) != sk_c10 )
| ( multiply(inverse(sk_c7),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_126,c_426]) ).
tcf(c_5223,plain,
multiply(identity,sk_c10) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_1985,c_165]) ).
tcf(c_5258,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(inverse(sk_c5),sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_139,c_1709]) ).
tcf(c_5277,plain,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(inverse(sk_c2),sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_135,c_1709]) ).
tcf(c_5289,plain,
multiply(inverse(identity),sk_c10) = sk_c10,
inference(superposition,[status(thm)],[c_5223,c_1709]) ).
tcf(c_5863,plain,
( ( inverse(sk_c4) = sk_c11 )
| ~ iPr_def_11
| ( inverse(sk_c1) != sk_c11 ) ),
inference(resolution,[status(thm)],[c_424,c_111]) ).
tcf(c_6027,plain,
( ( multiply(sk_c5,sk_c10) = sk_c9 )
| ~ iPr_def_12
| ( inverse(sk_c2) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_425,c_130]) ).
tcf(c_6308,plain,
( ( inverse(sk_c3) = sk_c11 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_4769,c_150,c_1206,c_4374,c_4364,c_4361]) ).
tcf(c_6310,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_6308,c_720,c_4374,c_4777,c_6308]) ).
tcf(c_6323,plain,
( ( inverse(sk_c4) = sk_c11 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_5863,c_120,c_1092,c_4655,c_4649,c_4652]) ).
tcf(c_6325,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_6323,c_1092,c_4655,c_4652,c_6323]) ).
tcf(c_6344,plain,
( ( sk_c10 = multiply(sk_c1,sk_c11) )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(resolution,[status(thm)],[c_2922,c_117]) ).
tcf(c_6355,plain,
( ( sk_c11 = inverse(sk_c6) )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(resolution,[status(thm)],[c_2922,c_123]) ).
tcf(c_6363,plain,
( ( sk_c10 = multiply(sk_c7,sk_c8) )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2922,c_116]) ).
tcf(c_6365,plain,
( ( sk_c10 = multiply(sk_c8,sk_c9) )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(resolution,[status(thm)],[c_2922,c_127]) ).
tcf(c_6366,plain,
( ( sk_c10 = multiply(sk_c8,sk_c9) )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2922,c_145]) ).
tcf(c_6368,plain,
( ( sk_c10 = multiply(sk_c8,sk_c9) )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2922,c_118]) ).
tcf(c_6376,plain,
( ( sk_c9 = multiply(sk_c2,sk_c10) )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2922,c_134]) ).
tcf(c_6378,plain,
( ( sk_c10 = inverse(sk_c2) )
| ( inverse(sk_c4) = sk_c11 ) ),
inference(resolution,[status(thm)],[c_2922,c_138]) ).
tcf(c_6381,plain,
( ( sk_c10 = inverse(sk_c2) )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(resolution,[status(thm)],[c_2922,c_144]) ).
tcf(c_7004,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != multiply(sk_c2,sk_c10) )
| ( X0 != multiply(sk_c2,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_913]) ).
tcf(c_7526,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c11) = multiply(inverse(X0),X0) )
| ( multiply(sk_c1,sk_c11) != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_2419]) ).
tcf(c_9185,plain,
( ( inverse(sk_c2) = sk_c10 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_5020,c_140,c_1174,c_5031,c_5020,c_5017]) ).
tcf(c_9187,plain,
~ iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_9185,c_718,c_5031,c_6027,c_9185]) ).
tcf(c_9289,plain,
! [X0: $i] : multiply(identity,multiply(X0,sk_c10)) = multiply(X0,sk_c10),
inference(superposition,[status(thm)],[c_5289,c_2014]) ).
tcf(c_10279,plain,
( ( inverse(sk_c2) = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( inverse(sk_c2) != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2967]) ).
tcf(c_11434,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c7),sk_c9) = X0 )
| ( X0 != multiply(sk_c8,sk_c9) )
| ( multiply(inverse(sk_c7),sk_c9) != multiply(sk_c8,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_11435,plain,
( ( multiply(inverse(sk_c7),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c8,sk_c9) )
| ( multiply(inverse(sk_c7),sk_c9) != multiply(sk_c8,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_11434]) ).
tcf(c_11460,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c2),sk_c9) = X0 )
| ( X0 != multiply(sk_c10,sk_c9) )
| ( multiply(inverse(sk_c2),sk_c9) != multiply(sk_c10,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_11461,plain,
( ( multiply(inverse(sk_c2),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c10,sk_c9) )
| ( multiply(inverse(sk_c2),sk_c9) != multiply(sk_c10,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_11460]) ).
tcf(c_11556,plain,
inverse(sk_c1) = sk_c11,
inference(global_subsumption_just,[status(thm)],[c_6355,c_150,c_140,c_126,c_120,c_125,c_427,c_1092,c_1174,c_1206,c_1563,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_4833,c_5031,c_5020,c_5017,c_5055,c_6365,c_11435]) ).
tcf(c_11583,plain,
sk_c10 = inverse(sk_c2),
inference(global_subsumption_just,[status(thm)],[c_6378,c_143,c_434,c_427,c_1171,c_1563,c_4833,c_5054,c_6310,c_6325,c_6366,c_6381,c_9187,c_11435]) ).
tcf(c_11792,plain,
( ( sk_c10 = multiply(sk_c7,sk_c8) )
| ( sk_c10 = multiply(sk_c1,sk_c11) ) ),
inference(resolution,[status(thm)],[c_6363,c_2922]) ).
tcf(c_11799,plain,
( ( sk_c10 = multiply(sk_c8,sk_c9) )
| ( sk_c10 = multiply(sk_c1,sk_c11) ) ),
inference(resolution,[status(thm)],[c_6368,c_2922]) ).
tcf(c_12222,plain,
inverse(sk_c2) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_5258,c_150,c_140,c_120,c_143,c_434,c_427,c_1092,c_1171,c_1174,c_1206,c_1563,c_2125,c_3728,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_4833,c_5031,c_5020,c_5017,c_5054,c_6366,c_6381,c_11435]) ).
tcf(c_12226,plain,
( ~ iPr_def_13
| ( multiply(sk_c2,sk_c10) != sk_c10 )
| ( multiply(inverse(sk_c2),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_12222,c_426]) ).
tcf(c_12889,plain,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c10,sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_12222,c_5277]) ).
tcf(c_13164,plain,
( ( sk_c10 = multiply(identity,sk_c9) )
| ( sk_c10 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_886]) ).
tcf(c_13507,negated_conjecture,
inverse(sk_c1) = sk_c11,
inference(global_subsumption_just,[status(thm)],[c_120,c_11556]) ).
tcf(c_13509,negated_conjecture,
inverse(sk_c2) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_138,c_150,c_140,c_120,c_143,c_434,c_427,c_1092,c_1171,c_1174,c_1206,c_1563,c_2125,c_3728,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_4833,c_5031,c_5020,c_5017,c_5054,c_6366,c_6381,c_11435]) ).
tcf(c_13516,plain,
multiply(sk_c10,sk_c2) = identity,
inference(superposition,[status(thm)],[c_13509,c_108]) ).
tcf(c_13569,plain,
( ( multiply(identity,sk_c9) = sk_c9 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_112,c_9289]) ).
tcf(c_13593,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_107,c_109]) ).
tcf(c_13620,plain,
multiply(identity,sk_c9) = sk_c9,
inference(global_subsumption_just,[status(thm)],[c_13569,c_2531]) ).
tcf(c_13636,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) != sk_c10 )
| ( multiply(inverse(X0),sk_c9) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_426,c_150,c_140,c_120,c_426,c_427,c_1092,c_1174,c_1206,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_5031,c_5020,c_5017]) ).
tcf(c_13637,negated_conjecture,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X0,inverse(X0)) != sk_c10 ) ),
inference(renaming,[status(thm)],[c_13636]) ).
tcf(c_13642,plain,
( ( multiply(sk_c2,sk_c10) != sk_c10 )
| ( multiply(inverse(sk_c2),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_13509,c_13637]) ).
tcf(c_13645,plain,
! [X0: $i] : multiply(sk_c10,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_13516,c_109]) ).
tcf(c_13682,plain,
( ( multiply(sk_c8,sk_c9) = sk_c10 )
| ( multiply(sk_c10,sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_136,c_13645]) ).
tcf(c_13774,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_1709,c_1709]) ).
tcf(c_14309,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_107,c_13774]) ).
tcf(c_15454,plain,
( ( multiply(inverse(sk_c2),sk_c9) = multiply(identity,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_4856]) ).
tcf(c_17876,plain,
! [X0: $i] : multiply(identity,multiply(X0,inverse(X0))) = identity,
inference(superposition,[status(thm)],[c_14309,c_108]) ).
tcf(c_18289,plain,
multiply(identity,multiply(sk_c1,sk_c11)) = identity,
inference(superposition,[status(thm)],[c_13507,c_17876]) ).
tcf(c_18290,plain,
multiply(identity,multiply(sk_c2,sk_c10)) = identity,
inference(superposition,[status(thm)],[c_13509,c_17876]) ).
tcf(c_19229,plain,
multiply(sk_c1,sk_c11) = identity,
inference(superposition,[status(thm)],[c_18289,c_13593]) ).
tcf(c_19471,plain,
( ( multiply(identity,sk_c9) = identity )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_136,c_18290]) ).
tcf(c_19472,plain,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(identity,sk_c9) = identity ) ),
inference(superposition,[status(thm)],[c_135,c_18290]) ).
tcf(c_19488,plain,
multiply(sk_c2,sk_c10) = identity,
inference(superposition,[status(thm)],[c_18290,c_13593]) ).
tcf(c_19601,plain,
! [X0: $i] :
( ( inverse(sk_c2) = multiply(inverse(sk_c9),sk_c9) )
| ( inverse(sk_c2) != X0 )
| ( multiply(inverse(sk_c9),sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_2968]) ).
tcf(c_19615,plain,
( ( inverse(sk_c2) = multiply(inverse(sk_c9),sk_c9) )
| ( inverse(sk_c2) != sk_c10 )
| ( multiply(inverse(sk_c9),sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_19601]) ).
tcf(c_20162,plain,
( ( identity = multiply(sk_c2,sk_c10) )
| ( identity != identity )
| ( multiply(sk_c2,sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_1368]) ).
tcf(c_20960,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_21202,plain,
( ( sk_c9 = identity )
| ( identity != multiply(sk_c2,sk_c10) )
| ( sk_c9 != multiply(sk_c2,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_7004]) ).
tcf(c_21714,plain,
( ( sk_c10 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c10 != multiply(sk_c1,sk_c11) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_858]) ).
tcf(c_21715,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X0 )
| ( X0 != multiply(sk_c1,sk_c11) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_21716,plain,
( ( multiply(inverse(sk_c9),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c1,sk_c11) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(sk_c1,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_21715]) ).
tcf(c_22249,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_19472,c_13620]) ).
tcf(c_22970,plain,
! [X0: $i] :
( ( sk_c10 = multiply(sk_c10,sk_c9) )
| ( sk_c10 != multiply(identity,X0) )
| ( multiply(sk_c10,sk_c9) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_1067]) ).
tcf(c_22977,plain,
( ( sk_c10 = multiply(sk_c10,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(sk_c10,sk_c9) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_22970]) ).
tcf(c_23486,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_19471,c_13620]) ).
tcf(c_24926,plain,
( ( multiply(inverse(sk_c2),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c9) )
| ( multiply(inverse(sk_c2),sk_c9) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_25425,plain,
( ( sk_c10 = multiply(sk_c1,sk_c11) )
| ( multiply(sk_c7,sk_c8) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_11792,c_2922]) ).
tcf(c_25511,plain,
( ( sk_c10 = multiply(sk_c1,sk_c11) )
| ( multiply(sk_c8,sk_c9) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_11799,c_2922]) ).
tcf(c_29547,plain,
( ( sk_c10 = sk_c9 )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c10 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_971]) ).
tcf(c_29750,negated_conjecture,
inverse(sk_c7) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_126,c_165,c_108,c_135,c_434,c_862,c_887,c_978,c_1157,c_1563,c_2125,c_3728,c_4746,c_4835,c_6344,c_7526,c_11461,c_11583,c_12889,c_13642,c_19229,c_20960,c_21714,c_22249,c_22977,c_29547]) ).
tcf(c_29758,negated_conjecture,
multiply(sk_c7,sk_c8) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_116,c_108,c_150,c_140,c_120,c_143,c_134,c_434,c_427,c_862,c_978,c_1092,c_1157,c_1171,c_1174,c_1206,c_1563,c_2125,c_2531,c_3160,c_3728,c_4073,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_4746,c_4833,c_5031,c_5020,c_5017,c_5054,c_6366,c_6376,c_6381,c_7526,c_10279,c_11435,c_12226,c_13164,c_15454,c_19229,c_19488,c_19615,c_20162,c_20960,c_21202,c_21716,c_21714,c_24926,c_25425,c_29547]) ).
tcf(c_29775,negated_conjecture,
multiply(sk_c8,sk_c9) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_118,c_165,c_108,c_150,c_140,c_120,c_143,c_136,c_434,c_427,c_862,c_887,c_978,c_1092,c_1157,c_1171,c_1174,c_1206,c_1563,c_2125,c_3728,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_4746,c_4833,c_4835,c_5031,c_5020,c_5017,c_5054,c_6366,c_6381,c_7526,c_11435,c_11461,c_13642,c_13682,c_19229,c_20960,c_21714,c_22977,c_23486,c_25511,c_29547]) ).
tcf(c_29833,plain,
! [X0: $i] :
( ( multiply(X0,inverse(X0)) != sk_c10 )
| ( multiply(inverse(X0),sk_c9) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_426,c_150,c_140,c_120,c_426,c_427,c_1092,c_1174,c_1206,c_4374,c_4364,c_4361,c_4655,c_4649,c_4652,c_5031,c_5020,c_5017]) ).
tcf(c_29834,negated_conjecture,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X0,inverse(X0)) != sk_c10 ) ),
inference(renaming,[status(thm)],[c_29833]) ).
tcf(c_29840,plain,
( ( multiply(sk_c7,sk_c8) != sk_c10 )
| ( multiply(inverse(sk_c7),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_29750,c_29834]) ).
tcf(c_29844,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_29840,c_29775,c_29758,c_29750,c_11435,c_4833,c_1563,c_885,c_434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 14:20:56 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 10.53/7.28 % SZS status Started for theBenchmark.p
% 10.53/7.28 % SZS status Unsatisfiable for theBenchmark.p
% 10.53/7.28
% 10.53/7.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.53/7.28
% 10.53/7.28 % ------ iProver source info
% 10.53/7.28
% 10.53/7.28 % git: date: 2026-07-19 20:42:38 +0200
% 10.53/7.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.53/7.28 % git: non_committed_changes: false
% 10.53/7.28
% 10.53/7.28 % ------ Parsing...% successful
% 10.53/7.28
% 10.53/7.28
% 10.53/7.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.53/7.28
% 10.53/7.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.53/7.28
% 10.53/7.28 % ------ Preprocessing... gs_s sp: 7 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.53/7.28
% 10.53/7.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.53/7.28 % ------ Proving...
% 10.53/7.28 % ------ Problem Properties
% 10.53/7.28
% 10.53/7.28 %
% 10.53/7.28 % clauses 62
% 10.53/7.28 % conjectures 59
% 10.53/7.28 % EPR 1
% 10.53/7.28 % Horn 7
% 10.53/7.28 % unary 3
% 10.53/7.28 % binary 54
% 10.53/7.28 % lits 127
% 10.53/7.28 % lits eq 119
% 10.53/7.28 % fd_pure 0
% 10.53/7.28 % fd_pseudo 0
% 10.53/7.28 % fd_cond 0
% 10.53/7.28 % fd_pseudo_cond 0
% 10.53/7.28 % AC symbols 0
% 10.53/7.28
% 10.53/7.28 % ------ Input Options Time Limit: Unbounded
% 10.53/7.28
% 10.53/7.28
% 10.53/7.28 % ------
% 10.53/7.28 % Current options:
% 10.53/7.28 % ------
% 10.53/7.28
% 10.53/7.28
% 10.53/7.28 %
% 10.53/7.28
% 10.53/7.28 % ------ Proving...
% 10.53/7.28 %
% 10.53/7.28
% 10.53/7.28 % SZS status Unsatisfiable for theBenchmark.p
% 10.53/7.28
% 10.53/7.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.53/7.28
% 10.53/7.28
%------------------------------------------------------------------------------