%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP257-1 : 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 : n026.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 01:32:37 PM UTC 2026
% Result : Unsatisfiable 14.60s 2.84s
% Output : CNFRefutation 14.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 45
% Syntax : Number of formulae : 296 ( 113 unt; 13 def)
% Number of atoms : 838 ( 517 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 457 ( 181 ~; 276 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 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 : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 62 :)
% 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_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c6)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c6)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f55,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f73,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c8 = inverse(sk_c6)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c9
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c8 != inverse(X6)
| multiply(X6,sk_c8) != X5
| sk_c9 != multiply(sk_c8,X5)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c8,sk_c7) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c6,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_133,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c8 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(X5,sk_c9) != sk_c8 )
| ( multiply(X4,sk_c9) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c9 )
| ( multiply(X1,sk_c10) != sk_c9 )
| ( multiply(X0,sk_c10) != sk_c9 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c9 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_537,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_140]) ).
tcf(c_538,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_539,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_140]) ).
tcf(c_540,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_541,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_140]) ).
tcf(c_542,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_543,definition,
iPr_def_15 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_544,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_545,definition,
iPr_def_17 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_546,definition,
iPr_def_18 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_547,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_548,definition,
iPr_def_20 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_549,definition,
iPr_def_21 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_550,definition,
iPr_def_22 = multiply(sk_c4,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_551,definition,
iPr_def_23 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_552,definition,
iPr_def_24 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_553,definition,
iPr_def_25 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_554,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_555,definition,
iPr_def_27 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_556,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_542]) ).
tcf(c_557,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_558,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_540]) ).
tcf(c_560,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_539]) ).
tcf(c_561,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_538]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_537]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_139,c_544,c_543]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_138,c_545]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_137,c_546]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_136,c_547]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_135,c_548]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_21 = sk_c10 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_134,c_549]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_133,c_550]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_132,c_551]) ).
tcf(c_575,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_576,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_552]) ).
tcf(c_578,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118,c_553]) ).
tcf(c_585,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_554]) ).
tcf(c_592,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_594,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_595,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_598,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104,c_555]) ).
tcf(c_599,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_600,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_601,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_602,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_603,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_604,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_22 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1073,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_570,c_546]) ).
tcf(c_1102,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_575,c_550]) ).
tcf(c_1108,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_577,c_553]) ).
tcf(c_1109,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_576,c_553]) ).
tcf(c_1135,plain,
multiply(iPr_def_21,sk_c4) = identity,
inference(superposition,[status(thm)],[c_549,c_96]) ).
tcf(c_1136,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_547,c_96]) ).
tcf(c_1137,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_544,c_96]) ).
tcf(c_1138,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_554,c_96]) ).
tcf(c_1139,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_552,c_96]) ).
tcf(c_1140,plain,
multiply(iPr_def_23,sk_c3) = identity,
inference(superposition,[status(thm)],[c_551,c_96]) ).
tcf(c_1385,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_584,c_570]) ).
tcf(c_1682,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_591,c_555]) ).
tcf(c_1765,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_594,c_555]) ).
tcf(c_1804,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_595,c_555]) ).
tcf(c_2865,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_543,c_558]) ).
tcf(c_2866,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_558]) ).
tcf(c_2890,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_23 )
| ( sk_c8 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2865,c_551]) ).
tcf(c_3088,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_560]) ).
tcf(c_3267,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_555,c_561]) ).
tcf(c_3270,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_96,c_561]) ).
tcf(c_3289,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_27 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3267,c_554]) ).
tcf(c_3396,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_548,c_562]) ).
tcf(c_3398,plain,
( ~ iPr_def_10
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_562]) ).
tcf(c_3417,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3396,c_547]) ).
tcf(c_3514,plain,
( ~ iPr_def_14
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_20) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_548,c_557]) ).
tcf(c_3515,plain,
( ~ iPr_def_14
| ( inverse(sk_c6) != sk_c8 )
| ( multiply(sk_c8,iPr_def_17) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_545,c_557]) ).
tcf(c_3517,plain,
( ~ iPr_def_14
| ( inverse(inverse(sk_c8)) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_96,c_557]) ).
tcf(c_3531,plain,
( ~ iPr_def_14
| ( sk_c8 != iPr_def_16 )
| ( multiply(sk_c8,iPr_def_17) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3515,c_544]) ).
tcf(c_3535,plain,
( ~ iPr_def_14
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_20) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3514,c_547]) ).
tcf(c_3965,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_548,c_97]) ).
tcf(c_3966,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_546,c_97]) ).
tcf(c_3969,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c9,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_543,c_97]) ).
tcf(c_3971,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_3974,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1135,c_97]) ).
tcf(c_3975,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1136,c_97]) ).
tcf(c_3976,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1137,c_97]) ).
tcf(c_3977,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1138,c_97]) ).
tcf(c_3978,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1139,c_97]) ).
tcf(c_3979,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1140,c_97]) ).
tcf(c_3986,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3979,c_95]) ).
tcf(c_3987,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3978,c_95]) ).
tcf(c_3988,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3977,c_95]) ).
tcf(c_3989,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3976,c_95]) ).
tcf(c_3990,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3975,c_95]) ).
tcf(c_3991,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3974,c_95]) ).
tcf(c_4078,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1385,c_546]) ).
tcf(c_5310,plain,
multiply(iPr_def_23,iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_543,c_3986]) ).
tcf(c_5354,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_15,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5310,c_97]) ).
tcf(c_5356,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_3987]) ).
tcf(c_5359,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(iPr_def_25,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5356,c_97]) ).
tcf(c_5422,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c10,
inference(superposition,[status(thm)],[c_555,c_3988]) ).
tcf(c_5788,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(iPr_def_27,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_5422,c_97]) ).
tcf(c_5790,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_545,c_3989]) ).
tcf(c_5810,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5790,c_97]) ).
tcf(c_5812,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_548,c_3990]) ).
tcf(c_5824,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5812,c_97]) ).
tcf(c_5826,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c10,
inference(superposition,[status(thm)],[c_550,c_3991]) ).
tcf(c_5829,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_5826,c_97]) ).
tcf(c_10124,plain,
multiply(sk_c5,iPr_def_18) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_546,c_3965]) ).
tcf(c_11646,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3971,c_95]) ).
tcf(c_11656,plain,
multiply(inverse(sk_c8),iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_546,c_11646]) ).
tcf(c_11658,plain,
multiply(inverse(sk_c2),iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_11646]) ).
tcf(c_11660,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_11646]) ).
tcf(c_11661,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_11646]) ).
tcf(c_11694,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(inverse(iPr_def_23),iPr_def_18) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1073,c_11646]) ).
tcf(c_11732,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(inverse(sk_c2),iPr_def_25) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1109,c_11646]) ).
tcf(c_11815,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3991,c_11646]) ).
tcf(c_11816,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3990,c_11646]) ).
tcf(c_11817,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3989,c_11646]) ).
tcf(c_11818,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3988,c_11646]) ).
tcf(c_11819,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3987,c_11646]) ).
tcf(c_11820,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3986,c_11646]) ).
tcf(c_11821,plain,
multiply(inverse(iPr_def_23),sk_c9) = iPr_def_15,
inference(superposition,[status(thm)],[c_5310,c_11646]) ).
tcf(c_11850,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11646,c_11646]) ).
tcf(c_12396,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 )
| ( inverse(inverse(identity)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11660,c_560]) ).
tcf(c_12519,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11661,c_11850]) ).
tcf(c_12527,plain,
multiply(sk_c10,identity) = multiply(iPr_def_26,iPr_def_27),
inference(superposition,[status(thm)],[c_12519,c_5788]) ).
tcf(c_12530,plain,
multiply(sk_c10,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_12519,c_5829]) ).
tcf(c_12531,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_12519,c_5824]) ).
tcf(c_12534,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_12519,c_3966]) ).
tcf(c_12535,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_17),
inference(superposition,[status(thm)],[c_12519,c_5810]) ).
tcf(c_12536,plain,
multiply(sk_c9,identity) = multiply(iPr_def_24,iPr_def_25),
inference(superposition,[status(thm)],[c_12519,c_5359]) ).
tcf(c_12537,plain,
multiply(sk_c3,sk_c9) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_12519,c_3969]) ).
tcf(c_12539,plain,
multiply(sk_c9,identity) = multiply(iPr_def_23,iPr_def_15),
inference(superposition,[status(thm)],[c_12519,c_5354]) ).
tcf(c_12546,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12519,c_11660]) ).
tcf(c_12547,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_12539,c_5310]) ).
tcf(c_12549,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_12537,c_543]) ).
tcf(c_12551,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12535,c_5790]) ).
tcf(c_12552,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_12534,c_546]) ).
tcf(c_12556,plain,
multiply(sk_c10,identity) = sk_c10,
inference(light_normalisation,[status(thm)],[c_12530,c_5826]) ).
tcf(c_14176,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c10 )
| ( multiply(sk_c4,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11815,c_561]) ).
tcf(c_14177,plain,
multiply(sk_c4,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_11815,c_96]) ).
tcf(c_14184,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_11815,c_11646]) ).
tcf(c_14185,plain,
multiply(sk_c4,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_11815,c_12519]) ).
tcf(c_14195,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( inverse(inverse(iPr_def_21)) != sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_14176,c_550]) ).
tcf(c_14206,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1102,c_14177]) ).
tcf(c_14225,plain,
inverse(iPr_def_21) = sk_c4,
inference(demodulation,[status(thm)],[c_14185,c_12519]) ).
tcf(c_14964,plain,
multiply(sk_c4,sk_c10) = iPr_def_22,
inference(superposition,[status(thm)],[c_5826,c_14184]) ).
tcf(c_15448,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11816,c_562]) ).
tcf(c_15449,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_19)) != sk_c9 )
| ( multiply(sk_c5,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11816,c_560]) ).
tcf(c_15450,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c5,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11816,c_558]) ).
tcf(c_15451,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_11816,c_11646]) ).
tcf(c_15452,plain,
multiply(sk_c5,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_11816,c_12519]) ).
tcf(c_15459,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_15448,c_548]) ).
tcf(c_15751,plain,
inverse(iPr_def_19) = sk_c5,
inference(demodulation,[status(thm)],[c_15452,c_12519]) ).
tcf(c_15758,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm)],[c_1136,c_15451]) ).
tcf(c_15760,plain,
multiply(sk_c5,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_5812,c_15451]) ).
tcf(c_15821,plain,
multiply(sk_c6,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11817,c_96]) ).
tcf(c_15828,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11817,c_11646]) ).
tcf(c_15829,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11817,c_12519]) ).
tcf(c_16013,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_15821,c_3989]) ).
tcf(c_16762,plain,
inverse(iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_15829,c_12519]) ).
tcf(c_16775,plain,
multiply(sk_c6,identity) = sk_c6,
inference(superposition,[status(thm)],[c_1137,c_15828]) ).
tcf(c_16776,plain,
multiply(sk_c6,sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_5790,c_15828]) ).
tcf(c_17250,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_11818,c_96]) ).
tcf(c_17257,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_26,X0)) = X0,
inference(superposition,[status(thm)],[c_11818,c_11646]) ).
tcf(c_17258,plain,
multiply(sk_c1,identity) = inverse(iPr_def_26),
inference(superposition,[status(thm)],[c_11818,c_12519]) ).
tcf(c_17278,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1765,c_17250]) ).
tcf(c_17280,plain,
( ( identity = iPr_def_27 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1682,c_17250]) ).
tcf(c_18026,plain,
multiply(iPr_def_26,identity) = iPr_def_26,
inference(superposition,[status(thm)],[c_17250,c_3988]) ).
tcf(c_18653,plain,
inverse(iPr_def_26) = sk_c1,
inference(demodulation,[status(thm)],[c_17258,c_12519]) ).
tcf(c_18658,plain,
multiply(sk_c1,sk_c10) = iPr_def_27,
inference(superposition,[status(thm)],[c_5422,c_17257]) ).
tcf(c_18773,plain,
( ( identity = iPr_def_27 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_17278,c_546]) ).
tcf(c_21102,plain,
( ( identity = iPr_def_27 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_17280,c_546]) ).
tcf(c_21105,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_17280,c_545]) ).
tcf(c_21109,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_21105,c_15821]) ).
tcf(c_22061,plain,
multiply(sk_c2,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_11819,c_96]) ).
tcf(c_22064,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c2,sk_c8)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11819,c_557]) ).
tcf(c_22065,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c2,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11819,c_562]) ).
tcf(c_22066,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c2,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11819,c_560]) ).
tcf(c_22067,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c2,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11819,c_558]) ).
tcf(c_22068,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_11819,c_11646]) ).
tcf(c_22069,plain,
multiply(sk_c2,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_11819,c_12519]) ).
tcf(c_22070,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( inverse(inverse(iPr_def_24)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_22067,c_553]) ).
tcf(c_22074,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_25 )
| ( inverse(inverse(iPr_def_24)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_22066,c_553]) ).
tcf(c_22092,plain,
( ( identity = iPr_def_25 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1108,c_22061]) ).
tcf(c_22113,plain,
inverse(iPr_def_24) = sk_c2,
inference(demodulation,[status(thm)],[c_22069,c_12519]) ).
tcf(c_22118,plain,
multiply(sk_c2,sk_c9) = iPr_def_25,
inference(superposition,[status(thm)],[c_5356,c_22068]) ).
tcf(c_23587,plain,
( ( identity = iPr_def_25 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_22092,c_546]) ).
tcf(c_27074,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2866,c_12546]) ).
tcf(c_27426,plain,
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3088,c_12546]) ).
tcf(c_27845,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3398,c_12546]) ).
tcf(c_31408,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c5,iPr_def_18) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_18773,c_15451]) ).
tcf(c_33478,plain,
( ~ iPr_def_14
| ( sk_c9 != sk_c8 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_3517,c_12519]) ).
tcf(c_33497,plain,
( ( identity = iPr_def_27 )
| ~ iPr_def_14
| ( sk_c9 != sk_c8 )
| ( inverse(inverse(iPr_def_19)) != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_17278,c_33478]) ).
tcf(c_33630,plain,
( ( identity = iPr_def_27 )
| ~ iPr_def_14
| ( sk_c9 != sk_c8 ) ),
inference(ground_joinability,[status(thm)],[c_33497,c_547,c_15751]) ).
tcf(c_36889,plain,
multiply(sk_c3,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11820,c_12519]) ).
tcf(c_41003,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_36889,c_33630,c_31408,c_27845,c_27426,c_27074,c_23587,c_22118,c_22113,c_22074,c_22070,c_22065,c_22064,c_22061,c_21109,c_21102,c_18658,c_18653,c_18026,c_17250,c_16776,c_16775,c_16762,c_16013,c_15821,c_15760,c_15758,c_15751,c_15459,c_15450,c_15449,c_14964,c_14225,c_14206,c_14195,c_14177,c_12556,c_12552,c_12551,c_12549,c_12547,c_12537,c_12536,c_12535,c_12534,c_12531,c_12527,c_12546,c_12396,c_11821,c_11732,c_11694,c_11658,c_11656,c_10124,c_4078,c_3535,c_3531,c_3417,c_3289,c_3270,c_2890,c_1804,c_1765,c_604,c_603,c_602,c_601,c_600,c_599,c_598,c_593,c_592,c_586,c_585,c_579,c_578,c_569,c_568,c_567,c_566,c_565,c_564,c_563,c_554,c_552,c_549,c_547,c_556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP257-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Sep 23 14:19:57 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 14.60/2.84 % SZS status Started for theBenchmark.p
% 14.60/2.84 % SZS status Unsatisfiable for theBenchmark.p
% 14.60/2.84
% 14.60/2.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.60/2.84
% 14.60/2.84 % ------ iProver source info
% 14.60/2.84
% 14.60/2.84 % git: date: 2026-07-19 20:42:38 +0200
% 14.60/2.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.60/2.84 % git: non_committed_changes: false
% 14.60/2.84
% 14.60/2.84 % ------ Parsing...% successful
% 14.60/2.84
% 14.60/2.84
% 14.60/2.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.60/2.84
% 14.60/2.84 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 14.60/2.84
% 14.60/2.84 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.60/2.84
% 14.60/2.84 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 14.60/2.84 % ------ Proving...
% 14.60/2.84 % ------ Problem Properties
% 14.60/2.84
% 14.60/2.84 %
% 14.60/2.84 % clauses 64
% 14.60/2.84 % conjectures 48
% 14.60/2.84 % EPR 43
% 14.60/2.84 % Horn 21
% 14.60/2.84 % unary 16
% 14.60/2.84 % binary 42
% 14.60/2.84 % lits 120
% 14.60/2.84 % lits eq 110
% 14.60/2.84 % fd_pure 0
% 14.60/2.84 % fd_pseudo 0
% 14.60/2.84 % fd_cond 0
% 14.60/2.84 % fd_pseudo_cond 0
% 14.60/2.84 % AC symbols 0
% 14.60/2.84
% 14.60/2.84 % ------ Schedule dynamic 5 is on
% 14.60/2.84
% 14.60/2.84 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.60/2.84
% 14.60/2.84
% 14.60/2.84 % ------
% 14.60/2.84 % Current options:
% 14.60/2.84 % ------
% 14.60/2.84
% 14.60/2.84
% 14.60/2.84 %
% 14.60/2.84
% 14.60/2.84 % ------ Proving...
% 14.60/2.84 %
% 14.60/2.84
% 14.60/2.84 % SZS status Unsatisfiable for theBenchmark.p
% 14.60/2.84
% 14.60/2.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.60/2.85
% 14.60/2.85
%------------------------------------------------------------------------------