%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP369-1 : 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 : n018.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 01:33:25 PM UTC 2026
% Result : Unsatisfiable 15.08s 3.24s
% Output : CNFRefutation 15.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 47
% Syntax : Number of formulae : 307 ( 108 unt; 13 def)
% Number of atoms : 921 ( 549 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 453 ( 163 ~; 290 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = inverse(sk_c8)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c8)
| sk_c8 = multiply(sk_c9,sk_c2) ),
inference(reorient_equations,[],[f19]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c9,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c8)
| sk_c2 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c2 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c6)
| sk_c2 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f57,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c8)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f61]) ).
fof(f67,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f67]) ).
fof(f71,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = inverse(sk_c8)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(X5,sk_c9)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c7 != inverse(sk_c8)
| sk_c7 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X1)
| multiply(X1,sk_c9) != X0
| sk_c8 != multiply(sk_c9,X0)
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X1,X4,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(X5,sk_c9)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c7 != inverse(sk_c8)
| sk_c7 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| multiply(sk_c7,sk_c9) != sk_c8 ),
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,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c7,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c9,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c9,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c9,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c9) = sk_c2 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c2 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c2 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c2 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_129,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_131,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c3,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_133,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c7,sk_c9) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c9 )
| ( multiply(X2,sk_c7) != sk_c9 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c9) != sk_c7 )
| ( multiply(sk_c9,multiply(X4,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_537,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
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_c7 )
| ( multiply(X0,sk_c7) != 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_c7 ) ),
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_c8) != sk_c9 ) ),
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_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
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
| ( inverse(sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_543,definition,
iPr_def_15 = multiply(sk_c7,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_544,definition,
iPr_def_16 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_545,definition,
iPr_def_17 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_546,definition,
iPr_def_18 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_547,definition,
iPr_def_19 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_548,definition,
iPr_def_20 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_549,definition,
iPr_def_21 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_550,definition,
iPr_def_22 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_551,definition,
iPr_def_23 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_552,definition,
iPr_def_24 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_553,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_554,definition,
iPr_def_26 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_555,definition,
iPr_def_27 = multiply(sk_c9,sk_c2),
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
| ( iPr_def_16 != sk_c7 )
| ( iPr_def_15 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_542,c_544,c_543]) ).
tcf(c_557,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_558,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_540]) ).
tcf(c_559,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_539]) ).
tcf(c_560,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_538]) ).
tcf(c_561,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_537]) ).
tcf(c_562,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_139,c_546,c_545]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_138,c_547]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_137,c_548]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_136,c_549]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_135,c_550]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_134,c_551]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_132,c_552]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_572,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_575,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_576,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_125,c_553]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_582,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_583,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_118,c_554]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_589,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_590,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111,c_555]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_596,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_597,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_598,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_599,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_600,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_601,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_602,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_603,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1106,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_575,c_570]) ).
tcf(c_1236,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_568,c_552]) ).
tcf(c_1293,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_25,sk_c2) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_576,c_555]) ).
tcf(c_1302,plain,
multiply(iPr_def_16,sk_c8) = identity,
inference(superposition,[status(thm)],[c_544,c_96]) ).
tcf(c_1303,plain,
multiply(iPr_def_22,sk_c4) = identity,
inference(superposition,[status(thm)],[c_550,c_96]) ).
tcf(c_1304,plain,
multiply(iPr_def_20,sk_c5) = identity,
inference(superposition,[status(thm)],[c_548,c_96]) ).
tcf(c_1305,plain,
multiply(iPr_def_17,sk_c6) = identity,
inference(superposition,[status(thm)],[c_545,c_96]) ).
tcf(c_1306,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_553,c_96]) ).
tcf(c_1307,plain,
multiply(iPr_def_18,sk_c3) = identity,
inference(superposition,[status(thm)],[c_546,c_96]) ).
tcf(c_1359,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,sk_c2) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_579,c_555]) ).
tcf(c_1498,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c9 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_582,c_577]) ).
tcf(c_1994,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c8 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_596,c_591]) ).
tcf(c_2058,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_597,c_590]) ).
tcf(c_2340,plain,
( ( iPr_def_15 = iPr_def_27 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_600,c_593]) ).
tcf(c_2631,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_603,c_598]) ).
tcf(c_2670,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c9,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_543,c_97]) ).
tcf(c_2671,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_551,c_97]) ).
tcf(c_2672,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_549,c_97]) ).
tcf(c_2674,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c2,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_555,c_97]) ).
tcf(c_2676,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_552,c_97]) ).
tcf(c_2678,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_2680,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1302,c_97]) ).
tcf(c_2681,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1303,c_97]) ).
tcf(c_2682,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1304,c_97]) ).
tcf(c_2683,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1305,c_97]) ).
tcf(c_2684,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1306,c_97]) ).
tcf(c_2685,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1307,c_97]) ).
tcf(c_2687,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2685,c_95]) ).
tcf(c_2688,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2684,c_95]) ).
tcf(c_2689,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2683,c_95]) ).
tcf(c_2690,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2682,c_95]) ).
tcf(c_2691,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2681,c_95]) ).
tcf(c_2692,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2680,c_95]) ).
tcf(c_3182,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_23 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_551,c_558]) ).
tcf(c_3184,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_558]) ).
tcf(c_3187,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( inverse(iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_1302,c_558]) ).
tcf(c_3210,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_22 )
| ( sk_c9 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3182,c_550]) ).
tcf(c_3318,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_26 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_554,c_559]) ).
tcf(c_3320,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_96,c_559]) ).
tcf(c_3332,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_25 )
| ( sk_c7 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_3318,c_553]) ).
tcf(c_3454,plain,
( ~ iPr_def_11
| ( sk_c7 != sk_c9 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_95,c_560]) ).
tcf(c_3665,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_95,c_561]) ).
tcf(c_3668,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_1302,c_561]) ).
tcf(c_3839,plain,
( ~ iPr_def_14
| ( inverse(sk_c6) != sk_c9 )
| ( multiply(sk_c9,iPr_def_19) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_547,c_557]) ).
tcf(c_3840,plain,
( ~ iPr_def_14
| ( inverse(sk_c1) != sk_c9 )
| ( multiply(sk_c9,iPr_def_26) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_554,c_557]) ).
tcf(c_3854,plain,
( ~ iPr_def_14
| ( sk_c9 != iPr_def_25 )
| ( multiply(sk_c9,iPr_def_26) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3840,c_553]) ).
tcf(c_3858,plain,
( ~ iPr_def_14
| ( sk_c9 != iPr_def_17 )
| ( multiply(sk_c9,iPr_def_19) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3839,c_545]) ).
tcf(c_3948,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_24,sk_c2) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_1106,c_555]) ).
tcf(c_4544,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1498,c_554]) ).
tcf(c_4921,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2340,c_2058]) ).
tcf(c_5447,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2631,c_1994]) ).
tcf(c_5564,plain,
multiply(iPr_def_18,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_552,c_2687]) ).
tcf(c_5569,plain,
multiply(iPr_def_25,iPr_def_26) = sk_c9,
inference(superposition,[status(thm)],[c_554,c_2688]) ).
tcf(c_5575,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(iPr_def_26,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5569,c_97]) ).
tcf(c_5599,plain,
multiply(iPr_def_17,iPr_def_19) = sk_c9,
inference(superposition,[status(thm)],[c_547,c_2689]) ).
tcf(c_5604,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_549,c_2690]) ).
tcf(c_5611,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5604,c_97]) ).
tcf(c_5690,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_551,c_2691]) ).
tcf(c_5693,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_5690,c_97]) ).
tcf(c_8929,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_583,c_1293]) ).
tcf(c_8931,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_8929,c_5569]) ).
tcf(c_9266,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_586,c_1359]) ).
tcf(c_9271,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_9266,c_5569]) ).
tcf(c_9344,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_8931,c_569]) ).
tcf(c_9575,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( sk_c9 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_9271,c_572]) ).
tcf(c_10612,plain,
( ( iPr_def_24 = iPr_def_27 )
| ( iPr_def_17 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_9575,c_9344]) ).
tcf(c_12454,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10612,c_4921]) ).
tcf(c_13759,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( multiply(iPr_def_18,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_12454,c_5564]) ).
tcf(c_15982,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_24,sk_c9),
inference(superposition,[status(thm)],[c_543,c_2676]) ).
tcf(c_19373,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2678,c_95]) ).
tcf(c_19401,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_543,c_19373]) ).
tcf(c_19408,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_19373]) ).
tcf(c_19409,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_19373]) ).
tcf(c_19577,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2692,c_19373]) ).
tcf(c_19578,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2691,c_19373]) ).
tcf(c_19579,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2690,c_19373]) ).
tcf(c_19580,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2689,c_19373]) ).
tcf(c_19581,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2688,c_19373]) ).
tcf(c_19582,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2687,c_19373]) ).
tcf(c_19637,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_19373,c_19373]) ).
tcf(c_20741,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_19409,c_19637]) ).
tcf(c_20747,plain,
multiply(sk_c7,sk_c9) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_20741,c_2670]) ).
tcf(c_20752,plain,
multiply(sk_c8,identity) = multiply(iPr_def_22,iPr_def_23),
inference(superposition,[status(thm)],[c_20741,c_5693]) ).
tcf(c_20756,plain,
multiply(sk_c8,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_20741,c_5611]) ).
tcf(c_20758,plain,
multiply(sk_c9,sk_c2) = multiply(iPr_def_27,identity),
inference(superposition,[status(thm)],[c_20741,c_2674]) ).
tcf(c_20759,plain,
multiply(sk_c9,identity) = multiply(iPr_def_25,iPr_def_26),
inference(superposition,[status(thm)],[c_20741,c_5575]) ).
tcf(c_20767,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_20741,c_19408]) ).
tcf(c_20770,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_20759,c_5569]) ).
tcf(c_20771,plain,
multiply(iPr_def_27,identity) = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_20758,c_555]) ).
tcf(c_20777,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_20747,c_543]) ).
tcf(c_20793,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_20767,c_96]) ).
tcf(c_21378,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_19577,c_557]) ).
tcf(c_21380,plain,
multiply(sk_c8,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_19577,c_96]) ).
tcf(c_21387,plain,
multiply(sk_c8,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_19577,c_20741]) ).
tcf(c_21523,plain,
multiply(sk_c5,identity) = multiply(iPr_def_21,iPr_def_16),
inference(superposition,[status(thm)],[c_21380,c_2672]) ).
tcf(c_21524,plain,
multiply(sk_c4,identity) = multiply(iPr_def_23,iPr_def_16),
inference(superposition,[status(thm)],[c_21380,c_2671]) ).
tcf(c_21525,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(superposition,[status(thm)],[c_21380,c_2692]) ).
tcf(c_21717,plain,
inverse(iPr_def_16) = sk_c8,
inference(demodulation,[status(thm)],[c_21387,c_20741]) ).
tcf(c_22127,plain,
multiply(iPr_def_21,iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_21523,c_20741]) ).
tcf(c_22476,plain,
multiply(iPr_def_23,iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_21524,c_20741]) ).
tcf(c_22689,plain,
multiply(sk_c4,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_19578,c_96]) ).
tcf(c_22692,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_22)) != sk_c8 )
| ( multiply(sk_c4,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19578,c_561]) ).
tcf(c_22694,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c4,sk_c7) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_19578,c_560]) ).
tcf(c_22695,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_19578,c_19373]) ).
tcf(c_22696,plain,
multiply(sk_c4,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_19578,c_20741]) ).
tcf(c_22712,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_23 )
| ( inverse(inverse(iPr_def_22)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_22692,c_551]) ).
tcf(c_22792,plain,
inverse(iPr_def_22) = sk_c4,
inference(demodulation,[status(thm)],[c_22696,c_20741]) ).
tcf(c_22809,plain,
multiply(sk_c4,sk_c8) = iPr_def_23,
inference(superposition,[status(thm)],[c_5690,c_22695]) ).
tcf(c_24112,plain,
multiply(sk_c5,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_19579,c_96]) ).
tcf(c_24118,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_19579,c_19373]) ).
tcf(c_24119,plain,
multiply(sk_c5,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_19579,c_20741]) ).
tcf(c_25408,plain,
inverse(iPr_def_20) = sk_c5,
inference(demodulation,[status(thm)],[c_24119,c_20741]) ).
tcf(c_25425,plain,
multiply(sk_c5,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_5604,c_24118]) ).
tcf(c_26302,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c9 )
| ( multiply(sk_c6,sk_c9) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19580,c_559]) ).
tcf(c_26303,plain,
multiply(sk_c6,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_19580,c_96]) ).
tcf(c_26309,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_19580,c_19373]) ).
tcf(c_26310,plain,
multiply(sk_c6,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_19580,c_20741]) ).
tcf(c_26320,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( inverse(inverse(iPr_def_17)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_26302,c_547]) ).
tcf(c_26590,plain,
inverse(iPr_def_17) = sk_c6,
inference(demodulation,[status(thm)],[c_26310,c_20741]) ).
tcf(c_26600,plain,
multiply(sk_c6,sk_c9) = iPr_def_19,
inference(superposition,[status(thm)],[c_5599,c_26309]) ).
tcf(c_27067,plain,
multiply(sk_c1,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_19581,c_96]) ).
tcf(c_27073,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_19581,c_19373]) ).
tcf(c_27108,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_4544,c_27067]) ).
tcf(c_27667,plain,
multiply(sk_c1,sk_c9) = iPr_def_26,
inference(superposition,[status(thm)],[c_5569,c_27073]) ).
tcf(c_28754,plain,
multiply(sk_c3,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_19582,c_96]) ).
tcf(c_28759,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_19582,c_560]) ).
tcf(c_28760,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_19582,c_19373]) ).
tcf(c_28761,plain,
multiply(sk_c3,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_19582,c_20741]) ).
tcf(c_28762,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_24 )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_28759,c_552]) ).
tcf(c_28783,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1236,c_28754]) ).
tcf(c_28884,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(superposition,[status(thm)],[c_28754,c_2687]) ).
tcf(c_28892,plain,
inverse(iPr_def_18) = sk_c3,
inference(demodulation,[status(thm)],[c_28761,c_20741]) ).
tcf(c_30150,plain,
multiply(sk_c3,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_5564,c_28760]) ).
tcf(c_30481,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_28783,c_563]) ).
tcf(c_44036,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_30481,c_552]) ).
tcf(c_44050,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_44036,c_28754]) ).
tcf(c_44184,plain,
( ( iPr_def_24 = iPr_def_26 )
| ( iPr_def_16 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_44050,c_27108]) ).
tcf(c_44196,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_44050,c_95]) ).
tcf(c_48775,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3184,c_20767]) ).
tcf(c_50184,plain,
( ~ iPr_def_13
| ( sk_c9 != identity ) ),
inference(ground_joinability,[status(thm)],[c_3187,c_21717]) ).
tcf(c_50734,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c7 != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3454,c_20767]) ).
tcf(c_51633,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c7 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3665,c_20767]) ).
tcf(c_51848,plain,
( ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_3668,c_21717]) ).
tcf(c_69290,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( sk_c2 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_44196,c_3948]) ).
tcf(c_70261,plain,
( ( iPr_def_26 = iPr_def_27 )
| ( iPr_def_16 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_69290,c_589]) ).
tcf(c_70266,plain,
( ( iPr_def_26 = iPr_def_27 )
| ( iPr_def_16 = iPr_def_19 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_69290,c_584]) ).
tcf(c_80522,plain,
( ( iPr_def_26 = iPr_def_27 )
| ( iPr_def_16 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_70266,c_70261]) ).
tcf(c_82004,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_80522,c_5447]) ).
tcf(c_82656,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_82004,c_44184]) ).
tcf(c_82920,plain,
( ( iPr_def_16 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_82656,c_5564]) ).
tcf(c_100232,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_82920,c_51848,c_51633,c_50734,c_50184,c_48775,c_30150,c_28892,c_28884,c_28762,c_28754,c_27667,c_27067,c_26600,c_26590,c_26320,c_26303,c_25425,c_25408,c_24112,c_22809,c_22792,c_22712,c_22694,c_22689,c_22476,c_22127,c_21717,c_21525,c_21378,c_21387,c_21380,c_20777,c_20771,c_20770,c_20759,c_20758,c_20756,c_20752,c_20747,c_20767,c_19401,c_15982,c_13759,c_3858,c_3854,c_3332,c_3320,c_3210,c_20793,c_1302,c_603,c_602,c_601,c_600,c_599,c_596,c_593,c_589,c_586,c_582,c_579,c_575,c_572,c_568,c_567,c_566,c_565,c_564,c_563,c_562,c_556,c_550,c_546,c_545,c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP369-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:38:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 15.08/3.24 % SZS status Started for theBenchmark.p
% 15.08/3.24 % SZS status Unsatisfiable for theBenchmark.p
% 15.08/3.24
% 15.08/3.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.08/3.24
% 15.08/3.24 % ------ iProver source info
% 15.08/3.24
% 15.08/3.24 % git: date: 2026-07-19 20:42:38 +0200
% 15.08/3.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.08/3.24 % git: non_committed_changes: false
% 15.08/3.24
% 15.08/3.24 % ------ Parsing...% successful
% 15.08/3.24
% 15.08/3.24
% 15.08/3.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.08/3.24
% 15.08/3.24 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 15.08/3.24
% 15.08/3.24 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.08/3.24
% 15.08/3.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 15.08/3.24 % ------ Proving...
% 15.08/3.24 % ------ Problem Properties
% 15.08/3.24
% 15.08/3.24 %
% 15.08/3.24 % clauses 64
% 15.08/3.24 % conjectures 48
% 15.08/3.24 % EPR 43
% 15.08/3.24 % Horn 21
% 15.08/3.24 % unary 16
% 15.08/3.24 % binary 42
% 15.08/3.24 % lits 122
% 15.08/3.24 % lits eq 112
% 15.08/3.24 % fd_pure 0
% 15.08/3.24 % fd_pseudo 0
% 15.08/3.24 % fd_cond 0
% 15.08/3.24 % fd_pseudo_cond 0
% 15.08/3.24 % AC symbols 0
% 15.08/3.24
% 15.08/3.24 % ------ Schedule dynamic 5 is on
% 15.08/3.24
% 15.08/3.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.08/3.24
% 15.08/3.24
% 15.08/3.24 % ------
% 15.08/3.24 % Current options:
% 15.08/3.24 % ------
% 15.08/3.24
% 15.08/3.24
% 15.08/3.24 %
% 15.08/3.24
% 15.08/3.24 % ------ Proving...
% 15.08/3.24 %
% 15.08/3.24
% 15.08/3.24 % SZS status Unsatisfiable for theBenchmark.p
% 15.08/3.24
% 15.08/3.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.08/3.24
% 15.08/3.24
%------------------------------------------------------------------------------