%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP293-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 01:32:45 PM UTC 2026
% Result : Unsatisfiable 32.65s 6.40s
% Output : CNFRefutation 27.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 383 ( 110 unt; 12 def)
% Number of atoms : 1378 ( 730 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 582 ( 194 ~; 388 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c7 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X1)
| sk_c6 != multiply(X1,sk_c8)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X0,X1,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c7 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X1)
| sk_c6 != multiply(X1,sk_c8)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f78]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_119,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_478,definition,
iPr_def_14 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c6 )
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_477,c_480,c_479,c_478]) ).
tcf(c_491,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_492,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_127,c_482,c_481]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_126,c_483]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_125,c_484]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124,c_485]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_123,c_486]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_121,c_487]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_503,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_504,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_488]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_489]) ).
tcf(c_522,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_523,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_527,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_531,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_816,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_499,c_478]) ).
tcf(c_828,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_499,c_479]) ).
tcf(c_829,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_18,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_495,c_479]) ).
tcf(c_840,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_21,sk_c8) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_498,c_480]) ).
tcf(c_863,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_503,c_479]) ).
tcf(c_900,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_506,c_500]) ).
tcf(c_986,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_510,c_486]) ).
tcf(c_989,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_498,c_486]) ).
tcf(c_1007,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1017,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_485,c_90]) ).
tcf(c_1018,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_481,c_90]) ).
tcf(c_1019,plain,
multiply(iPr_def_24,sk_c1) = identity,
inference(superposition,[status(thm)],[c_488,c_90]) ).
tcf(c_1020,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_1021,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_1022,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1027,plain,
( ( sk_c6 = multiply(identity,sk_c6) )
| ( sk_c6 != sk_c6 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_1028,plain,
multiply(identity,sk_c6) = sk_c6,
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_1030,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1032,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_1068,plain,
( ( sk_c6 = iPr_def_23 )
| ( iPr_def_23 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_1104,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != multiply(identity,sk_c6) )
| ( X0 != multiply(identity,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_1116,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1007]) ).
tcf(c_1133,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_24,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_513,c_478]) ).
tcf(c_1135,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_513,c_495]) ).
tcf(c_1217,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1232,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_516,c_486]) ).
tcf(c_1264,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_24,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_517,c_478]) ).
tcf(c_1294,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c6) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c6) != X0 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1363,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_519,c_507]) ).
tcf(c_1479,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1030]) ).
tcf(c_1579,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_523,c_511]) ).
tcf(c_1615,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1669,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1294]) ).
tcf(c_1691,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_525,c_506]) ).
tcf(c_1696,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_525,c_501]) ).
tcf(c_1864,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_528,c_504]) ).
tcf(c_1896,plain,
! [X0: $i] :
( ( multiply(identity,sk_c6) = X0 )
| ( X0 != sk_c6 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1338]) ).
tcf(c_1932,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_529,c_505]) ).
tcf(c_2061,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_480,c_492]) ).
tcf(c_2062,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_483,c_492]) ).
tcf(c_2063,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_489,c_492]) ).
tcf(c_2064,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_487,c_492]) ).
tcf(c_2066,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_90,c_492]) ).
tcf(c_2074,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_23 )
| ( sk_c8 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_2064,c_482]) ).
tcf(c_2078,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_25 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2063,c_488]) ).
tcf(c_2082,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_19 )
| ( sk_c8 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2062,c_481]) ).
tcf(c_2140,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_483,c_493]) ).
tcf(c_2144,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_90,c_493]) ).
tcf(c_2160,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( sk_c8 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2140,c_481]) ).
tcf(c_2212,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_23 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1669]) ).
tcf(c_2222,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_14 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_478,c_494]) ).
tcf(c_2224,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_89,c_494]) ).
tcf(c_2332,plain,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_23 != iPr_def_23 )
| ( sk_c6 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1479]) ).
tcf(c_2333,plain,
iPr_def_23 = iPr_def_23,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_2355,plain,
( ~ iPr_def_13
| ( inverse(sk_c1) != sk_c8 )
| ( multiply(sk_c8,iPr_def_25) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_489,c_491]) ).
tcf(c_2370,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_24 )
| ( multiply(sk_c8,iPr_def_25) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2355,c_488]) ).
tcf(c_2721,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_478,c_91]) ).
tcf(c_2722,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_480,c_91]) ).
tcf(c_2723,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_486,c_91]) ).
tcf(c_2724,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_484,c_91]) ).
tcf(c_2727,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_479,c_91]) ).
tcf(c_2728,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_487,c_91]) ).
tcf(c_2730,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2732,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1017,c_91]) ).
tcf(c_2733,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1018,c_91]) ).
tcf(c_2734,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1019,c_91]) ).
tcf(c_2735,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1020,c_91]) ).
tcf(c_2741,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2735,c_89]) ).
tcf(c_2742,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2734,c_89]) ).
tcf(c_2743,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2733,c_89]) ).
tcf(c_2744,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2732,c_89]) ).
tcf(c_2953,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1135,c_483]) ).
tcf(c_2957,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1135,c_499]) ).
tcf(c_3116,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1615]) ).
tcf(c_3167,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1363,c_483]) ).
tcf(c_3265,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1579,c_1363]) ).
tcf(c_3400,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1696,c_483]) ).
tcf(c_3531,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1864,c_486]) ).
tcf(c_3534,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_21,sk_c8) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1864,c_480]) ).
tcf(c_3581,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1932,c_1696]) ).
tcf(c_3593,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_22,sk_c5) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1932,c_484]) ).
tcf(c_3597,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1932,c_478]) ).
tcf(c_3640,plain,
( ( multiply(identity,sk_c6) = iPr_def_23 )
| ( iPr_def_23 != sk_c6 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1896]) ).
tcf(c_3995,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_500,c_828]) ).
tcf(c_4053,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_18,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_501,c_829]) ).
tcf(c_4166,plain,
multiply(iPr_def_18,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_487,c_2741]) ).
tcf(c_4177,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_23,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4166,c_91]) ).
tcf(c_4179,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c8,
inference(superposition,[status(thm)],[c_489,c_2742]) ).
tcf(c_4184,plain,
multiply(iPr_def_17,iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_483,c_2743]) ).
tcf(c_4187,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_19,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4184,c_91]) ).
tcf(c_4189,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_486,c_2744]) ).
tcf(c_4192,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4189,c_91]) ).
tcf(c_4278,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_499,c_840]) ).
tcf(c_4284,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4278,c_4189]) ).
tcf(c_4363,plain,
! [X0: $i] :
( ( multiply(identity,sk_c6) = X0 )
| ( X0 != iPr_def_23 )
| ( multiply(identity,sk_c6) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1338]) ).
tcf(c_4653,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4284,c_816]) ).
tcf(c_6914,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_519,c_1133]) ).
tcf(c_6925,plain,
( ( sk_c8 = iPr_def_17 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6914,c_4179]) ).
tcf(c_6992,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6925,c_483]) ).
tcf(c_6993,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6925,c_480]) ).
tcf(c_8081,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_523,c_1264]) ).
tcf(c_8095,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8081,c_4179]) ).
tcf(c_8181,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_8095,c_480]) ).
tcf(c_8723,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != multiply(identity,sk_c6) )
| ( sk_c6 != multiply(identity,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_8730,plain,
( ( iPr_def_16 = multiply(identity,sk_c6) )
| ( iPr_def_16 != iPr_def_16 )
| ( multiply(identity,sk_c6) != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_3116]) ).
tcf(c_10976,plain,
multiply(sk_c8,iPr_def_16) = multiply(iPr_def_14,sk_c8),
inference(superposition,[status(thm)],[c_480,c_2721]) ).
tcf(c_11168,plain,
( ( sk_c8 = iPr_def_17 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4053,c_4166]) ).
tcf(c_11231,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_11168,c_863]) ).
tcf(c_11251,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_11168,c_483]) ).
tcf(c_11844,plain,
multiply(sk_c7,iPr_def_20) = multiply(iPr_def_16,sk_c5),
inference(superposition,[status(thm)],[c_484,c_2722]) ).
tcf(c_11845,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_479,c_2722]) ).
tcf(c_12687,plain,
multiply(sk_c3,iPr_def_16) = multiply(iPr_def_22,sk_c8),
inference(superposition,[status(thm)],[c_480,c_2723]) ).
tcf(c_12695,plain,
multiply(sk_c3,multiply(iPr_def_16,sk_c5)) = multiply(iPr_def_22,iPr_def_20),
inference(superposition,[status(thm)],[c_11844,c_2723]) ).
tcf(c_12811,plain,
multiply(iPr_def_21,multiply(iPr_def_22,sk_c8)) = iPr_def_16,
inference(superposition,[status(thm)],[c_12687,c_2744]) ).
tcf(c_14036,plain,
( ( multiply(identity,sk_c6) = iPr_def_16 )
| ( iPr_def_16 != iPr_def_23 )
| ( multiply(identity,sk_c6) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_4363]) ).
tcf(c_14117,plain,
( ~ iPr_def_13
| ( inverse(sk_c6) != sk_c8 )
| ( multiply(iPr_def_15,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_2727,c_491]) ).
tcf(c_14227,plain,
multiply(sk_c2,iPr_def_20) = multiply(iPr_def_23,sk_c5),
inference(superposition,[status(thm)],[c_484,c_2728]) ).
tcf(c_14228,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_23,sk_c6),
inference(superposition,[status(thm)],[c_479,c_2728]) ).
tcf(c_14775,plain,
multiply(iPr_def_18,multiply(iPr_def_23,sk_c5)) = iPr_def_20,
inference(superposition,[status(thm)],[c_14227,c_2741]) ).
tcf(c_14839,plain,
multiply(iPr_def_18,multiply(iPr_def_23,sk_c6)) = iPr_def_15,
inference(superposition,[status(thm)],[c_14228,c_2741]) ).
tcf(c_16388,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1691,c_506,c_530,c_1022,c_1032,c_2212]) ).
tcf(c_16423,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_16388,c_479]) ).
tcf(c_16425,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_16423,c_10976]) ).
tcf(c_16592,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1932,c_3534]) ).
tcf(c_16607,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_16592,c_4189]) ).
tcf(c_16862,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_16607,c_478]) ).
tcf(c_16869,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_16862,c_10976]) ).
tcf(c_18059,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_4653,c_3995]) ).
tcf(c_18164,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_18059,c_487]) ).
tcf(c_19184,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2730,c_89]) ).
tcf(c_19189,plain,
multiply(inverse(sk_c8),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_478,c_19184]) ).
tcf(c_19190,plain,
multiply(inverse(sk_c7),iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_480,c_19184]) ).
tcf(c_19192,plain,
multiply(inverse(sk_c8),iPr_def_20) = sk_c5,
inference(superposition,[status(thm)],[c_484,c_19184]) ).
tcf(c_19195,plain,
multiply(inverse(sk_c8),iPr_def_15) = sk_c6,
inference(superposition,[status(thm)],[c_479,c_19184]) ).
tcf(c_19197,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_19184]) ).
tcf(c_19198,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_19184]) ).
tcf(c_19225,plain,
multiply(inverse(sk_c8),multiply(iPr_def_14,sk_c8)) = iPr_def_16,
inference(superposition,[status(thm)],[c_10976,c_19184]) ).
tcf(c_19339,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2744,c_19184]) ).
tcf(c_19340,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2743,c_19184]) ).
tcf(c_19341,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2742,c_19184]) ).
tcf(c_19342,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2741,c_19184]) ).
tcf(c_19403,plain,
multiply(inverse(sk_c7),multiply(iPr_def_16,sk_c5)) = iPr_def_20,
inference(superposition,[status(thm)],[c_11844,c_19184]) ).
tcf(c_19412,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_19184,c_19184]) ).
tcf(c_21387,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_22 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_2957,c_517]) ).
tcf(c_21831,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_19198,c_19412]) ).
tcf(c_21843,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_21831,c_2721]) ).
tcf(c_21847,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_21831,c_2722]) ).
tcf(c_21848,plain,
multiply(sk_c7,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_21831,c_4192]) ).
tcf(c_21849,plain,
multiply(sk_c8,sk_c5) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_21831,c_2724]) ).
tcf(c_21850,plain,
multiply(sk_c8,identity) = multiply(iPr_def_17,iPr_def_19),
inference(superposition,[status(thm)],[c_21831,c_4187]) ).
tcf(c_21852,plain,
multiply(sk_c8,sk_c6) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_21831,c_2727]) ).
tcf(c_21853,plain,
multiply(sk_c8,identity) = multiply(iPr_def_18,iPr_def_23),
inference(superposition,[status(thm)],[c_21831,c_4177]) ).
tcf(c_21858,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_21831,c_19197]) ).
tcf(c_21859,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_21853,c_4166]) ).
tcf(c_21860,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_21852,c_479]) ).
tcf(c_21863,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_21849,c_484]) ).
tcf(c_21864,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_21848,c_4189]) ).
tcf(c_21865,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_21847,c_480]) ).
tcf(c_21869,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_21843,c_478]) ).
tcf(c_23673,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(sk_c7),iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_6993,c_19184]) ).
tcf(c_26343,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_21)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c3,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_19339,c_491]) ).
tcf(c_26346,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_19339,c_90]) ).
tcf(c_26349,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_21)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_19339,c_494]) ).
tcf(c_26350,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_19339,c_19184]) ).
tcf(c_26351,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_19339,c_21831]) ).
tcf(c_26352,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( inverse(inverse(iPr_def_21)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_26349,c_486]) ).
tcf(c_26365,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_3531,c_26346]) ).
tcf(c_26366,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1232,c_26346]) ).
tcf(c_26367,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_989,c_26346]) ).
tcf(c_26368,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_986,c_26346]) ).
tcf(c_26614,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_26365,c_89]) ).
tcf(c_27225,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_26367,c_26366]) ).
tcf(c_27713,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_26368,c_522]) ).
tcf(c_27982,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_26351,c_21831]) ).
tcf(c_27991,plain,
multiply(sk_c3,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_4189,c_26350]) ).
tcf(c_28383,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(inverse(sk_c7),iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8181,c_19184]) ).
tcf(c_28491,plain,
multiply(sk_c4,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_19340,c_90]) ).
tcf(c_28495,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_19340,c_19184]) ).
tcf(c_28496,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_19340,c_21831]) ).
tcf(c_28512,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_6992,c_28491]) ).
tcf(c_28513,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_3400,c_28491]) ).
tcf(c_28514,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_3167,c_28491]) ).
tcf(c_28515,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_2953,c_28491]) ).
tcf(c_28607,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(superposition,[status(thm)],[c_28491,c_2743]) ).
tcf(c_28689,plain,
multiply(sk_c4,sk_c8) = iPr_def_19,
inference(superposition,[status(thm)],[c_4184,c_28495]) ).
tcf(c_29135,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_500,c_506]) ).
tcf(c_29600,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_29135,c_506,c_900,c_1022,c_1027,c_1028,c_1032,c_1217,c_3640,c_8723,c_8730,c_14036]) ).
tcf(c_29601,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c8 = iPr_def_18 ) ),
inference(renaming,[status(thm)],[c_29600]) ).
tcf(c_33495,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_28513,c_26365]) ).
tcf(c_33543,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_18 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_28515,c_27225]) ).
tcf(c_33609,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( multiply(iPr_def_18,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_33495,c_4166]) ).
tcf(c_33948,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_19341,c_19184]) ).
tcf(c_33949,plain,
multiply(sk_c1,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_19341,c_21831]) ).
tcf(c_35701,plain,
inverse(iPr_def_24) = sk_c1,
inference(demodulation,[status(thm)],[c_33949,c_21831]) ).
tcf(c_35703,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( inverse(iPr_def_18) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_33543,c_35701]) ).
tcf(c_35724,plain,
multiply(sk_c1,sk_c8) = iPr_def_25,
inference(superposition,[status(thm)],[c_4179,c_33948]) ).
tcf(c_36522,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_19342,c_90]) ).
tcf(c_36526,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_19342,c_19184]) ).
tcf(c_36527,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_19342,c_21831]) ).
tcf(c_36708,plain,
inverse(iPr_def_18) = sk_c2,
inference(demodulation,[status(thm)],[c_36527,c_21831]) ).
tcf(c_36724,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1020,c_36526]) ).
tcf(c_36729,plain,
multiply(sk_c2,sk_c8) = iPr_def_23,
inference(superposition,[status(thm)],[c_4166,c_36526]) ).
tcf(c_37479,plain,
( ( iPr_def_18 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_21387,c_1135]) ).
tcf(c_38301,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( inverse(iPr_def_18) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_37479,c_35701]) ).
tcf(c_38340,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_38301,c_36708]) ).
tcf(c_38865,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( identity = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_27713,c_486]) ).
tcf(c_38880,plain,
( ( iPr_def_15 = iPr_def_25 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_38865,c_26346]) ).
tcf(c_39705,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_38880,c_28514]) ).
tcf(c_40595,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( multiply(sk_c1,sk_c8) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_38340,c_487]) ).
tcf(c_40598,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_40595,c_35724]) ).
tcf(c_42972,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_40598,c_3265]) ).
tcf(c_43638,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_42972,c_3581]) ).
tcf(c_43856,plain,
( ~ iPr_def_12
| ( inverse(sk_c7) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_2061,c_506,c_1022,c_1032,c_1068,c_2074,c_2061,c_29601]) ).
tcf(c_47411,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2224,c_21858]) ).
tcf(c_48722,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_11251,c_28491]) ).
tcf(c_48784,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_48722,c_28512]) ).
tcf(c_50577,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_35703,c_36708]) ).
tcf(c_50605,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( multiply(sk_c1,sk_c8) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_50577,c_487]) ).
tcf(c_50608,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_19 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_50605,c_35724]) ).
tcf(c_53387,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_50608,c_39705]) ).
tcf(c_53525,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_53387,c_33495]) ).
tcf(c_53664,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_53525,c_43638]) ).
tcf(c_54065,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_16869,c_16425]) ).
tcf(c_54384,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( identity = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_18164,c_36522]) ).
tcf(c_54408,plain,
( ( iPr_def_19 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_54384,c_48784]) ).
tcf(c_54501,plain,
( ( iPr_def_14 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_54408,c_54065]) ).
tcf(c_54569,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_53664,c_54501]) ).
tcf(c_55552,plain,
( ( iPr_def_14 = iPr_def_23 )
| ~ iPr_def_13
| ( inverse(iPr_def_22) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_26614,c_491]) ).
tcf(c_55559,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_26614,c_3597]) ).
tcf(c_55567,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c5 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_26614,c_3593]) ).
tcf(c_55900,plain,
( ( iPr_def_14 = iPr_def_23 )
| ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_55559,c_47411]) ).
tcf(c_55902,plain,
( ( iPr_def_14 = iPr_def_23 )
| ~ iPr_def_12
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_55559,c_43856]) ).
tcf(c_55922,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_55559,c_16607]) ).
tcf(c_56396,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_55567,c_526]) ).
tcf(c_56401,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_55567,c_502]) ).
tcf(c_56636,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_56396,c_1116,c_2212,c_2332,c_2333,c_16388,c_55922,c_56401]) ).
tcf(c_56661,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_18,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_56636,c_4166]) ).
tcf(c_94286,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_56661,c_55902,c_55900,c_55552,c_54569,c_36729,c_36724,c_36708,c_36522,c_33609,c_28689,c_28607,c_28496,c_28491,c_28383,c_27991,c_27982,c_26352,c_26343,c_26351,c_26346,c_23673,c_21869,c_21865,c_21864,c_21863,c_21860,c_21859,c_21852,c_21850,c_21849,c_21848,c_21847,c_21843,c_19403,c_19225,c_19195,c_19192,c_19190,c_19189,c_14839,c_14775,c_14228,c_14227,c_14117,c_12811,c_12695,c_12687,c_11845,c_11231,c_2370,c_2222,c_2160,c_2144,c_2082,c_2078,c_2066,c_530,c_529,c_528,c_527,c_526,c_525,c_523,c_517,c_511,c_510,c_505,c_500,c_499,c_498,c_497,c_496,c_495,c_490,c_485,c_482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP293-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n007.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 14:21:08 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45
% 0.11/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.45
% 0.11/0.45 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 32.65/6.40 % SZS status Started for theBenchmark.p
% 32.65/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 32.65/6.40
% 32.65/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.65/6.40
% 32.65/6.40 % ------ iProver source info
% 32.65/6.40
% 32.65/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 32.65/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.65/6.40 % git: non_committed_changes: false
% 32.65/6.40
% 32.65/6.40 % ------ Parsing...% successful
% 32.65/6.40
% 32.65/6.40
% 32.65/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.65/6.40
% 32.65/6.40 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 32.65/6.40
% 32.65/6.40 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.65/6.40
% 32.65/6.40 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 32.65/6.40 % ------ Proving...
% 32.65/6.40 % ------ Problem Properties
% 32.65/6.40
% 32.65/6.40 %
% 32.65/6.40 % clauses 56
% 32.65/6.40 % conjectures 41
% 32.65/6.40 % EPR 37
% 32.65/6.40 % Horn 19
% 32.65/6.40 % unary 15
% 32.65/6.40 % binary 36
% 32.65/6.40 % lits 106
% 32.65/6.40 % lits eq 98
% 32.65/6.40 % fd_pure 0
% 32.65/6.40 % fd_pseudo 0
% 32.65/6.40 % fd_cond 0
% 32.65/6.40 % fd_pseudo_cond 0
% 32.65/6.40 % AC symbols 0
% 32.65/6.40
% 32.65/6.40 % ------ Schedule dynamic 5 is on
% 32.65/6.40
% 32.65/6.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.65/6.40
% 32.65/6.40
% 32.65/6.40 % ------
% 32.65/6.40 % Current options:
% 32.65/6.40 % ------
% 32.65/6.40
% 32.65/6.40
% 32.65/6.40 %
% 32.65/6.40
% 32.65/6.40 % ------ Proving...
% 32.65/6.40 %
% 32.65/6.40
% 32.65/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 32.65/6.40
% 32.65/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.46/6.41
% 27.46/6.41
%------------------------------------------------------------------------------