%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP302-1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:46 PM UTC 2026
% Result : Unsatisfiable 4.63s 2.10s
% Output : CNFRefutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 36
% Syntax : Number of formulae : 234 ( 70 unt; 11 def)
% Number of atoms : 776 ( 436 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 413 ( 154 ~; 259 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 54 :)
% 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_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c5) = sk_c4
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c4 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( inverse(sk_c5) = sk_c4
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c4 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c8)
| sk_c6 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f42,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c5) = sk_c4
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c4
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c4 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X3,sk_c8) != X4
| inverse(X4) != sk_c8
| inverse(X3) != X4
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4] :
( multiply(X3,sk_c8) != X4
| sk_c8 != inverse(X4)
| inverse(X3) != X4
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != inverse(X1)
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f54]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( inverse(X3) != multiply(X3,sk_c8)
| sk_c8 != inverse(inverse(X3))
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != inverse(X1)
| sk_c6 != multiply(X1,sk_c8)
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f55]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_81,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c5) = sk_c4 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c4 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c4 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(inverse(X0)) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != inverse(X0) ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(X0,sk_c8) != inverse(X0) )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( inverse(inverse(X0)) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_81,c_106]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(inverse(X0)) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != inverse(X0) ) ),
inference(renaming,[status(thm)],[c_111]) ).
tcf(c_352,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_112]) ).
tcf(c_353,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_112]) ).
tcf(c_354,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != sk_c8 )
| ( multiply(X0,sk_c8) != inverse(X0) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_112]) ).
tcf(c_355,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_112]) ).
tcf(c_356,definition,
iPr_def_13 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_357,definition,
iPr_def_14 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_358,definition,
iPr_def_15 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_359,definition,
iPr_def_16 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_360,definition,
iPr_def_17 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_361,definition,
iPr_def_18 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_362,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_363,definition,
iPr_def_20 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_364,definition,
iPr_def_21 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_365,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_366,definition,
iPr_def_23 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_367,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_355,c_356]) ).
tcf(c_368,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != sk_c8 )
| ( multiply(X0,sk_c8) != inverse(X0) ) ),
inference(demodulation,[status(thm)],[c_354]) ).
tcf(c_369,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_371,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_352]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_105,c_358,c_357]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104,c_359]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_17 = sk_c4 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_360]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102,c_361]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101,c_362]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_93,c_364]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_87,c_365]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_396,negated_conjecture,
iPr_def_23 = sk_c6,
inference(demodulation,[status(thm)],[c_81,c_366]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_593,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_372,c_374]) ).
tcf(c_621,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_377,c_367]) ).
tcf(c_635,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_374,c_359]) ).
tcf(c_643,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_373,c_357]) ).
tcf(c_744,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_383,c_396]) ).
tcf(c_786,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_385,c_357]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_398]) ).
tcf(c_857,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( multiply(sk_c8,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_744,c_366]) ).
tcf(c_858,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c8,iPr_def_13) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_377,c_366]) ).
tcf(c_907,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_365,c_79]) ).
tcf(c_908,plain,
multiply(iPr_def_13,sk_c8) = identity,
inference(superposition,[status(thm)],[c_356,c_79]) ).
tcf(c_910,plain,
multiply(iPr_def_17,sk_c5) = identity,
inference(superposition,[status(thm)],[c_360,c_79]) ).
tcf(c_912,plain,
multiply(iPr_def_15,sk_c2) = identity,
inference(superposition,[status(thm)],[c_358,c_79]) ).
tcf(c_920,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_386,c_384]) ).
tcf(c_922,plain,
( ( sk_c8 = iPr_def_21 )
| ( inverse(iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_386,c_359]) ).
tcf(c_932,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_13,iPr_def_19) = identity ) ),
inference(superposition,[status(thm)],[c_376,c_908]) ).
tcf(c_972,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_387,c_363]) ).
tcf(c_1011,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != iPr_def_16 )
| ( inverse(X0) != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_834]) ).
tcf(c_1031,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_388,c_363]) ).
tcf(c_1091,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_389,c_367]) ).
tcf(c_1149,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_391,c_363]) ).
tcf(c_1218,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_392,c_390]) ).
tcf(c_1221,plain,
( ( sk_c8 = iPr_def_22 )
| ( inverse(iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_392,c_359]) ).
tcf(c_1246,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_393,c_363]) ).
tcf(c_1324,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_394,c_363]) ).
tcf(c_1427,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_395,c_367]) ).
tcf(c_1453,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1455,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_907,c_80]) ).
tcf(c_1456,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_908,c_80]) ).
tcf(c_1458,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_910,c_80]) ).
tcf(c_1460,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1458,c_78]) ).
tcf(c_1462,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1456,c_78]) ).
tcf(c_1463,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1455,c_78]) ).
tcf(c_1544,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_912,c_80]) ).
tcf(c_1545,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1544,c_78]) ).
tcf(c_1689,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_369,c_396]) ).
tcf(c_1700,plain,
( ~ iPr_def_11
| ( iPr_def_20 != iPr_def_23 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_363,c_1689]) ).
tcf(c_1715,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_19) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_376,c_1689]) ).
tcf(c_1716,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_18) != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_375,c_1689]) ).
tcf(c_1724,plain,
( ~ iPr_def_11
| ( iPr_def_20 != iPr_def_23 )
| ( sk_c8 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1700,c_358]) ).
tcf(c_1881,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_361,c_371]) ).
tcf(c_1882,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_364,c_371]) ).
tcf(c_1886,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_395,c_371]) ).
tcf(c_1887,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_21 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_389,c_371]) ).
tcf(c_1893,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( sk_c8 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_1882,c_365]) ).
tcf(c_1897,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c8 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_1881,c_362]) ).
tcf(c_1984,plain,
( ~ iPr_def_12
| ( inverse(sk_c5) != iPr_def_14 )
| ( inverse(inverse(sk_c5)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_357,c_368]) ).
tcf(c_2013,plain,
( ~ iPr_def_12
| ( iPr_def_14 != iPr_def_17 )
| ( inverse(iPr_def_17) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1984,c_360]) ).
tcf(c_3205,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_357,c_1460]) ).
tcf(c_3267,plain,
multiply(iPr_def_13,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_366,c_1462]) ).
tcf(c_3436,plain,
multiply(iPr_def_22,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_364,c_1463]) ).
tcf(c_3565,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_643,c_1460]) ).
tcf(c_3566,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3565,c_3205]) ).
tcf(c_3584,plain,
multiply(iPr_def_15,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_363,c_1545]) ).
tcf(c_3730,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_14) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_786,c_1460]) ).
tcf(c_3731,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3730,c_3205]) ).
tcf(c_4482,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_972,c_1545]) ).
tcf(c_4483,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4482,c_3584]) ).
tcf(c_4607,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1031,c_1545]) ).
tcf(c_4608,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4607,c_3584]) ).
tcf(c_4970,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1149,c_1545]) ).
tcf(c_4971,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4970,c_3584]) ).
tcf(c_5292,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1246,c_1545]) ).
tcf(c_5293,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5292,c_3584]) ).
tcf(c_5366,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1324,c_1545]) ).
tcf(c_5367,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5366,c_3584]) ).
tcf(c_6490,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1453,c_78]) ).
tcf(c_6532,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_6490]) ).
tcf(c_6621,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_1462,c_6490]) ).
tcf(c_6633,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1545,c_6490]) ).
tcf(c_6660,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6490,c_6490]) ).
tcf(c_7063,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6532,c_6660]) ).
tcf(c_10601,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_1893,c_1897,c_1893,c_4483,c_4608]) ).
tcf(c_10603,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_10601,c_1897,c_5293,c_5367,c_10601]) ).
tcf(c_10609,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c7 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_367,c_10603]) ).
tcf(c_11582,plain,
multiply(sk_c8,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_6621,c_79]) ).
tcf(c_11585,plain,
( ~ iPr_def_12
| ( multiply(sk_c8,sk_c8) != inverse(inverse(iPr_def_13)) )
| ( inverse(inverse(inverse(iPr_def_13))) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_6621,c_368]) ).
tcf(c_11588,plain,
multiply(sk_c8,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_6621,c_7063]) ).
tcf(c_11598,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_857,c_11582]) ).
tcf(c_11600,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_858,c_11582]) ).
tcf(c_12466,plain,
inverse(iPr_def_13) = sk_c8,
inference(demodulation,[status(thm)],[c_11588,c_7063]) ).
tcf(c_16745,plain,
( ( inverse(iPr_def_17) = sk_c8 )
| ( sk_c8 != iPr_def_16 )
| ( inverse(iPr_def_17) != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_23831,negated_conjecture,
( iPr_def_12
| iPr_def_11
| ( iPr_def_13 != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_367,c_367,c_10603]) ).
tcf(c_23876,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_377,c_23831]) ).
tcf(c_23907,plain,
( ( sk_c8 = iPr_def_15 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_23876,c_593,c_621,c_635,c_2013,c_3566,c_10603,c_16745]) ).
tcf(c_23908,plain,
( iPr_def_11
| ( sk_c8 = iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_23907]) ).
tcf(c_24204,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_389,c_23831]) ).
tcf(c_24531,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c8 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_395,c_23831]) ).
tcf(c_24723,plain,
( ( sk_c8 = iPr_def_21 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_24204,c_920,c_922,c_1091,c_1897,c_2013,c_3731,c_5293,c_5367,c_10601,c_16745]) ).
tcf(c_24724,plain,
( iPr_def_11
| ( sk_c8 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_24723]) ).
tcf(c_24729,plain,
( ( sk_c8 = iPr_def_22 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_24531,c_1218,c_1221,c_1427,c_1897,c_2013,c_4971,c_5293,c_5367,c_10601,c_16745]) ).
tcf(c_24730,plain,
( iPr_def_11
| ( sk_c8 = iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_24729]) ).
tcf(c_27579,plain,
multiply(sk_c2,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_6633,c_79]) ).
tcf(c_30317,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ( multiply(X0,iPr_def_19) != iPr_def_23 )
| ( inverse(X0) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_1715,c_1715,c_23908]) ).
tcf(c_30318,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,iPr_def_19) != iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_30317]) ).
tcf(c_30337,plain,
( ( sk_c8 = iPr_def_15 )
| ( identity != iPr_def_23 )
| ( inverse(iPr_def_13) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_932,c_30318]) ).
tcf(c_30347,plain,
( ( sk_c8 = iPr_def_15 )
| ( identity != iPr_def_23 ) ),
inference(ground_joinability,[status(thm)],[c_30337,c_12466]) ).
tcf(c_30505,plain,
sk_c8 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_1716,c_11600,c_30347]) ).
tcf(c_30558,plain,
inverse(iPr_def_13) = iPr_def_15,
inference(demodulation,[status(thm)],[c_12466,c_30505]) ).
tcf(c_30561,plain,
multiply(iPr_def_15,iPr_def_13) = identity,
inference(demodulation,[status(thm)],[c_11582,c_30505]) ).
tcf(c_30584,plain,
( ~ iPr_def_11
| ( iPr_def_20 != iPr_def_23 )
| ( iPr_def_15 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1724,c_30505]) ).
tcf(c_30678,plain,
multiply(sk_c2,iPr_def_15) = iPr_def_20,
inference(demodulation,[status(thm)],[c_363,c_30505]) ).
tcf(c_30685,plain,
inverse(iPr_def_15) = iPr_def_13,
inference(demodulation,[status(thm)],[c_356,c_30505]) ).
tcf(c_30857,plain,
( ~ iPr_def_11
| ( iPr_def_20 != iPr_def_23 ) ),
inference(equality_resolution_simp,[status(thm)],[c_30584]) ).
tcf(c_30899,plain,
identity = iPr_def_20,
inference(demodulation,[status(thm)],[c_27579,c_30678]) ).
tcf(c_30925,plain,
iPr_def_20 = iPr_def_23,
inference(demodulation,[status(thm)],[c_11598,c_30899]) ).
tcf(c_30982,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_30857,c_30925]) ).
tcf(c_31014,plain,
multiply(iPr_def_13,iPr_def_20) = sk_c7,
inference(demodulation,[status(thm)],[c_3267,c_30925]) ).
tcf(c_31202,plain,
multiply(iPr_def_15,iPr_def_13) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_30561,c_30899]) ).
tcf(c_31203,plain,
multiply(inverse(iPr_def_15),iPr_def_20) = iPr_def_13,
inference(superposition,[status(thm)],[c_31202,c_6490]) ).
tcf(c_31205,plain,
sk_c7 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_31203,c_30685,c_31014]) ).
tcf(c_31216,plain,
multiply(iPr_def_22,iPr_def_21) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3436,c_31205]) ).
tcf(c_31379,plain,
sk_c8 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_1886,c_24730,c_30982]) ).
tcf(c_31381,plain,
iPr_def_15 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_31379,c_30505]) ).
tcf(c_31437,plain,
sk_c8 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_1887,c_24724,c_30982]) ).
tcf(c_31439,plain,
iPr_def_15 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_31437,c_30505]) ).
tcf(c_31490,plain,
( ( inverse(inverse(inverse(iPr_def_13))) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != inverse(inverse(iPr_def_13)) ) ),
inference(global_subsumption_just,[status(thm)],[c_11585,c_10609,c_11585,c_30982,c_31205]) ).
tcf(c_31491,plain,
( ( multiply(sk_c8,sk_c8) != inverse(inverse(iPr_def_13)) )
| ( inverse(inverse(inverse(iPr_def_13))) != sk_c8 ) ),
inference(renaming,[status(thm)],[c_31490]) ).
tcf(c_31492,plain,
multiply(sk_c8,sk_c8) != inverse(inverse(iPr_def_13)),
inference(ground_joinability,[status(thm)],[c_31491,c_30505,c_30558,c_30685]) ).
tcf(c_31493,plain,
multiply(iPr_def_15,iPr_def_15) != iPr_def_13,
inference(light_normalisation,[status(thm)],[c_31492,c_30505,c_30558,c_30685]) ).
tcf(c_31618,plain,
multiply(iPr_def_15,iPr_def_15) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_31216,c_31381,c_31439]) ).
tcf(c_31619,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31618,c_31493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 14:24:43 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 4.63/2.10 % SZS status Started for theBenchmark.p
% 4.63/2.10 % SZS status Unsatisfiable for theBenchmark.p
% 4.63/2.10
% 4.63/2.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.63/2.10
% 4.63/2.10 % ------ iProver source info
% 4.63/2.10
% 4.63/2.10 % git: date: 2026-07-19 20:42:38 +0200
% 4.63/2.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.63/2.10 % git: non_committed_changes: false
% 4.63/2.10
% 4.63/2.10 % ------ Parsing...% successful
% 4.63/2.10
% 4.63/2.10
% 4.63/2.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.63/2.10
% 4.63/2.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.63/2.10
% 4.63/2.10 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.63/2.10
% 4.63/2.10 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.63/2.10 % ------ Proving...
% 4.63/2.10 % ------ Problem Properties
% 4.63/2.10
% 4.63/2.10 %
% 4.63/2.10 % clauses 43
% 4.63/2.10 % conjectures 29
% 4.63/2.10 % EPR 26
% 4.63/2.10 % Horn 18
% 4.63/2.10 % unary 15
% 4.63/2.10 % binary 24
% 4.63/2.10 % lits 76
% 4.63/2.10 % lits eq 70
% 4.63/2.10 % fd_pure 0
% 4.63/2.10 % fd_pseudo 0
% 4.63/2.10 % fd_cond 0
% 4.63/2.10 % fd_pseudo_cond 0
% 4.63/2.10 % AC symbols 0
% 4.63/2.10
% 4.63/2.10 % ------ Schedule dynamic 5 is on
% 4.63/2.10
% 4.63/2.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.63/2.10
% 4.63/2.10
% 4.63/2.10 % ------
% 4.63/2.10 % Current options:
% 4.63/2.10 % ------
% 4.63/2.10
% 4.63/2.10
% 4.63/2.10 %
% 4.63/2.10
% 4.63/2.10 % ------ Proving...
% 4.63/2.10 %
% 4.63/2.10
% 4.63/2.10 % SZS status Unsatisfiable for theBenchmark.p
% 4.63/2.10
% 4.63/2.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.63/2.10
% 4.63/2.10
%------------------------------------------------------------------------------