%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP216-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 01:31:50 PM UTC 2026
% Result : Unsatisfiable 7.32s 1.73s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 290 ( 101 unt; 10 def)
% Number of atoms : 939 ( 497 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 420 ( 146 ~; 274 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 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/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = inverse(sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = inverse(sk_c7)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != inverse(X4)
| multiply(X4,sk_c7) != X3
| sk_c6 != multiply(sk_c7,X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != inverse(sk_c7)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X2,X0,X1,X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(sk_c7,multiply(X4,sk_c7))
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != inverse(sk_c7)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(equality_resolution,[],[f54]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(sk_c7,multiply(X3,sk_c7)) != sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_345,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_346,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_104]) ).
tcf(c_347,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_348,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_104]) ).
tcf(c_349,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_350,definition,
iPr_def_14 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_351,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_352,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_353,definition,
iPr_def_17 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_354,definition,
iPr_def_18 = multiply(sk_c7,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_355,definition,
iPr_def_19 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_356,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_357,definition,
iPr_def_21 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_358,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_359,definition,
iPr_def_23 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_360,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_349,c_350]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_348]) ).
tcf(c_362,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_347]) ).
tcf(c_363,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_346]) ).
tcf(c_364,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_345]) ).
tcf(c_365,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103,c_352,c_351]) ).
tcf(c_366,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_353]) ).
tcf(c_367,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101,c_354]) ).
tcf(c_368,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_355]) ).
tcf(c_369,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99,c_356]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97,c_357]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91,c_358]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85,c_359]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_631,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_372,c_354]) ).
tcf(c_686,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_374,c_353]) ).
tcf(c_699,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_375,c_353]) ).
tcf(c_717,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_376,c_373]) ).
tcf(c_718,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_376,c_355]) ).
tcf(c_753,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_377,c_353]) ).
tcf(c_775,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_378,c_354]) ).
tcf(c_915,plain,
multiply(iPr_def_14,sk_c7) = identity,
inference(superposition,[status(thm)],[c_350,c_78]) ).
tcf(c_916,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_356,c_78]) ).
tcf(c_917,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_351,c_78]) ).
tcf(c_918,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_358,c_78]) ).
tcf(c_919,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_352,c_78]) ).
tcf(c_962,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_14) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_382,c_357]) ).
tcf(c_1049,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_383,c_357]) ).
tcf(c_1118,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_384,c_354]) ).
tcf(c_1218,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_386,c_357]) ).
tcf(c_1225,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_386,c_368]) ).
tcf(c_1289,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_387,c_369]) ).
tcf(c_1378,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_388,c_357]) ).
tcf(c_1383,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_388,c_370]) ).
tcf(c_1455,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_382,c_360]) ).
tcf(c_1457,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_376,c_360]) ).
tcf(c_1596,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_355,c_362]) ).
tcf(c_1597,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_357,c_362]) ).
tcf(c_1617,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_21 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1597,c_352]) ).
tcf(c_1621,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1596,c_356]) ).
tcf(c_1833,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_359,c_79]) ).
tcf(c_1836,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_353,c_79]) ).
tcf(c_1839,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_78,c_79]) ).
tcf(c_1841,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_915,c_79]) ).
tcf(c_1842,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_916,c_79]) ).
tcf(c_1843,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_917,c_79]) ).
tcf(c_1844,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_918,c_79]) ).
tcf(c_1847,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1844,c_77]) ).
tcf(c_1848,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1843,c_77]) ).
tcf(c_1849,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1842,c_77]) ).
tcf(c_1850,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1841,c_77]) ).
tcf(c_1927,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_919,c_79]) ).
tcf(c_1928,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1927,c_77]) ).
tcf(c_1943,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_717,c_353]) ).
tcf(c_2462,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_359,c_363]) ).
tcf(c_2463,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_353,c_363]) ).
tcf(c_2486,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 )
| ( sk_c7 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_2463,c_351]) ).
tcf(c_2490,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_2462,c_358]) ).
tcf(c_2614,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_78,c_364]) ).
tcf(c_3072,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1289,c_350]) ).
tcf(c_3167,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1383,c_360]) ).
tcf(c_3407,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_359,c_1847]) ).
tcf(c_3423,plain,
multiply(iPr_def_15,iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_353,c_1848]) ).
tcf(c_3426,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_17,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3423,c_79]) ).
tcf(c_3428,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_355,c_1849]) ).
tcf(c_3431,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3428,c_79]) ).
tcf(c_3433,plain,
multiply(iPr_def_14,iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_354,c_1850]) ).
tcf(c_3442,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_14,multiply(iPr_def_22,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_381,c_1850]) ).
tcf(c_3443,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_14,multiply(iPr_def_22,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_380,c_1850]) ).
tcf(c_3550,plain,
( iPr_def_13
| ( iPr_def_16 = iPr_def_23 )
| iPr_def_10
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_3167,c_1225,c_1289,c_1621,c_3167]) ).
tcf(c_3551,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_3550]) ).
tcf(c_3673,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c6,
inference(superposition,[status(thm)],[c_357,c_1928]) ).
tcf(c_3676,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3673,c_79]) ).
tcf(c_4342,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_686,c_1848]) ).
tcf(c_4343,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4342,c_3423]) ).
tcf(c_4372,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_699,c_1848]) ).
tcf(c_4373,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4372,c_3423]) ).
tcf(c_4422,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_15,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_753,c_1848]) ).
tcf(c_4423,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4422,c_3423]) ).
tcf(c_4977,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_962,c_1928]) ).
tcf(c_4978,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4977,c_3673]) ).
tcf(c_5206,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1049,c_1928]) ).
tcf(c_5207,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5206,c_3673]) ).
tcf(c_5455,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1218,c_1928]) ).
tcf(c_5456,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5455,c_3673]) ).
tcf(c_5523,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1378,c_1928]) ).
tcf(c_5524,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5523,c_3673]) ).
tcf(c_5738,plain,
multiply(sk_c1,iPr_def_18) = multiply(iPr_def_23,sk_c5),
inference(superposition,[status(thm)],[c_354,c_1833]) ).
tcf(c_6941,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1839,c_77]) ).
tcf(c_6963,plain,
multiply(inverse(sk_c7),iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_354,c_6941]) ).
tcf(c_6966,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_77,c_6941]) ).
tcf(c_6967,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_78,c_6941]) ).
tcf(c_6980,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(inverse(sk_c7),iPr_def_18) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_631,c_6941]) ).
tcf(c_7046,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_1850,c_6941]) ).
tcf(c_7047,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1849,c_6941]) ).
tcf(c_7048,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1848,c_6941]) ).
tcf(c_7049,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1847,c_6941]) ).
tcf(c_7050,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1928,c_6941]) ).
tcf(c_7088,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6941,c_6941]) ).
tcf(c_7398,plain,
( ~ iPr_def_13
| ( inverse(inverse(identity)) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_6966,c_361]) ).
tcf(c_7474,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_6967,c_7088]) ).
tcf(c_7484,plain,
multiply(sk_c1,sk_c7) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_7474,c_1833]) ).
tcf(c_7486,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_7474,c_3431]) ).
tcf(c_7491,plain,
multiply(sk_c7,identity) = multiply(iPr_def_15,iPr_def_17),
inference(superposition,[status(thm)],[c_7474,c_3426]) ).
tcf(c_7492,plain,
multiply(sk_c6,identity) = multiply(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_7474,c_3676]) ).
tcf(c_7497,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_7474,c_6966]) ).
tcf(c_7498,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_7492,c_3673]) ).
tcf(c_7505,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_7484,c_359]) ).
tcf(c_7512,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_7497,c_78]) ).
tcf(c_7532,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_1617,c_1621,c_1617,c_4343,c_4373]) ).
tcf(c_7555,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_16 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_375,c_7532]) ).
tcf(c_7556,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12
| ( iPr_def_16 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_374,c_7532]) ).
tcf(c_7627,plain,
( ( iPr_def_16 != iPr_def_21 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_7555,c_1621,c_7556,c_7555]) ).
tcf(c_7628,plain,
( ~ iPr_def_12
| ( iPr_def_16 != iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_7627]) ).
tcf(c_7715,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_2486,c_2490,c_2486,c_4423,c_5207]) ).
tcf(c_7736,plain,
( ( sk_c6 = iPr_def_14 )
| ~ iPr_def_11
| ( iPr_def_17 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_388,c_7715]) ).
tcf(c_7842,plain,
( ( sk_c6 = iPr_def_14 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_7736,c_2490,c_4978,c_5524]) ).
tcf(c_7960,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_14)) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7046,c_363]) ).
tcf(c_7961,plain,
multiply(sk_c7,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_7046,c_78]) ).
tcf(c_7966,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_7046,c_6941]) ).
tcf(c_7967,plain,
multiply(sk_c7,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_7046,c_7474]) ).
tcf(c_8019,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_21,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_375,c_7961]) ).
tcf(c_8020,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_374,c_7961]) ).
tcf(c_8021,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_371,c_7961]) ).
tcf(c_8024,plain,
multiply(sk_c4,identity) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_7961,c_1836]) ).
tcf(c_8025,plain,
multiply(sk_c1,identity) = multiply(iPr_def_23,iPr_def_14),
inference(superposition,[status(thm)],[c_7961,c_1833]) ).
tcf(c_8081,plain,
inverse(iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_7967,c_7474]) ).
tcf(c_8120,plain,
multiply(sk_c7,sk_c5) = iPr_def_18,
inference(superposition,[status(thm)],[c_3433,c_7966]) ).
tcf(c_8125,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7966,c_361]) ).
tcf(c_8185,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 ) ),
inference(ground_joinability,[status(thm)],[c_8125,c_8081]) ).
tcf(c_8418,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(inverse(iPr_def_21),identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8019,c_6941]) ).
tcf(c_8430,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(iPr_def_21),identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8020,c_6941]) ).
tcf(c_8442,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(iPr_def_21),identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8021,c_6941]) ).
tcf(c_8748,plain,
( ( iPr_def_16 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1383,c_8185]) ).
tcf(c_8754,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_382,c_8185]) ).
tcf(c_8902,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_8024,c_7474]) ).
tcf(c_8903,plain,
multiply(inverse(iPr_def_17),sk_c4) = iPr_def_14,
inference(superposition,[status(thm)],[c_8902,c_6941]) ).
tcf(c_8908,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),multiply(sk_c4,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_8903,c_79]) ).
tcf(c_9614,plain,
multiply(iPr_def_23,iPr_def_14) = sk_c1,
inference(demodulation,[status(thm)],[c_8025,c_7474]) ).
tcf(c_9618,plain,
multiply(inverse(iPr_def_23),sk_c1) = iPr_def_14,
inference(superposition,[status(thm)],[c_9614,c_6941]) ).
tcf(c_9632,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),multiply(sk_c1,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_9618,c_79]) ).
tcf(c_10086,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_353,c_8908]) ).
tcf(c_10087,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_14,iPr_def_21) ) ),
inference(superposition,[status(thm)],[c_1943,c_8908]) ).
tcf(c_10107,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = identity,
inference(light_normalisation,[status(thm)],[c_10086,c_915]) ).
tcf(c_10234,plain,
multiply(inverse(iPr_def_23),iPr_def_23) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_359,c_9632]) ).
tcf(c_10250,plain,
multiply(inverse(iPr_def_23),multiply(iPr_def_23,sk_c5)) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_5738,c_9632]) ).
tcf(c_10251,plain,
multiply(inverse(iPr_def_23),sk_c1) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_7474,c_9632]) ).
tcf(c_10255,plain,
multiply(inverse(iPr_def_23),iPr_def_23) = identity,
inference(light_normalisation,[status(thm)],[c_10234,c_915]) ).
tcf(c_10256,plain,
multiply(inverse(iPr_def_23),multiply(iPr_def_23,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_10250,c_3433]) ).
tcf(c_10346,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c7,multiply(sk_c3,sk_c7)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7047,c_361]) ).
tcf(c_10347,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7047,c_363]) ).
tcf(c_10348,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7047,c_78]) ).
tcf(c_10353,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7047,c_6941]) ).
tcf(c_10354,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_7047,c_7474]) ).
tcf(c_10451,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_10354,c_7474]) ).
tcf(c_10453,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( sk_c3 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_3072,c_10451]) ).
tcf(c_10464,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_3428,c_10353]) ).
tcf(c_10700,plain,
( ( iPr_def_16 = iPr_def_23 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_10453,c_355]) ).
tcf(c_10910,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_7048,c_78]) ).
tcf(c_10913,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_15)) != sk_c6 )
| ( multiply(sk_c4,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7048,c_364]) ).
tcf(c_10915,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_7048,c_6941]) ).
tcf(c_10916,plain,
multiply(sk_c4,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_7048,c_7474]) ).
tcf(c_11166,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3407,c_3442]) ).
tcf(c_11179,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_11166,c_915]) ).
tcf(c_11366,plain,
( ( iPr_def_16 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10700,c_362]) ).
tcf(c_11378,plain,
( ( iPr_def_16 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_19 ) ),
inference(ground_joinability,[status(thm)],[c_11366,c_8081]) ).
tcf(c_11401,plain,
inverse(iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_10916,c_7474]) ).
tcf(c_11414,plain,
multiply(sk_c4,sk_c7) = iPr_def_17,
inference(superposition,[status(thm)],[c_3423,c_10915]) ).
tcf(c_11563,plain,
( ( identity = iPr_def_23 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_11179,c_350]) ).
tcf(c_11565,plain,
( ( identity = iPr_def_23 )
| ( sk_c3 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_11563,c_10451]) ).
tcf(c_11857,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3407,c_3443]) ).
tcf(c_11870,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_11857,c_915]) ).
tcf(c_12774,plain,
( ( identity = iPr_def_23 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_11565,c_355]) ).
tcf(c_13517,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_12774,c_362]) ).
tcf(c_13528,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_19 ) ),
inference(ground_joinability,[status(thm)],[c_13517,c_8081]) ).
tcf(c_14464,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_7049,c_7474]) ).
tcf(c_15156,plain,
inverse(iPr_def_22) = sk_c1,
inference(demodulation,[status(thm)],[c_14464,c_7474]) ).
tcf(c_17919,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_7050,c_78]) ).
tcf(c_17922,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7050,c_364]) ).
tcf(c_17924,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_7050,c_6941]) ).
tcf(c_17925,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_7050,c_7474]) ).
tcf(c_17930,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_17922,c_357]) ).
tcf(c_19057,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_17925,c_7474]) ).
tcf(c_19062,plain,
multiply(sk_c2,sk_c6) = iPr_def_21,
inference(superposition,[status(thm)],[c_3673,c_17924]) ).
tcf(c_20165,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_19062,c_19057,c_17930,c_17919,c_15156,c_13528,c_11870,c_11414,c_11401,c_11378,c_10913,c_10910,c_10464,c_10451,c_10347,c_10346,c_10348,c_10256,c_10255,c_10251,c_10250,c_10234,c_10107,c_10087,c_9618,c_9614,c_8748,c_8754,c_8442,c_8430,c_8418,c_8185,c_8120,c_8081,c_7960,c_7967,c_7842,c_7628,c_7505,c_7498,c_7491,c_7486,c_7497,c_7398,c_6980,c_6963,c_5456,c_3551,c_2614,c_2490,c_1621,c_1457,c_1455,c_1118,c_7512,c_775,c_718,c_372,c_370,c_369,c_368,c_367,c_366,c_365,c_360,c_356,c_352,c_351,c_350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP216-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 14:10:03 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 7.32/1.73 % SZS status Started for theBenchmark.p
% 7.32/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 7.32/1.73
% 7.32/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.32/1.73
% 7.32/1.73 % ------ iProver source info
% 7.32/1.73
% 7.32/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 7.32/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.32/1.73 % git: non_committed_changes: false
% 7.32/1.73
% 7.32/1.73 % ------ Parsing...% successful
% 7.32/1.73
% 7.32/1.73
% 7.32/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.32/1.73
% 7.32/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.32/1.73
% 7.32/1.73 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.32/1.73
% 7.32/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.32/1.73 % ------ Proving...
% 7.32/1.73 % ------ Problem Properties
% 7.32/1.73
% 7.32/1.73 %
% 7.32/1.73 % clauses 42
% 7.32/1.73 % conjectures 29
% 7.32/1.73 % EPR 25
% 7.32/1.73 % Horn 17
% 7.32/1.73 % unary 13
% 7.32/1.73 % binary 24
% 7.32/1.73 % lits 78
% 7.32/1.73 % lits eq 70
% 7.32/1.73 % fd_pure 0
% 7.32/1.73 % fd_pseudo 0
% 7.32/1.73 % fd_cond 0
% 7.32/1.73 % fd_pseudo_cond 0
% 7.32/1.73 % AC symbols 0
% 7.32/1.73
% 7.32/1.73 % ------ Schedule dynamic 5 is on
% 7.32/1.73
% 7.32/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.32/1.73
% 7.32/1.73
% 7.32/1.73 % ------
% 7.32/1.73 % Current options:
% 7.32/1.73 % ------
% 7.32/1.73
% 7.32/1.73
% 7.32/1.73 %
% 7.32/1.73
% 7.32/1.73 % ------ Proving...
% 7.32/1.73 %
% 7.32/1.73
% 7.32/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 7.32/1.73
% 7.32/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.32/1.74
% 7.32/1.74
%------------------------------------------------------------------------------