%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP354-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:19 PM UTC 2026
% Result : Unsatisfiable 34.71s 7.35s
% Output : CNFRefutation 34.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 35
% Syntax : Number of formulae : 228 ( 102 unt; 13 def)
% Number of atoms : 654 ( 398 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 352 ( 142 ~; 210 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 0 ?; 60 :)
% 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(f7,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c3)
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c9 = inverse(sk_c4)
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f37,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c7 = inverse(sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f73,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f81]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c9 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f93]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != multiply(X5,sk_c7)
| inverse(X4) != X5
| sk_c8 != multiply(X4,X5)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| sk_c7 != inverse(sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != multiply(inverse(X4),sk_c7)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7)
| sk_c7 != inverse(sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(equality_resolution,[],[f102]) ).
tcf(c_101,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_102,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c9,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c9 )
| ( multiply(sk_c8,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_130,negated_conjecture,
( ( inverse(sk_c9) = sk_c7 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_138,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_141,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_142,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_144,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_145,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_146,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_147,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_148,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_152,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c9) != sk_c7 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X3,sk_c9) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 )
| ( multiply(inverse(X1),sk_c7) != sk_c8 )
| ( multiply(X1,inverse(X1)) != sk_c8 ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_601,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_152]) ).
tcf(c_602,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_152]) ).
tcf(c_603,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_152]) ).
tcf(c_604,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_152]) ).
tcf(c_605,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c9) != sk_c7 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_152]) ).
tcf(c_606,definition,
iPr_def_14 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_607,definition,
iPr_def_15 = multiply(sk_c9,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_608,definition,
iPr_def_16 = inverse(sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_610,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_611,definition,
iPr_def_19 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_612,definition,
iPr_def_20 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_613,definition,
iPr_def_21 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_614,definition,
iPr_def_22 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_615,definition,
iPr_def_23 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_616,definition,
iPr_def_24 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_617,definition,
iPr_def_25 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_618,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_619,definition,
iPr_def_27 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_620,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c7 )
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_605,c_608,c_607,c_606]) ).
tcf(c_621,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_604]) ).
tcf(c_622,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_603]) ).
tcf(c_624,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_602]) ).
tcf(c_625,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_601]) ).
tcf(c_629,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_148,c_613]) ).
tcf(c_630,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_147,c_614]) ).
tcf(c_631,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_146]) ).
tcf(c_632,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_145,c_615]) ).
tcf(c_633,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_144,c_616]) ).
tcf(c_635,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_142]) ).
tcf(c_636,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_141]) ).
tcf(c_639,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_138]) ).
tcf(c_647,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_648,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_656,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_23 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_657,negated_conjecture,
( ( iPr_def_26 = sk_c9 )
| ( iPr_def_24 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_664,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_23 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_665,negated_conjecture,
( ( iPr_def_27 = sk_c8 )
| ( iPr_def_24 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_669,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_670,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_671,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_672,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_1119,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_635,c_612]) ).
tcf(c_1127,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_639,c_613]) ).
tcf(c_1130,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_636,c_613]) ).
tcf(c_1167,plain,
multiply(iPr_def_23,sk_c3) = identity,
inference(superposition,[status(thm)],[c_615,c_102]) ).
tcf(c_1168,plain,
multiply(iPr_def_22,sk_c4) = identity,
inference(superposition,[status(thm)],[c_614,c_102]) ).
tcf(c_1169,plain,
multiply(iPr_def_19,sk_c5) = identity,
inference(superposition,[status(thm)],[c_611,c_102]) ).
tcf(c_1170,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_618,c_102]) ).
tcf(c_1171,plain,
multiply(iPr_def_16,sk_c9) = identity,
inference(superposition,[status(thm)],[c_608,c_102]) ).
tcf(c_1172,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_610,c_102]) ).
tcf(c_1775,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_656,c_619]) ).
tcf(c_1835,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_657,c_613]) ).
tcf(c_2365,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_27) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_664,c_613]) ).
tcf(c_2435,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_27) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_665,c_613]) ).
tcf(c_3471,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_616,c_624]) ).
tcf(c_3472,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_27 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_619,c_624]) ).
tcf(c_3488,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_26 )
| ( sk_c8 != iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_3472,c_618]) ).
tcf(c_3492,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_23 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_3471,c_615]) ).
tcf(c_3554,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_102,c_625]) ).
tcf(c_4084,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c9,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_616,c_103]) ).
tcf(c_4085,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_607,c_103]) ).
tcf(c_4089,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c9,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_619,c_103]) ).
tcf(c_4090,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_617,c_103]) ).
tcf(c_4092,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_102,c_103]) ).
tcf(c_4095,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1167,c_103]) ).
tcf(c_4096,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1168,c_103]) ).
tcf(c_4097,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1169,c_103]) ).
tcf(c_4098,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1170,c_103]) ).
tcf(c_4099,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c9,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1171,c_103]) ).
tcf(c_4100,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1172,c_103]) ).
tcf(c_4106,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4100,c_101]) ).
tcf(c_4107,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c9,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4099,c_101]) ).
tcf(c_4108,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4098,c_101]) ).
tcf(c_4109,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4097,c_101]) ).
tcf(c_4110,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4096,c_101]) ).
tcf(c_4111,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4095,c_101]) ).
tcf(c_7964,plain,
multiply(iPr_def_18,iPr_def_25) = sk_c7,
inference(superposition,[status(thm)],[c_617,c_4106]) ).
tcf(c_7967,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_25,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_7964,c_103]) ).
tcf(c_8002,plain,
multiply(iPr_def_16,iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_607,c_4107]) ).
tcf(c_8187,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_15,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_8002,c_103]) ).
tcf(c_8189,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c9,
inference(superposition,[status(thm)],[c_619,c_4108]) ).
tcf(c_8975,plain,
multiply(iPr_def_22,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_613,c_4110]) ).
tcf(c_8980,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c9,
inference(superposition,[status(thm)],[c_616,c_4111]) ).
tcf(c_11288,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1127,c_4110]) ).
tcf(c_11289,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_11288,c_8975]) ).
tcf(c_11611,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1130,c_4110]) ).
tcf(c_11612,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_11611,c_8975]) ).
tcf(c_15877,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1775,c_4108]) ).
tcf(c_15878,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c9 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_15877,c_8189]) ).
tcf(c_16034,plain,
( ( sk_c9 = iPr_def_26 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1835,c_4110]) ).
tcf(c_16035,plain,
( ( sk_c9 = iPr_def_26 )
| ( sk_c8 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_16034,c_8975]) ).
tcf(c_16936,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2365,c_4110]) ).
tcf(c_16937,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c8 = iPr_def_27 ) ),
inference(light_normalisation,[status(thm)],[c_16936,c_8975]) ).
tcf(c_17206,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2435,c_4110]) ).
tcf(c_17207,plain,
( ( sk_c8 = iPr_def_27 )
| ( sk_c8 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_17206,c_8975]) ).
tcf(c_18591,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_24,sk_c7),
inference(superposition,[status(thm)],[c_607,c_4084]) ).
tcf(c_24789,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_4092,c_101]) ).
tcf(c_24823,plain,
multiply(inverse(sk_c8),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_606,c_24789]) ).
tcf(c_24832,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_102,c_24789]) ).
tcf(c_25063,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_4111,c_24789]) ).
tcf(c_25064,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_4110,c_24789]) ).
tcf(c_25065,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4109,c_24789]) ).
tcf(c_25066,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_4108,c_24789]) ).
tcf(c_25067,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4107,c_24789]) ).
tcf(c_25068,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_4106,c_24789]) ).
tcf(c_25143,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_24789,c_24789]) ).
tcf(c_26612,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_24832,c_25143]) ).
tcf(c_26625,plain,
multiply(sk_c7,identity) = multiply(iPr_def_16,iPr_def_15),
inference(superposition,[status(thm)],[c_26612,c_8187]) ).
tcf(c_26628,plain,
multiply(sk_c7,identity) = multiply(iPr_def_18,iPr_def_25),
inference(superposition,[status(thm)],[c_26612,c_7967]) ).
tcf(c_26654,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_26628,c_7964]) ).
tcf(c_26986,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_26 ) ),
inference(global_subsumption_just,[status(thm)],[c_3488,c_3492,c_3488,c_16937,c_17207]) ).
tcf(c_26988,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_26986,c_3492,c_15878,c_16035,c_26986]) ).
tcf(c_26990,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c9 != iPr_def_14 )
| ( sk_c7 != iPr_def_16 )
| ( sk_c8 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_620,c_26988]) ).
tcf(c_27284,plain,
multiply(sk_c3,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_25063,c_102]) ).
tcf(c_27285,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_23)) != sk_c9 )
| ( multiply(sk_c3,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_25063,c_622]) ).
tcf(c_27288,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_25063,c_24789]) ).
tcf(c_27289,plain,
multiply(sk_c3,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_25063,c_26612]) ).
tcf(c_27391,plain,
inverse(iPr_def_23) = sk_c3,
inference(demodulation,[status(thm)],[c_27289,c_26612]) ).
tcf(c_27419,plain,
multiply(sk_c3,sk_c9) = iPr_def_24,
inference(superposition,[status(thm)],[c_8980,c_27288]) ).
tcf(c_29016,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_25064,c_24789]) ).
tcf(c_29017,plain,
multiply(sk_c4,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_25064,c_26612]) ).
tcf(c_29312,plain,
multiply(sk_c4,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_8975,c_29016]) ).
tcf(c_31870,plain,
multiply(sk_c5,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_25065,c_102]) ).
tcf(c_31890,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1119,c_31870]) ).
tcf(c_35051,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_26)) != sk_c9 )
| ( multiply(sk_c1,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_25066,c_622]) ).
tcf(c_35055,plain,
multiply(sk_c1,identity) = inverse(iPr_def_26),
inference(superposition,[status(thm)],[c_25066,c_26612]) ).
tcf(c_35210,plain,
inverse(iPr_def_26) = sk_c1,
inference(demodulation,[status(thm)],[c_35055,c_26612]) ).
tcf(c_42747,plain,
multiply(sk_c9,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_25067,c_102]) ).
tcf(c_42751,plain,
! [X0: $i] : multiply(sk_c9,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_25067,c_24789]) ).
tcf(c_42752,plain,
multiply(sk_c9,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_25067,c_26612]) ).
tcf(c_42955,plain,
multiply(sk_c1,identity) = multiply(iPr_def_27,iPr_def_16),
inference(superposition,[status(thm)],[c_42747,c_4089]) ).
tcf(c_42956,plain,
multiply(sk_c3,identity) = multiply(iPr_def_24,iPr_def_16),
inference(superposition,[status(thm)],[c_42747,c_4084]) ).
tcf(c_44679,plain,
inverse(iPr_def_16) = sk_c9,
inference(demodulation,[status(thm)],[c_42752,c_26612]) ).
tcf(c_44700,plain,
( ~ iPr_def_13
| ( multiply(iPr_def_16,sk_c9) != sk_c8 )
| ( multiply(inverse(iPr_def_16),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_44679,c_621]) ).
tcf(c_44702,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_15 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_44700,c_607,c_1171,c_44679]) ).
tcf(c_44775,plain,
multiply(sk_c9,sk_c7) = iPr_def_15,
inference(superposition,[status(thm)],[c_8002,c_42751]) ).
tcf(c_50107,plain,
multiply(iPr_def_27,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_42955,c_26612]) ).
tcf(c_50351,plain,
multiply(iPr_def_24,iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_42956,c_26612]) ).
tcf(c_72293,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_25068,c_102]) ).
tcf(c_72294,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c9 )
| ( multiply(sk_c2,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_25068,c_622]) ).
tcf(c_72297,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_25068,c_24789]) ).
tcf(c_72298,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_25068,c_26612]) ).
tcf(c_73114,plain,
inverse(iPr_def_18) = sk_c2,
inference(demodulation,[status(thm)],[c_72298,c_26612]) ).
tcf(c_73118,plain,
( ~ iPr_def_13
| ( multiply(iPr_def_18,sk_c2) != sk_c8 )
| ( multiply(inverse(iPr_def_18),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_73114,c_621]) ).
tcf(c_73123,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_73118,c_617,c_1172,c_73114]) ).
tcf(c_73127,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1172,c_72297]) ).
tcf(c_73128,plain,
multiply(sk_c2,sk_c7) = iPr_def_25,
inference(superposition,[status(thm)],[c_7964,c_72297]) ).
tcf(c_109256,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_23 )
| ( multiply(sk_c3,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_27285,c_615,c_27391]) ).
tcf(c_112742,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_26 )
| ( multiply(sk_c1,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_35051,c_618,c_35210]) ).
tcf(c_139448,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_18 )
| ( multiply(sk_c2,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_72294,c_610,c_73114]) ).
tcf(c_148289,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_25143,c_102]) ).
tcf(c_148293,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_25143,c_24789]) ).
tcf(c_148294,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_25143,c_26612]) ).
tcf(c_148295,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_148294,c_26612]) ).
tcf(c_148428,plain,
! [X0: $i] :
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_621,c_148289]) ).
tcf(c_148432,plain,
( ~ iPr_def_10
| ( sk_c8 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3554,c_148295]) ).
tcf(c_150024,plain,
multiply(iPr_def_25,inverse(sk_c7)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_148289,c_4090]) ).
tcf(c_150026,plain,
multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c9,identity),
inference(superposition,[status(thm)],[c_148289,c_4085]) ).
tcf(c_150030,plain,
multiply(iPr_def_16,identity) = inverse(sk_c9),
inference(superposition,[status(thm)],[c_148289,c_4107]) ).
tcf(c_151561,plain,
inverse(sk_c9) = iPr_def_16,
inference(superposition,[status(thm)],[c_44679,c_148295]) ).
tcf(c_155999,plain,
( ~ iPr_def_13
| ( sk_c8 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_148428,c_11289,c_44702,c_73123]) ).
tcf(c_157985,plain,
multiply(sk_c8,sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_24823,c_148293]) ).
tcf(c_158562,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_157985,c_155999,c_151561,c_150030,c_150026,c_150024,c_148432,c_139448,c_112742,c_109256,c_73128,c_73127,c_73114,c_72293,c_50351,c_50107,c_44775,c_44679,c_42956,c_42955,c_42752,c_42747,c_35210,c_31890,c_29312,c_29017,c_27419,c_27391,c_27284,c_26990,c_26988,c_26654,c_26625,c_18591,c_11612,c_1171,c_672,c_671,c_670,c_669,c_664,c_656,c_648,c_647,c_633,c_632,c_631,c_630,c_629,c_620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP354-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.37 % Computer : n015.cluster.edu
% 0.07/0.37 % Model : x86_64 x86_64
% 0.07/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.37 % Memory : 8046.5625MB
% 0.07/0.37 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Wed Sep 23 14:36:39 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.41 Running first-order theorem proving
% 0.07/0.41 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
% 0.07/0.42
% 0.07/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.42
% 0.07/0.42 % Detected problem language: tptp
% 0.07/0.43 % Proving...
% 34.71/7.35 % SZS status Started for theBenchmark.p
% 34.71/7.35 % SZS status Unsatisfiable for theBenchmark.p
% 34.71/7.35
% 34.71/7.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.71/7.35
% 34.71/7.35 % ------ iProver source info
% 34.71/7.35
% 34.71/7.35 % git: date: 2026-07-19 20:42:38 +0200
% 34.71/7.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.71/7.35 % git: non_committed_changes: false
% 34.71/7.35
% 34.71/7.35 % ------ Parsing...% successful
% 34.71/7.35
% 34.71/7.35
% 34.71/7.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.71/7.35
% 34.71/7.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.71/7.35
% 34.71/7.35 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.71/7.35
% 34.71/7.35 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 34.71/7.35 % ------ Proving...
% 34.71/7.35 % ------ Problem Properties
% 34.71/7.35
% 34.71/7.35 %
% 34.71/7.35 % clauses 70
% 34.71/7.35 % conjectures 53
% 34.71/7.35 % EPR 49
% 34.71/7.35 % Horn 21
% 34.71/7.35 % unary 17
% 34.71/7.35 % binary 48
% 34.71/7.35 % lits 132
% 34.71/7.35 % lits eq 124
% 34.71/7.35 % fd_pure 0
% 34.71/7.35 % fd_pseudo 0
% 34.71/7.35 % fd_cond 0
% 34.71/7.35 % fd_pseudo_cond 0
% 34.71/7.35 % AC symbols 0
% 34.71/7.35
% 34.71/7.35 % ------ Schedule dynamic 5 is on
% 34.71/7.35
% 34.71/7.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.71/7.35
% 34.71/7.35
% 34.71/7.35 % ------
% 34.71/7.35 % Current options:
% 34.71/7.35 % ------
% 34.71/7.35
% 34.71/7.35
% 34.71/7.35 %
% 34.71/7.35
% 34.71/7.35 % ------ Proving...
% 34.71/7.35 %
% 34.71/7.35
% 34.71/7.35 % SZS status Unsatisfiable for theBenchmark.p
% 34.71/7.35
% 34.71/7.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.71/7.35
% 34.71/7.35
%------------------------------------------------------------------------------