%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP223-1 : 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 : n010.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 01:31:51 PM UTC 2026
% Result : Unsatisfiable 10.63s 2.74s
% Output : CNFRefutation 10.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 259 ( 100 unt; 11 def)
% Number of atoms : 782 ( 460 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 338 ( 110 ~; 228 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 51 :)
% 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,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c5 = inverse(sk_c4)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c9 = inverse(sk_c6)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c5 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = inverse(sk_c4)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f35,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f47,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c5 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5
| sk_c8 != multiply(sk_c9,X5)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X3) != X4
| sk_c9 != multiply(X3,X4)
| sk_c9 != inverse(X2)
| multiply(X2,sk_c9) != X1
| sk_c8 != multiply(sk_c9,X1)
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X6,X4,X5] :
( sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5
| sk_c8 != multiply(sk_c9,X5)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X3) != X4
| sk_c9 != multiply(X3,X4)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X3,X0,X6,X5] :
( sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5
| sk_c8 != multiply(sk_c9,X5)
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(equality_resolution,[],[f67]) ).
fof(f69,plain,
! [X2,X3,X0,X6] :
( sk_c9 != inverse(X6)
| sk_c8 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(equality_resolution,[],[f68]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c9,sk_c3) = sk_c8 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c7 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 )
| ( multiply(inverse(X1),sk_c8) != sk_c9 )
| ( multiply(X1,inverse(X1)) != sk_c9 )
| ( multiply(sk_c9,multiply(X3,sk_c9)) != sk_c8 )
| ( multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_401,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_402,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_403,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_404,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_405,definition,
iPr_def_13 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_406,definition,
iPr_def_14 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_407,definition,
iPr_def_15 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_408,definition,
iPr_def_16 = multiply(sk_c9,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_409,definition,
iPr_def_17 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_410,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_411,definition,
iPr_def_19 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_412,definition,
iPr_def_20 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_413,definition,
iPr_def_21 = multiply(sk_c9,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_414,definition,
iPr_def_22 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_415,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_416,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_404]) ).
tcf(c_418,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_403]) ).
tcf(c_419,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_402]) ).
tcf(c_420,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_401]) ).
tcf(c_421,negated_conjecture,
( ( iPr_def_14 = sk_c9 )
| ( iPr_def_13 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_115,c_406,c_405]) ).
tcf(c_422,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114,c_407]) ).
tcf(c_423,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_113,c_408]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112,c_409]) ).
tcf(c_425,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111,c_410]) ).
tcf(c_426,negated_conjecture,
( ( iPr_def_19 = sk_c9 )
| ( iPr_def_14 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_110,c_411]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_20 = sk_c3 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_20 = sk_c3 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_20 = sk_c3 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_20 = sk_c3 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_13 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_97,c_414]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_13 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_91,c_415]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_685,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_426,c_424]) ).
tcf(c_723,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_425,c_411]) ).
tcf(c_793,plain,
( ( sk_c5 = iPr_def_18 )
| ( multiply(sk_c9,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_431,c_413]) ).
tcf(c_795,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c9,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_429,c_413]) ).
tcf(c_822,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_415,c_84]) ).
tcf(c_823,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_410,c_84]) ).
tcf(c_824,plain,
multiply(iPr_def_13,sk_c6) = identity,
inference(superposition,[status(thm)],[c_405,c_84]) ).
tcf(c_825,plain,
multiply(iPr_def_14,sk_c2) = identity,
inference(superposition,[status(thm)],[c_406,c_84]) ).
tcf(c_845,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_437,c_411]) ).
tcf(c_886,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c9 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_439,c_421]) ).
tcf(c_1004,plain,
( ( sk_c9 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_443,c_411]) ).
tcf(c_1064,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c9 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_445,c_439]) ).
tcf(c_1066,plain,
( ( sk_c9 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_445,c_412]) ).
tcf(c_1169,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_448,c_442]) ).
tcf(c_1217,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_449,c_411]) ).
tcf(c_1240,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c9 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_450,c_444]) ).
tcf(c_1289,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c9 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_685,c_444]) ).
tcf(c_1290,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_685,c_442]) ).
tcf(c_1369,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_19 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_886,c_426]) ).
tcf(c_1370,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_17 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_886,c_424]) ).
tcf(c_1556,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_17 )
| ( inverse(sk_c5) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_409,c_420]) ).
tcf(c_1557,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_22 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_414,c_420]) ).
tcf(c_1570,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_23 )
| ( sk_c9 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1557,c_415]) ).
tcf(c_1679,plain,
( ~ iPr_def_12
| ( multiply(sk_c9,identity) != sk_c8 )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_84,c_418]) ).
tcf(c_2000,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1169,c_1064]) ).
tcf(c_2142,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_17 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1240,c_1169]) ).
tcf(c_2145,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1240,c_1064]) ).
tcf(c_2355,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_411,c_85]) ).
tcf(c_2357,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_408,c_85]) ).
tcf(c_2358,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c9,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_407,c_85]) ).
tcf(c_2361,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c9,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_412,c_85]) ).
tcf(c_2363,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2367,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_822,c_85]) ).
tcf(c_2368,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_823,c_85]) ).
tcf(c_2369,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_824,c_85]) ).
tcf(c_2370,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_825,c_85]) ).
tcf(c_2375,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2370,c_83]) ).
tcf(c_2376,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2369,c_83]) ).
tcf(c_2377,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2368,c_83]) ).
tcf(c_2378,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2367,c_83]) ).
tcf(c_2448,plain,
multiply(iPr_def_14,iPr_def_20) = sk_c9,
inference(superposition,[status(thm)],[c_412,c_2375]) ).
tcf(c_2451,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_20,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_2448,c_85]) ).
tcf(c_2453,plain,
multiply(iPr_def_13,iPr_def_15) = sk_c9,
inference(superposition,[status(thm)],[c_407,c_2376]) ).
tcf(c_2783,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_411,c_2377]) ).
tcf(c_2796,plain,
multiply(iPr_def_23,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_2378]) ).
tcf(c_2828,plain,
( ( iPr_def_13 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2145,c_2796]) ).
tcf(c_2829,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2142,c_2796]) ).
tcf(c_2830,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_22) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2000,c_2796]) ).
tcf(c_5212,plain,
( ( sk_c9 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1066,c_2375]) ).
tcf(c_5213,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5212,c_2448]) ).
tcf(c_6488,plain,
multiply(sk_c4,iPr_def_17) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_409,c_2355]) ).
tcf(c_6687,plain,
multiply(sk_c6,iPr_def_21) = multiply(iPr_def_15,sk_c3),
inference(superposition,[status(thm)],[c_413,c_2358]) ).
tcf(c_6694,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c6,iPr_def_21) = multiply(iPr_def_15,iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_795,c_2358]) ).
tcf(c_7328,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1290,c_1289]) ).
tcf(c_7897,plain,
multiply(sk_c2,iPr_def_16) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_408,c_2361]) ).
tcf(c_7898,plain,
multiply(sk_c2,iPr_def_21) = multiply(iPr_def_20,sk_c3),
inference(superposition,[status(thm)],[c_413,c_2361]) ).
tcf(c_8683,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_19 )
| ( sk_c9 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1369,c_444]) ).
tcf(c_8946,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_17 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1370,c_442]) ).
tcf(c_9871,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_7328,c_2829]) ).
tcf(c_11137,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2363,c_83]) ).
tcf(c_11142,plain,
multiply(inverse(sk_c4),iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_411,c_11137]) ).
tcf(c_11143,plain,
multiply(inverse(sk_c5),iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_409,c_11137]) ).
tcf(c_11144,plain,
multiply(inverse(sk_c9),iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_408,c_11137]) ).
tcf(c_11146,plain,
multiply(inverse(sk_c1),iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_11137]) ).
tcf(c_11147,plain,
multiply(inverse(sk_c9),iPr_def_21) = sk_c3,
inference(superposition,[status(thm)],[c_413,c_11137]) ).
tcf(c_11149,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_11137]) ).
tcf(c_11150,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11137]) ).
tcf(c_11199,plain,
( ( sk_c5 = iPr_def_18 )
| ( multiply(inverse(sk_c9),iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_793,c_11137]) ).
tcf(c_11210,plain,
multiply(inverse(iPr_def_13),identity) = sk_c6,
inference(superposition,[status(thm)],[c_824,c_11137]) ).
tcf(c_11268,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2378,c_11137]) ).
tcf(c_11269,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2377,c_11137]) ).
tcf(c_11270,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2376,c_11137]) ).
tcf(c_11271,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2375,c_11137]) ).
tcf(c_11311,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11137,c_11137]) ).
tcf(c_12481,plain,
multiply(sk_c6,identity) = sk_c6,
inference(demodulation,[status(thm)],[c_11210,c_11270]) ).
tcf(c_12482,plain,
multiply(inverse(sk_c6),sk_c6) = identity,
inference(superposition,[status(thm)],[c_12481,c_11137]) ).
tcf(c_13900,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11150,c_11311]) ).
tcf(c_13915,plain,
multiply(sk_c9,sk_c7) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_13900,c_2357]) ).
tcf(c_13921,plain,
multiply(sk_c9,identity) = multiply(iPr_def_14,iPr_def_20),
inference(superposition,[status(thm)],[c_13900,c_2451]) ).
tcf(c_13926,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13900,c_11149]) ).
tcf(c_13927,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_13921,c_2448]) ).
tcf(c_13933,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_13915,c_408]) ).
tcf(c_13987,plain,
( ( sk_c9 = iPr_def_13 )
| ~ iPr_def_10
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_439,c_1570]) ).
tcf(c_14263,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_13926,c_84]) ).
tcf(c_14281,plain,
( ( sk_c9 = iPr_def_13 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_13987,c_5213,c_13987]) ).
tcf(c_17825,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_11268,c_11137]) ).
tcf(c_17826,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11268,c_13900]) ).
tcf(c_19445,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_8683,c_886]) ).
tcf(c_19463,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_17826,c_13900]) ).
tcf(c_19491,plain,
multiply(sk_c1,sk_c8) = iPr_def_22,
inference(superposition,[status(thm)],[c_2796,c_17825]) ).
tcf(c_19599,plain,
( ( iPr_def_13 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_19445,c_2828]) ).
tcf(c_20083,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_8946,c_886]) ).
tcf(c_20603,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_20083,c_2830]) ).
tcf(c_20879,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11269,c_84]) ).
tcf(c_20882,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_11269,c_11137]) ).
tcf(c_20883,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11269,c_13900]) ).
tcf(c_20893,plain,
( ( identity = iPr_def_19 )
| ( sk_c9 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1217,c_20879]) ).
tcf(c_20894,plain,
( ( identity = iPr_def_19 )
| ( sk_c9 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1004,c_20879]) ).
tcf(c_20895,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_845,c_20879]) ).
tcf(c_20896,plain,
( ( identity = iPr_def_19 )
| ( sk_c9 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_723,c_20879]) ).
tcf(c_21302,plain,
multiply(inverse(sk_c4),identity) = iPr_def_18,
inference(superposition,[status(thm)],[c_20879,c_11137]) ).
tcf(c_21380,plain,
( ( identity = iPr_def_19 )
| ( multiply(inverse(iPr_def_23),iPr_def_21) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_20893,c_11147]) ).
tcf(c_21442,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_21) = sk_c3 ) ),
inference(light_normalisation,[status(thm)],[c_21380,c_19463]) ).
tcf(c_22120,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_20895,c_414]) ).
tcf(c_22163,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_20883,c_13900]) ).
tcf(c_22187,plain,
multiply(sk_c4,sk_c5) = iPr_def_19,
inference(superposition,[status(thm)],[c_2783,c_20882]) ).
tcf(c_22337,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_20896,c_20894]) ).
tcf(c_23016,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_13)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11270,c_418]) ).
tcf(c_23017,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_13,X0)) = X0,
inference(superposition,[status(thm)],[c_11270,c_11137]) ).
tcf(c_23018,plain,
multiply(sk_c6,identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_11270,c_13900]) ).
tcf(c_23022,plain,
( ~ iPr_def_12
| ( multiply(sk_c9,iPr_def_15) != sk_c8 )
| ( inverse(inverse(iPr_def_13)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_23016,c_407]) ).
tcf(c_23442,plain,
inverse(iPr_def_13) = sk_c6,
inference(demodulation,[status(thm)],[c_23018,c_13900]) ).
tcf(c_23464,plain,
multiply(sk_c6,sk_c9) = iPr_def_15,
inference(superposition,[status(thm)],[c_2453,c_23017]) ).
tcf(c_24606,plain,
( ~ iPr_def_10
| ( multiply(sk_c2,sk_c8) != sk_c9 )
| ( inverse(inverse(iPr_def_14)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_11271,c_420]) ).
tcf(c_24609,plain,
multiply(sk_c2,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_11271,c_84]) ).
tcf(c_24612,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_11271,c_11137]) ).
tcf(c_24613,plain,
multiply(sk_c2,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_11271,c_13900]) ).
tcf(c_25314,plain,
inverse(iPr_def_14) = sk_c2,
inference(demodulation,[status(thm)],[c_24613,c_13900]) ).
tcf(c_25327,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_825,c_24612]) ).
tcf(c_25328,plain,
multiply(sk_c2,sk_c9) = iPr_def_20,
inference(superposition,[status(thm)],[c_2448,c_24612]) ).
tcf(c_39155,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(inverse(iPr_def_14),sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9871,c_11137]) ).
tcf(c_42714,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_11311,c_84]) ).
tcf(c_42717,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_11311,c_11137]) ).
tcf(c_42718,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_11311,c_13900]) ).
tcf(c_42719,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_42718,c_13900]) ).
tcf(c_42744,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_419,c_42714]) ).
tcf(c_42750,plain,
inverse(inverse(sk_c9)) = sk_c9,
inference(instantiation,[status(thm)],[c_42719]) ).
tcf(c_42789,plain,
inverse(sk_c1) = iPr_def_23,
inference(superposition,[status(thm)],[c_19463,c_42719]) ).
tcf(c_42790,plain,
inverse(sk_c2) = iPr_def_14,
inference(superposition,[status(thm)],[c_25314,c_42719]) ).
tcf(c_42791,plain,
inverse(sk_c6) = iPr_def_13,
inference(superposition,[status(thm)],[c_23442,c_42719]) ).
tcf(c_43548,plain,
multiply(iPr_def_16,inverse(sk_c7)) = multiply(sk_c9,identity),
inference(superposition,[status(thm)],[c_42714,c_2357]) ).
tcf(c_43569,plain,
multiply(iPr_def_14,identity) = inverse(sk_c2),
inference(superposition,[status(thm)],[c_42714,c_2375]) ).
tcf(c_45707,plain,
( ~ iPr_def_11
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_84,c_42744]) ).
tcf(c_45761,plain,
( ~ iPr_def_12
| ( multiply(sk_c9,identity) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_1679,c_1679,c_42750]) ).
tcf(c_45763,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_16,inverse(sk_c7)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_45761,c_43548]) ).
tcf(c_45774,plain,
( ( sk_c3 = iPr_def_20 )
| ~ iPr_def_12
| ( multiply(iPr_def_16,inverse(iPr_def_15)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_428,c_45763]) ).
tcf(c_51827,plain,
multiply(sk_c9,sk_c7) = iPr_def_16,
inference(superposition,[status(thm)],[c_11144,c_42717]) ).
tcf(c_51828,plain,
multiply(sk_c9,sk_c3) = iPr_def_21,
inference(superposition,[status(thm)],[c_11147,c_42717]) ).
tcf(c_52493,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_51828,c_51827,c_45774,c_45761,c_45707,c_43569,c_43548,c_42791,c_42790,c_42789,c_39155,c_25328,c_25327,c_25314,c_24606,c_24609,c_23464,c_23442,c_23022,c_23018,c_22337,c_22187,c_22163,c_22120,c_21442,c_21302,c_20883,c_20879,c_20603,c_19599,c_19491,c_19463,c_14281,c_13933,c_13927,c_13926,c_12482,c_11199,c_11147,c_11146,c_11144,c_11143,c_11142,c_7898,c_7897,c_6694,c_6687,c_6488,c_14263,c_1570,c_1556,c_825,c_450,c_444,c_438,c_435,c_434,c_432,c_428,c_426,c_425,c_424,c_423,c_422,c_421,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP223-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:11:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.63/2.74 % SZS status Started for theBenchmark.p
% 10.63/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/2.74
% 10.63/2.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.63/2.74
% 10.63/2.74 % ------ iProver source info
% 10.63/2.74
% 10.63/2.74 % git: date: 2026-07-19 20:42:38 +0200
% 10.63/2.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.63/2.74 % git: non_committed_changes: false
% 10.63/2.74
% 10.63/2.74 % ------ Parsing...% successful
% 10.63/2.74
% 10.63/2.74
% 10.63/2.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.63/2.74
% 10.63/2.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.63/2.74
% 10.63/2.74 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.63/2.74
% 10.63/2.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.63/2.74 % ------ Proving...
% 10.63/2.74 % ------ Problem Properties
% 10.63/2.74
% 10.63/2.74 %
% 10.63/2.74 % clauses 48
% 10.63/2.74 % conjectures 34
% 10.63/2.74 % EPR 31
% 10.63/2.74 % Horn 17
% 10.63/2.74 % unary 14
% 10.63/2.74 % binary 30
% 10.63/2.74 % lits 86
% 10.63/2.74 % lits eq 80
% 10.63/2.74 % fd_pure 0
% 10.63/2.74 % fd_pseudo 0
% 10.63/2.74 % fd_cond 0
% 10.63/2.74 % fd_pseudo_cond 0
% 10.63/2.74 % AC symbols 0
% 10.63/2.74
% 10.63/2.74 % ------ Schedule dynamic 5 is on
% 10.63/2.74
% 10.63/2.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.63/2.74
% 10.63/2.74
% 10.63/2.74 % ------
% 10.63/2.74 % Current options:
% 10.63/2.74 % ------
% 10.63/2.74
% 10.63/2.74
% 10.63/2.74 %
% 10.63/2.74
% 10.63/2.74 % ------ Proving...
% 10.63/2.74 %
% 10.63/2.74
% 10.63/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/2.74
% 10.63/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.63/2.74
% 10.63/2.74
%------------------------------------------------------------------------------