%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP219-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 4.37s 2.27s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 276 ( 84 unt; 12 def)
% Number of atoms : 930 ( 516 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 448 ( 160 ~; 288 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = inverse(sk_c6)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c7)
| inverse(sk_c1) = sk_c9 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c7)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c7)
| sk_c8 = multiply(sk_c9,sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f57,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c7)
| sk_c5 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c7)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != sk_c9
| multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5)
| sk_c9 != inverse(X4)
| multiply(X4,sk_c9) != X3
| sk_c8 != multiply(sk_c9,X3)
| sk_c8 != multiply(X2,sk_c9)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(reorient_equations,[],[f69]) ).
fof(f71,plain,
! [X3,X0,X1,X6,X4,X5] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5)
| sk_c9 != inverse(X4)
| multiply(X4,sk_c9) != X3
| sk_c8 != multiply(sk_c9,X3)
| sk_c8 != multiply(inverse(X1),sk_c9)
| sk_c8 != multiply(X1,inverse(X1))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(equality_resolution,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X6,X4,X5] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c9 != multiply(X5,sk_c8)
| sk_c9 != inverse(X5)
| sk_c9 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sk_c8 != multiply(inverse(X1),sk_c9)
| sk_c8 != multiply(X1,inverse(X1))
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 ),
inference(equality_resolution,[],[f71]) ).
tcf(c_85,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_86,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c6,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c4,sk_c9) = sk_c5 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c9) = sk_c5 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c6,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_120,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X2,sk_c8) != sk_c9 )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 )
| ( multiply(inverse(X4),sk_c9) != sk_c8 )
| ( multiply(X4,inverse(X4)) != sk_c8 )
| ( multiply(sk_c9,multiply(X3,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_429,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_120]) ).
tcf(c_430,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_120]) ).
tcf(c_431,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_120]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_120]) ).
tcf(c_433,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_120]) ).
tcf(c_434,definition,
iPr_def_14 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_435,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_436,definition,
iPr_def_16 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_437,definition,
iPr_def_17 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_438,definition,
iPr_def_18 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_439,definition,
iPr_def_19 = multiply(sk_c4,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_440,definition,
iPr_def_20 = multiply(sk_c9,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_441,definition,
iPr_def_21 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_442,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_443,definition,
iPr_def_23 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_444,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_445,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_446,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_447,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_432]) ).
tcf(c_448,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_431]) ).
tcf(c_449,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c9) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_430]) ).
tcf(c_451,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_429]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_15 = sk_c9 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_119,c_435,c_434]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_118,c_436]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_117,c_437]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_15 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_116,c_438]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_439]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_440]) ).
tcf(c_461,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_464,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107,c_441]) ).
tcf(c_468,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_442]) ).
tcf(c_469,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_472,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99,c_443]) ).
tcf(c_473,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_475,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_477,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_478,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_479,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_480,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91,c_445]) ).
tcf(c_481,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_482,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_483,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_729,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_454]) ).
tcf(c_730,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c9 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_453]) ).
tcf(c_747,plain,
( ( sk_c9 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_452,c_436]) ).
tcf(c_838,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_464,c_460]) ).
tcf(c_915,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c9,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_457,c_440]) ).
tcf(c_916,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c9,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_456,c_440]) ).
tcf(c_945,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_461,c_444]) ).
tcf(c_971,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_445,c_86]) ).
tcf(c_972,plain,
multiply(iPr_def_18,sk_c6) = identity,
inference(superposition,[status(thm)],[c_438,c_86]) ).
tcf(c_973,plain,
multiply(iPr_def_14,sk_c7) = identity,
inference(superposition,[status(thm)],[c_434,c_86]) ).
tcf(c_974,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_442,c_86]) ).
tcf(c_975,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_435,c_86]) ).
tcf(c_1039,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_468,c_443]) ).
tcf(c_1049,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_469,c_443]) ).
tcf(c_1050,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_22,sk_c9) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_469,c_441]) ).
tcf(c_1092,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_472,c_464]) ).
tcf(c_1147,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c7,iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_473,c_436]) ).
tcf(c_1430,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_478,c_439]) ).
tcf(c_1463,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_479,c_439]) ).
tcf(c_1524,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_480,c_436]) ).
tcf(c_1599,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_481,c_477]) ).
tcf(c_1653,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_482,c_478]) ).
tcf(c_1657,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_482,c_439]) ).
tcf(c_1728,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_483,c_479]) ).
tcf(c_1733,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_483,c_439]) ).
tcf(c_1799,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_16 )
| ( inverse(sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_436,c_448]) ).
tcf(c_1801,plain,
( ~ iPr_def_12
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_85,c_448]) ).
tcf(c_1802,plain,
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_86,c_448]) ).
tcf(c_1825,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_14 )
| ( sk_c9 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1799,c_434]) ).
tcf(c_1979,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_17 )
| ( inverse(sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_437,c_451]) ).
tcf(c_1981,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_444,c_451]) ).
tcf(c_2002,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_1981,c_445]) ).
tcf(c_2010,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_18 )
| ( sk_c9 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1979,c_438]) ).
tcf(c_2199,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c9 )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_85,c_447]) ).
tcf(c_2314,plain,
( ~ iPr_def_11
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_85,c_449]) ).
tcf(c_2478,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_729,c_479]) ).
tcf(c_2479,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c9 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_729,c_478]) ).
tcf(c_2592,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_730,c_479]) ).
tcf(c_2594,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_730,c_477]) ).
tcf(c_2674,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_444,c_87]) ).
tcf(c_2675,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c3,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_443,c_87]) ).
tcf(c_2680,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_2683,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_971,c_87]) ).
tcf(c_2684,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_972,c_87]) ).
tcf(c_2685,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_973,c_87]) ).
tcf(c_2686,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_974,c_87]) ).
tcf(c_2687,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_975,c_87]) ).
tcf(c_2693,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2687,c_85]) ).
tcf(c_2694,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2686,c_85]) ).
tcf(c_2695,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2685,c_85]) ).
tcf(c_2696,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2684,c_85]) ).
tcf(c_2697,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2683,c_85]) ).
tcf(c_2810,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_838,c_436]) ).
tcf(c_3323,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1092,c_436]) ).
tcf(c_4447,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1728,c_1653]) ).
tcf(c_4448,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1728,c_1599]) ).
tcf(c_4511,plain,
multiply(iPr_def_15,iPr_def_19) = sk_c9,
inference(superposition,[status(thm)],[c_439,c_2693]) ).
tcf(c_4514,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(iPr_def_19,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4511,c_87]) ).
tcf(c_4521,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_436,c_2695]) ).
tcf(c_4527,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_16,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4521,c_87]) ).
tcf(c_4573,plain,
multiply(iPr_def_18,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_437,c_2696]) ).
tcf(c_4579,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4573,c_87]) ).
tcf(c_4715,plain,
multiply(iPr_def_25,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_444,c_2697]) ).
tcf(c_4718,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(iPr_def_24,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4715,c_87]) ).
tcf(c_5144,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_24,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_477,c_915]) ).
tcf(c_5414,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_24) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_4447,c_4715]) ).
tcf(c_5428,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_24) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_4448,c_4715]) ).
tcf(c_5732,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_481,c_1050]) ).
tcf(c_5735,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_477,c_1050]) ).
tcf(c_6662,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1430,c_2693]) ).
tcf(c_6663,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6662,c_4511]) ).
tcf(c_6704,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1463,c_2693]) ).
tcf(c_6705,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6704,c_4511]) ).
tcf(c_7038,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1657,c_2693]) ).
tcf(c_7039,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7038,c_4511]) ).
tcf(c_7083,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1733,c_2693]) ).
tcf(c_7084,plain,
( ( sk_c9 = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_7083,c_4511]) ).
tcf(c_8357,plain,
multiply(sk_c2,iPr_def_21) = multiply(iPr_def_23,sk_c9),
inference(superposition,[status(thm)],[c_441,c_2675]) ).
tcf(c_10853,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2479,c_2478]) ).
tcf(c_11940,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_2594,c_2592]) ).
tcf(c_11995,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2680,c_85]) ).
tcf(c_12002,plain,
multiply(inverse(sk_c7),iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_436,c_11995]) ).
tcf(c_12003,plain,
multiply(inverse(sk_c1),iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_444,c_11995]) ).
tcf(c_12008,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_85,c_11995]) ).
tcf(c_12009,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_86,c_11995]) ).
tcf(c_12091,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(inverse(sk_c1),iPr_def_24) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_945,c_11995]) ).
tcf(c_12123,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(inverse(sk_c7),iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1147,c_11995]) ).
tcf(c_12162,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2695,c_11995]) ).
tcf(c_12163,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2694,c_11995]) ).
tcf(c_12164,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2693,c_11995]) ).
tcf(c_12185,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11995,c_11995]) ).
tcf(c_12965,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12009,c_12185]) ).
tcf(c_12973,plain,
multiply(sk_c1,sk_c8) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_12965,c_2674]) ).
tcf(c_12976,plain,
multiply(sk_c2,sk_c3) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_12965,c_2675]) ).
tcf(c_12985,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12965,c_12008]) ).
tcf(c_12989,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_12976,c_443]) ).
tcf(c_12992,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_12973,c_444]) ).
tcf(c_12998,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_12985,c_86]) ).
tcf(c_13068,plain,
multiply(sk_c9,identity) = multiply(iPr_def_15,iPr_def_19),
inference(superposition,[status(thm)],[c_12965,c_4514]) ).
tcf(c_13071,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_13068,c_4511]) ).
tcf(c_13125,plain,
multiply(sk_c8,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_12965,c_4527]) ).
tcf(c_13129,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_13125,c_4521]) ).
tcf(c_13157,plain,
multiply(sk_c8,identity) = multiply(iPr_def_18,iPr_def_17),
inference(superposition,[status(thm)],[c_12965,c_4579]) ).
tcf(c_13289,plain,
multiply(sk_c8,identity) = multiply(iPr_def_25,iPr_def_24),
inference(superposition,[status(thm)],[c_12965,c_4718]) ).
tcf(c_14337,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_2002,c_2010,c_2002,c_6663,c_6705]) ).
tcf(c_14339,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_14337,c_2010,c_7039,c_7084,c_14337]) ).
tcf(c_14341,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_446,c_14339]) ).
tcf(c_14615,plain,
( ~ iPr_def_12
| ( multiply(sk_c7,sk_c8) != sk_c9 )
| ( inverse(inverse(iPr_def_14)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12162,c_448]) ).
tcf(c_14618,plain,
multiply(sk_c7,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_12162,c_86]) ).
tcf(c_14620,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_14)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c7,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12162,c_447]) ).
tcf(c_14621,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_12162,c_11995]) ).
tcf(c_14622,plain,
multiply(sk_c7,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_12162,c_12965]) ).
tcf(c_14623,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_16 )
| ( inverse(inverse(iPr_def_14)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_14615,c_436]) ).
tcf(c_14634,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( identity = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_3323,c_14618]) ).
tcf(c_14635,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_2810,c_14618]) ).
tcf(c_14636,plain,
( ( identity = iPr_def_16 )
| ( sk_c9 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1524,c_14618]) ).
tcf(c_14638,plain,
( ( identity = iPr_def_16 )
| ( sk_c9 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_747,c_14618]) ).
tcf(c_14673,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(superposition,[status(thm)],[c_14618,c_2695]) ).
tcf(c_15024,plain,
inverse(iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_14622,c_12965]) ).
tcf(c_15033,plain,
multiply(sk_c7,identity) = sk_c7,
inference(superposition,[status(thm)],[c_973,c_14621]) ).
tcf(c_15034,plain,
multiply(sk_c7,sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_4521,c_14621]) ).
tcf(c_15600,plain,
( ( identity = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_14638,c_439]) ).
tcf(c_16600,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_12163,c_86]) ).
tcf(c_16603,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_12163,c_11995]) ).
tcf(c_16616,plain,
( ( identity = iPr_def_23 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1049,c_16600]) ).
tcf(c_16617,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1039,c_16600]) ).
tcf(c_17253,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_16617,c_436]) ).
tcf(c_17254,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_17253,c_14618]) ).
tcf(c_17294,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_1050,c_16603]) ).
tcf(c_17300,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_5732,c_16603]) ).
tcf(c_17303,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_5735,c_16603]) ).
tcf(c_17308,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c9) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_17303,c_8357]) ).
tcf(c_17317,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c9) = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_17300,c_8357]) ).
tcf(c_17329,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c9) = sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_17294,c_8357]) ).
tcf(c_17808,plain,
multiply(sk_c4,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_12164,c_86]) ).
tcf(c_17809,plain,
( ~ iPr_def_11
| ( multiply(sk_c4,inverse(inverse(iPr_def_15))) != sk_c8 )
| ( multiply(inverse(inverse(iPr_def_15)),sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12164,c_449]) ).
tcf(c_17811,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_12164,c_11995]) ).
tcf(c_17812,plain,
multiply(sk_c4,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_12164,c_12965]) ).
tcf(c_18299,plain,
inverse(iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_17812,c_12965]) ).
tcf(c_18313,plain,
multiply(sk_c4,sk_c9) = iPr_def_19,
inference(superposition,[status(thm)],[c_4511,c_17811]) ).
tcf(c_18574,plain,
( ( identity = iPr_def_19 )
| ( identity = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_15600,c_17808]) ).
tcf(c_18598,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_18574,c_14635]) ).
tcf(c_18599,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_19 )
| ( identity = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_18574,c_14634]) ).
tcf(c_21511,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1801,c_12985]) ).
tcf(c_21543,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_475,c_21511]) ).
tcf(c_21545,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_473,c_21511]) ).
tcf(c_21546,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_472,c_21511]) ).
tcf(c_23762,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(sk_c9,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2199,c_12985]) ).
tcf(c_23816,plain,
( ( identity = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c9 != identity )
| ( multiply(iPr_def_25,iPr_def_25) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14636,c_23762]) ).
tcf(c_24808,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(identity,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2314,c_12985]) ).
tcf(c_24809,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_24808,c_85]) ).
tcf(c_24843,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_473,c_24809]) ).
tcf(c_27177,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_15) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_10853,c_5414]) ).
tcf(c_27351,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_15,iPr_def_15) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_11940,c_5428]) ).
tcf(c_27399,plain,
( ( sk_c9 != iPr_def_23 )
| ( sk_c8 != identity )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_21543,c_1825,c_21546,c_21545]) ).
tcf(c_27400,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c9 != iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_27399]) ).
tcf(c_27431,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_12
| ( identity != iPr_def_23 )
| ( sk_c9 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_473,c_27400]) ).
tcf(c_28708,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_27431,c_27351,c_27177,c_24843,c_24808,c_23816,c_23762,c_18599,c_18598,c_18313,c_18299,c_17809,c_17808,c_17329,c_17317,c_17308,c_17254,c_16616,c_15034,c_15033,c_15024,c_14673,c_14623,c_14620,c_14618,c_14341,c_13289,c_13157,c_13129,c_13125,c_13071,c_13068,c_12992,c_12989,c_12123,c_12091,c_12003,c_12002,c_12998,c_5144,c_1802,c_973,c_916,c_455,c_454,c_453,c_452,c_435,c_434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP219-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.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 14:10:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 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...
% 4.37/2.27 % SZS status Started for theBenchmark.p
% 4.37/2.27 % SZS status Unsatisfiable for theBenchmark.p
% 4.37/2.27
% 4.37/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.37/2.27
% 4.37/2.27 % ------ iProver source info
% 4.37/2.27
% 4.37/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.37/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.37/2.27 % git: non_committed_changes: false
% 4.37/2.27
% 4.37/2.27 % ------ Parsing...% successful
% 4.37/2.27
% 4.37/2.27
% 4.37/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.37/2.27
% 4.37/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.37/2.27
% 4.37/2.27 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.37/2.27
% 4.37/2.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.37/2.27 % ------ Proving...
% 4.37/2.27 % ------ Problem Properties
% 4.37/2.27
% 4.37/2.27 %
% 4.37/2.27 % clauses 52
% 4.37/2.27 % conjectures 37
% 4.37/2.27 % EPR 33
% 4.37/2.27 % Horn 19
% 4.37/2.27 % unary 15
% 4.37/2.27 % binary 32
% 4.37/2.27 % lits 95
% 4.37/2.27 % lits eq 87
% 4.37/2.27 % fd_pure 0
% 4.37/2.27 % fd_pseudo 0
% 4.37/2.27 % fd_cond 0
% 4.37/2.27 % fd_pseudo_cond 0
% 4.37/2.27 % AC symbols 0
% 4.37/2.27
% 4.37/2.27 % ------ Schedule dynamic 5 is on
% 4.37/2.27
% 4.37/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.37/2.27
% 4.37/2.27
% 4.37/2.27 % ------
% 4.37/2.27 % Current options:
% 4.37/2.27 % ------
% 4.37/2.27
% 4.37/2.27
% 4.37/2.27 %
% 4.37/2.27
% 4.37/2.27 % ------ Proving...
% 4.37/2.27 %
% 4.37/2.27
% 4.37/2.27 % SZS status Unsatisfiable for theBenchmark.p
% 4.37/2.27
% 4.37/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.37/2.28
% 4.37/2.28
%------------------------------------------------------------------------------