%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP320-1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:50 PM UTC 2026
% Result : Unsatisfiable 4.48s 2.10s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 246 ( 97 unt; 11 def)
% Number of atoms : 706 ( 429 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 334 ( 118 ~; 216 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f55,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c6,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c7)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c7)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
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,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c6,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c8,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_417]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_418]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_419]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_420]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_423]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_424]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_789,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_18,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_442,c_415]) ).
tcf(c_841,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_445,c_414]) ).
tcf(c_876,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_437,c_422]) ).
tcf(c_928,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_929,plain,
multiply(iPr_def_17,sk_c5) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_930,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_931,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_948,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_446,c_414]) ).
tcf(c_1033,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_449,c_414]) ).
tcf(c_1420,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_458,c_415]) ).
tcf(c_2052,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_418,c_428]) ).
tcf(c_2053,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_428]) ).
tcf(c_2069,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2053,c_423]) ).
tcf(c_2073,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_18 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2052,c_417]) ).
tcf(c_2192,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_420,c_429]) ).
tcf(c_2217,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2192,c_419]) ).
tcf(c_2352,plain,
( ~ iPr_def_13
| ( inverse(sk_c6) != sk_c8 )
| ( multiply(sk_c8,iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_426]) ).
tcf(c_2712,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2714,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2715,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2716,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2718,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2720,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2723,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_928,c_85]) ).
tcf(c_2724,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_929,c_85]) ).
tcf(c_2725,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_930,c_85]) ).
tcf(c_2726,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_931,c_85]) ).
tcf(c_2732,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2726,c_83]) ).
tcf(c_2733,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2725,c_83]) ).
tcf(c_2734,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2724,c_83]) ).
tcf(c_2735,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2723,c_83]) ).
tcf(c_2815,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2732]) ).
tcf(c_2818,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2815,c_85]) ).
tcf(c_2829,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_2733]) ).
tcf(c_2832,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2829,c_85]) ).
tcf(c_3423,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_2734]) ).
tcf(c_3443,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_420,c_2735]) ).
tcf(c_3446,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3443,c_85]) ).
tcf(c_3976,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_450,c_841]) ).
tcf(c_3986,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3976,c_2829]) ).
tcf(c_4102,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_3986,c_418]) ).
tcf(c_5977,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_451,c_948]) ).
tcf(c_5988,plain,
( ( sk_c7 = iPr_def_17 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5977,c_2829]) ).
tcf(c_6056,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_5988,c_418]) ).
tcf(c_6057,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_17,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5988,c_414]) ).
tcf(c_6586,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_454,c_1033]) ).
tcf(c_6599,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6586,c_2829]) ).
tcf(c_6690,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_6599,c_418]) ).
tcf(c_8746,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_13
| ( inverse(iPr_def_14) != sk_c8 )
| ( multiply(sk_c8,iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1420,c_426]) ).
tcf(c_9904,plain,
multiply(sk_c7,iPr_def_22) = multiply(iPr_def_14,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2712]) ).
tcf(c_9907,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_22) = multiply(iPr_def_14,iPr_def_21) ) ),
inference(superposition,[status(thm)],[c_876,c_2712]) ).
tcf(c_10492,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2714]) ).
tcf(c_10503,plain,
multiply(sk_c5,multiply(iPr_def_14,sk_c3)) = multiply(iPr_def_18,iPr_def_22),
inference(superposition,[status(thm)],[c_9904,c_2714]) ).
tcf(c_10596,plain,
multiply(iPr_def_17,multiply(iPr_def_18,sk_c8)) = iPr_def_14,
inference(superposition,[status(thm)],[c_10492,c_2734]) ).
tcf(c_10607,plain,
multiply(sk_c6,iPr_def_22) = multiply(iPr_def_15,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2715]) ).
tcf(c_10786,plain,
multiply(sk_c1,multiply(iPr_def_14,sk_c3)) = multiply(iPr_def_24,iPr_def_22),
inference(superposition,[status(thm)],[c_9904,c_2716]) ).
tcf(c_11012,plain,
multiply(sk_c2,iPr_def_22) = multiply(iPr_def_21,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2718]) ).
tcf(c_11086,plain,
multiply(iPr_def_16,multiply(iPr_def_21,sk_c3)) = iPr_def_22,
inference(superposition,[status(thm)],[c_11012,c_2732]) ).
tcf(c_14238,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2720,c_83]) ).
tcf(c_14243,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_14238]) ).
tcf(c_14245,plain,
multiply(inverse(sk_c5),iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_14238]) ).
tcf(c_14248,plain,
multiply(inverse(sk_c8),iPr_def_22) = sk_c3,
inference(superposition,[status(thm)],[c_422,c_14238]) ).
tcf(c_14250,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_14238]) ).
tcf(c_14251,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_14238]) ).
tcf(c_14352,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_4102,c_14238]) ).
tcf(c_14365,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_6056,c_14238]) ).
tcf(c_14380,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_6690,c_14238]) ).
tcf(c_14390,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c3)) = iPr_def_22,
inference(superposition,[status(thm)],[c_9904,c_14238]) ).
tcf(c_14408,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2735,c_14238]) ).
tcf(c_14409,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2734,c_14238]) ).
tcf(c_14410,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2733,c_14238]) ).
tcf(c_14411,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2732,c_14238]) ).
tcf(c_14449,plain,
multiply(inverse(sk_c6),multiply(iPr_def_15,sk_c3)) = iPr_def_22,
inference(superposition,[status(thm)],[c_10607,c_14238]) ).
tcf(c_14493,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_14238,c_14238]) ).
tcf(c_15539,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 )
| ( inverse(inverse(identity)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14250,c_427]) ).
tcf(c_15594,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_14251,c_14493]) ).
tcf(c_15606,plain,
multiply(sk_c6,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_15594,c_2715]) ).
tcf(c_15608,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_15594,c_2712]) ).
tcf(c_15609,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_15594,c_3446]) ).
tcf(c_15613,plain,
multiply(sk_c7,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_15594,c_2832]) ).
tcf(c_15615,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_15594,c_2818]) ).
tcf(c_15620,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15594,c_14250]) ).
tcf(c_15621,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_15615,c_2815]) ).
tcf(c_15623,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_15613,c_2829]) ).
tcf(c_15628,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_15608,c_414]) ).
tcf(c_15630,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_15606,c_415]) ).
tcf(c_22859,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_14408,c_84]) ).
tcf(c_22863,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c4,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14408,c_429]) ).
tcf(c_22864,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_14408,c_14238]) ).
tcf(c_22865,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_14408,c_15594]) ).
tcf(c_22866,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_22863,c_420]) ).
tcf(c_22908,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_22865,c_15594]) ).
tcf(c_22916,plain,
multiply(sk_c4,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_3443,c_22864]) ).
tcf(c_24591,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_14409,c_427]) ).
tcf(c_24592,plain,
multiply(sk_c5,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_14409,c_84]) ).
tcf(c_24597,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_14409,c_14238]) ).
tcf(c_24598,plain,
multiply(sk_c5,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_14409,c_15594]) ).
tcf(c_24604,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( inverse(inverse(iPr_def_17)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_24591,c_418]) ).
tcf(c_24612,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_6056,c_24592]) ).
tcf(c_28905,plain,
inverse(iPr_def_17) = sk_c5,
inference(demodulation,[status(thm)],[c_24598,c_15594]) ).
tcf(c_28913,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_6057,c_24597]) ).
tcf(c_28918,plain,
multiply(sk_c5,sk_c7) = iPr_def_18,
inference(superposition,[status(thm)],[c_3423,c_24597]) ).
tcf(c_28937,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_18,sk_c8) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_28913,c_10492]) ).
tcf(c_30171,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_14410,c_84]) ).
tcf(c_30176,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_14410,c_14238]) ).
tcf(c_30177,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_14410,c_15594]) ).
tcf(c_32235,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_30177,c_15594]) ).
tcf(c_32270,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_2829,c_30176]) ).
tcf(c_33793,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_16)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14411,c_428]) ).
tcf(c_33795,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_14411,c_84]) ).
tcf(c_33798,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_16)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c2,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14411,c_426]) ).
tcf(c_33799,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c8 )
| ( multiply(sk_c2,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14411,c_429]) ).
tcf(c_33800,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_14411,c_14238]) ).
tcf(c_33801,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_14411,c_15594]) ).
tcf(c_34973,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_33801,c_15594]) ).
tcf(c_34980,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_931,c_33800]) ).
tcf(c_34981,plain,
multiply(sk_c2,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_2815,c_33800]) ).
tcf(c_37221,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_34981,c_34980,c_34973,c_33799,c_33798,c_33793,c_33795,c_32270,c_32235,c_30171,c_28937,c_28918,c_28905,c_24612,c_24604,c_24598,c_24592,c_22916,c_22908,c_22866,c_22859,c_15630,c_15628,c_15623,c_15621,c_15615,c_15613,c_15609,c_15608,c_15606,c_15620,c_15539,c_14449,c_14390,c_14380,c_14365,c_14352,c_14248,c_14245,c_14243,c_11086,c_11012,c_10786,c_10607,c_10596,c_10503,c_10492,c_9907,c_9904,c_8746,c_2352,c_2217,c_2073,c_2069,c_789,c_459,c_458,c_457,c_456,c_455,c_454,c_453,c_449,c_448,c_444,c_443,c_439,c_438,c_434,c_433,c_432,c_431,c_430,c_425,c_419,c_417,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP320-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Wed Sep 23 14:27:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.33 Running first-order theorem proving
% 0.03/0.33 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
% 0.03/0.34
% 0.03/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.34
% 0.03/0.34 % Detected problem language: tptp
% 0.03/0.35 % Proving...
% 4.48/2.10 % SZS status Started for theBenchmark.p
% 4.48/2.10 % SZS status Unsatisfiable for theBenchmark.p
% 4.48/2.10
% 4.48/2.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.48/2.10
% 4.48/2.10 % ------ iProver source info
% 4.48/2.10
% 4.48/2.10 % git: date: 2026-07-19 20:42:38 +0200
% 4.48/2.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.48/2.10 % git: non_committed_changes: false
% 4.48/2.10
% 4.48/2.10 % ------ Parsing...% successful
% 4.48/2.10
% 4.48/2.10
% 4.48/2.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.48/2.10
% 4.48/2.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.48/2.10
% 4.48/2.10 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.48/2.10
% 4.48/2.10 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.48/2.10 % ------ Proving...
% 4.48/2.10 % ------ Problem Properties
% 4.48/2.10
% 4.48/2.10 %
% 4.48/2.10 % clauses 49
% 4.48/2.10 % conjectures 35
% 4.48/2.10 % EPR 31
% 4.48/2.10 % Horn 18
% 4.48/2.10 % unary 14
% 4.48/2.10 % binary 30
% 4.48/2.10 % lits 92
% 4.48/2.10 % lits eq 84
% 4.48/2.10 % fd_pure 0
% 4.48/2.10 % fd_pseudo 0
% 4.48/2.10 % fd_cond 0
% 4.48/2.10 % fd_pseudo_cond 0
% 4.48/2.10 % AC symbols 0
% 4.48/2.10
% 4.48/2.10 % ------ Schedule dynamic 5 is on
% 4.48/2.10
% 4.48/2.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.48/2.10
% 4.48/2.10
% 4.48/2.10 % ------
% 4.48/2.10 % Current options:
% 4.48/2.10 % ------
% 4.48/2.10
% 4.48/2.10
% 4.48/2.10 %
% 4.48/2.10
% 4.48/2.10 % ------ Proving...
% 4.48/2.10 %
% 4.48/2.10
% 4.48/2.10 % SZS status Unsatisfiable for theBenchmark.p
% 4.48/2.10
% 4.48/2.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.48/2.11
% 4.48/2.11
%------------------------------------------------------------------------------