%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP275-1 : 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 01:32:42 PM UTC 2026
% Result : Unsatisfiable 10.40s 2.19s
% Output : CNFRefutation 10.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 33
% Syntax : Number of formulae : 258 ( 112 unt; 11 def)
% Number of atoms : 791 ( 443 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 319 ( 109 ~; 210 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?; 70 :)
% 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(f10,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f12]) ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c5 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f44]) ).
fof(f52,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c8) != sk_c7
| inverse(X3) != X4
| multiply(X3,X4) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c8)
| inverse(X3) != X4
| sk_c7 != multiply(X3,X4)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( sk_c7 != multiply(inverse(X3),sk_c8)
| sk_c7 != multiply(X3,inverse(X3))
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,sk_c6)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) ),
inference(equality_resolution,[],[f65]) ).
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_89,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(inverse(X3),sk_c8) != sk_c7 )
| ( multiply(X3,inverse(X3)) != sk_c7 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
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_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_413,definition,
iPr_def_13 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
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_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c6 )
| ( iPr_def_13 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412,c_414,c_413]) ).
tcf(c_425,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_13 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_459,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_855,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_443,c_416]) ).
tcf(c_905,plain,
! [X0: $i] :
( ( iPr_def_13 = sk_c7 )
| ( iPr_def_13 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_913,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_442,c_418]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_932,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_444,c_419]) ).
tcf(c_933,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_443,c_419]) ).
tcf(c_956,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_439,c_423]) ).
tcf(c_957,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_438,c_423]) ).
tcf(c_958,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_433,c_423]) ).
tcf(c_959,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_432,c_423]) ).
tcf(c_974,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_975,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_976,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_977,plain,
multiply(iPr_def_21,sk_c2) = identity,
inference(superposition,[status(thm)],[c_421,c_84]) ).
tcf(c_998,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_13) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_445,c_419]) ).
tcf(c_1043,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c8,iPr_def_14) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_446,c_413]) ).
tcf(c_1103,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_448,c_418]) ).
tcf(c_1117,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_927]) ).
tcf(c_1133,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_449,c_419]) ).
tcf(c_1195,plain,
( ( iPr_def_13 = sk_c7 )
| ( iPr_def_13 != iPr_def_13 )
| ( sk_c7 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_905]) ).
tcf(c_1233,plain,
iPr_def_13 = iPr_def_13,
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1333,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_454,c_418]) ).
tcf(c_1355,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_455,c_445]) ).
tcf(c_1356,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_455,c_419]) ).
tcf(c_1794,plain,
! [X0: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1234]) ).
tcf(c_2117,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_427]) ).
tcf(c_2248,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_419,c_428]) ).
tcf(c_2249,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_16 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_416,c_428]) ).
tcf(c_2270,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 )
| ( sk_c8 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2249,c_421]) ).
tcf(c_2274,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2248,c_420]) ).
tcf(c_2510,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( iPr_def_23 != sk_c7 )
| ( iPr_def_13 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1794]) ).
tcf(c_2609,plain,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_23 != iPr_def_23 )
| ( sk_c7 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1117]) ).
tcf(c_2610,plain,
iPr_def_23 = iPr_def_23,
inference(instantiation,[status(thm)],[c_459]) ).
tcf(c_2855,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_423,c_85]) ).
tcf(c_2856,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_2857,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2858,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2859,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2863,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2865,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_974,c_85]) ).
tcf(c_2866,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_975,c_85]) ).
tcf(c_2867,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_976,c_85]) ).
tcf(c_2868,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_977,c_85]) ).
tcf(c_2873,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2868,c_83]) ).
tcf(c_2874,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2867,c_83]) ).
tcf(c_2875,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2866,c_83]) ).
tcf(c_2876,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2865,c_83]) ).
tcf(c_3025,plain,
multiply(iPr_def_21,iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_416,c_2873]) ).
tcf(c_3030,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_16,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3025,c_85]) ).
tcf(c_3638,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_423,c_2874]) ).
tcf(c_3677,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_418,c_2875]) ).
tcf(c_3680,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3677,c_85]) ).
tcf(c_3686,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_419,c_2876]) ).
tcf(c_4662,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(iPr_def_21,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_855,c_2873]) ).
tcf(c_4663,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_4662,c_3025]) ).
tcf(c_5128,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_956,c_2874]) ).
tcf(c_5129,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5128,c_3638]) ).
tcf(c_5144,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_957,c_2874]) ).
tcf(c_5145,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5144,c_3638]) ).
tcf(c_5204,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_958,c_2874]) ).
tcf(c_5205,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5204,c_3638]) ).
tcf(c_5216,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_959,c_2874]) ).
tcf(c_5217,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5216,c_3638]) ).
tcf(c_6585,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1356,c_2876]) ).
tcf(c_6586,plain,
( ( sk_c7 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6585,c_3686]) ).
tcf(c_8545,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(sk_c7,iPr_def_13) = multiply(iPr_def_14,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_1043,c_2856]) ).
tcf(c_8838,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2858]) ).
tcf(c_8919,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_1355,c_1195,c_1233,c_2510,c_2609,c_2610,c_4663,c_6586]) ).
tcf(c_8987,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( multiply(iPr_def_18,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_8919,c_414]) ).
tcf(c_9046,plain,
multiply(sk_c5,iPr_def_13) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_413,c_2859]) ).
tcf(c_9130,plain,
multiply(sk_c4,multiply(iPr_def_15,sk_c6)) = multiply(iPr_def_18,iPr_def_13),
inference(superposition,[status(thm)],[c_9046,c_2858]) ).
tcf(c_10619,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2863,c_83]) ).
tcf(c_10626,plain,
multiply(inverse(sk_c3),iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_419,c_10619]) ).
tcf(c_10628,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_10619]) ).
tcf(c_10629,plain,
multiply(inverse(sk_c8),iPr_def_13) = sk_c6,
inference(superposition,[status(thm)],[c_413,c_10619]) ).
tcf(c_10631,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_10619]) ).
tcf(c_10632,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_10619]) ).
tcf(c_10703,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_998,c_10619]) ).
tcf(c_10704,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_932,c_10619]) ).
tcf(c_10706,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1133,c_10619]) ).
tcf(c_10709,plain,
( ( sk_c7 = iPr_def_13 )
| ( multiply(inverse(sk_c3),iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_933,c_10619]) ).
tcf(c_10768,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2876,c_10619]) ).
tcf(c_10769,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2875,c_10619]) ).
tcf(c_10770,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2874,c_10619]) ).
tcf(c_10771,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2873,c_10619]) ).
tcf(c_10811,plain,
multiply(inverse(sk_c5),multiply(iPr_def_15,sk_c6)) = iPr_def_13,
inference(superposition,[status(thm)],[c_9046,c_10619]) ).
tcf(c_10813,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_10619,c_10619]) ).
tcf(c_11599,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_10632,c_10813]) ).
tcf(c_11611,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_11599,c_2856]) ).
tcf(c_11612,plain,
multiply(sk_c1,sk_c8) = multiply(iPr_def_23,identity),
inference(superposition,[status(thm)],[c_11599,c_2855]) ).
tcf(c_11616,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_11599,c_3680]) ).
tcf(c_11617,plain,
multiply(sk_c4,sk_c5) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_11599,c_2858]) ).
tcf(c_11619,plain,
multiply(sk_c7,identity) = multiply(iPr_def_21,iPr_def_16),
inference(superposition,[status(thm)],[c_11599,c_3030]) ).
tcf(c_11624,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_11599,c_10631]) ).
tcf(c_11625,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_11619,c_3025]) ).
tcf(c_11627,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_11617,c_418]) ).
tcf(c_11628,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_11616,c_3677]) ).
tcf(c_11632,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(light_normalisation,[status(thm)],[c_11612,c_423]) ).
tcf(c_11633,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11611,c_414]) ).
tcf(c_12028,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_2270,c_2274,c_2270,c_5205,c_5217]) ).
tcf(c_12030,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_12028,c_2274,c_5129,c_5145,c_12028]) ).
tcf(c_12032,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c6 != iPr_def_14 )
| ( sk_c7 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_424,c_12030]) ).
tcf(c_12328,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_10768,c_10619]) ).
tcf(c_12564,plain,
multiply(sk_c3,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_3686,c_12328]) ).
tcf(c_12630,plain,
multiply(sk_c4,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_10769,c_84]) ).
tcf(c_12633,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_10769,c_11599]) ).
tcf(c_12640,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1333,c_12630]) ).
tcf(c_12641,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_1103,c_12630]) ).
tcf(c_12644,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_913,c_12630]) ).
tcf(c_13067,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_12640,c_414]) ).
tcf(c_13326,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_12641,c_423]) ).
tcf(c_13930,plain,
inverse(iPr_def_17) = sk_c4,
inference(demodulation,[status(thm)],[c_12633,c_11599]) ).
tcf(c_14057,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_12644,c_12640]) ).
tcf(c_14365,plain,
! [X0: $i] :
( ( iPr_def_13 = iPr_def_23 )
| ( multiply(iPr_def_18,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_14057,c_83]) ).
tcf(c_14847,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_10770,c_84]) ).
tcf(c_14849,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_10770,c_10619]) ).
tcf(c_14850,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_10770,c_11599]) ).
tcf(c_14868,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_13326,c_14847]) ).
tcf(c_14913,plain,
inverse(iPr_def_22) = sk_c1,
inference(demodulation,[status(thm)],[c_14850,c_11599]) ).
tcf(c_14944,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_976,c_14849]) ).
tcf(c_14949,plain,
multiply(sk_c1,sk_c8) = iPr_def_23,
inference(superposition,[status(thm)],[c_3638,c_14849]) ).
tcf(c_15124,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_14868,c_83]) ).
tcf(c_15761,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_10771,c_10619]) ).
tcf(c_15762,plain,
multiply(sk_c2,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_10771,c_11599]) ).
tcf(c_15943,plain,
inverse(iPr_def_21) = sk_c2,
inference(demodulation,[status(thm)],[c_15762,c_11599]) ).
tcf(c_15961,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_977,c_15761]) ).
tcf(c_15962,plain,
multiply(sk_c2,sk_c7) = iPr_def_16,
inference(superposition,[status(thm)],[c_3025,c_15761]) ).
tcf(c_17098,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_14365,c_8987]) ).
tcf(c_17226,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_15124,c_13067]) ).
tcf(c_17574,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_17098,c_414]) ).
tcf(c_17899,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_17226,c_414]) ).
tcf(c_22208,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_10813,c_84]) ).
tcf(c_22211,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_10813,c_11599]) ).
tcf(c_22212,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_22211,c_11599]) ).
tcf(c_22229,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( multiply(inverse(X0),sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_425,c_22208]) ).
tcf(c_22233,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2117,c_22212]) ).
tcf(c_22254,plain,
( ~ iPr_def_12
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_84,c_22229]) ).
tcf(c_22702,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_22208,c_85]) ).
tcf(c_22711,plain,
multiply(iPr_def_14,inverse(sk_c8)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_22208,c_2856]) ).
tcf(c_22717,plain,
multiply(iPr_def_19,inverse(sk_c7)) = multiply(sk_c3,identity),
inference(superposition,[status(thm)],[c_22208,c_2857]) ).
tcf(c_22730,plain,
multiply(sk_c7,inverse(iPr_def_16)) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_22208,c_3030]) ).
tcf(c_22732,plain,
multiply(iPr_def_17,identity) = inverse(sk_c4),
inference(superposition,[status(thm)],[c_22208,c_2875]) ).
tcf(c_22733,plain,
multiply(iPr_def_22,identity) = inverse(sk_c1),
inference(superposition,[status(thm)],[c_22208,c_2874]) ).
tcf(c_22735,plain,
multiply(iPr_def_21,identity) = inverse(sk_c2),
inference(superposition,[status(thm)],[c_22208,c_2873]) ).
tcf(c_23042,plain,
inverse(sk_c4) = iPr_def_17,
inference(superposition,[status(thm)],[c_13930,c_22212]) ).
tcf(c_23044,plain,
inverse(sk_c2) = iPr_def_21,
inference(superposition,[status(thm)],[c_15943,c_22212]) ).
tcf(c_23045,plain,
inverse(sk_c1) = iPr_def_22,
inference(superposition,[status(thm)],[c_14913,c_22212]) ).
tcf(c_23503,plain,
multiply(sk_c1,multiply(iPr_def_22,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_14847,c_22702]) ).
tcf(c_23547,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,multiply(X0,inverse(X0))) = identity ) ),
inference(superposition,[status(thm)],[c_15124,c_22702]) ).
tcf(c_23610,plain,
multiply(iPr_def_20,multiply(iPr_def_19,inverse(sk_c7))) = identity,
inference(superposition,[status(thm)],[c_3686,c_22702]) ).
tcf(c_23664,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c7,multiply(iPr_def_14,inverse(iPr_def_14))) = identity ) ),
inference(superposition,[status(thm)],[c_17899,c_22702]) ).
tcf(c_23665,plain,
( ( iPr_def_13 = iPr_def_23 )
| ( multiply(sk_c7,multiply(iPr_def_14,inverse(iPr_def_14))) = identity ) ),
inference(superposition,[status(thm)],[c_17574,c_22702]) ).
tcf(c_23701,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(X0,inverse(multiply(sk_c8,X0)))) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_22702,c_2856]) ).
tcf(c_23705,plain,
multiply(iPr_def_14,inverse(multiply(sk_c7,sk_c8))) = identity,
inference(superposition,[status(thm)],[c_22702,c_2856]) ).
tcf(c_23747,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_20,X0))) = multiply(sk_c3,identity),
inference(superposition,[status(thm)],[c_22702,c_12328]) ).
tcf(c_23778,plain,
multiply(iPr_def_14,inverse(iPr_def_14)) = identity,
inference(light_normalisation,[status(thm)],[c_23705,c_414]) ).
tcf(c_23783,plain,
multiply(sk_c1,multiply(iPr_def_22,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_23503,c_11624]) ).
tcf(c_23800,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_20,X0))) = multiply(iPr_def_19,inverse(sk_c7)),
inference(light_normalisation,[status(thm)],[c_23747,c_22717]) ).
tcf(c_23838,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(X0,inverse(multiply(sk_c8,X0)))) = multiply(iPr_def_14,inverse(sk_c8)),
inference(light_normalisation,[status(thm)],[c_23701,c_22711]) ).
tcf(c_24007,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,identity) = identity ) ),
inference(light_normalisation,[status(thm)],[c_23547,c_22208]) ).
tcf(c_29296,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_24007,c_23838,c_23800,c_23783,c_23778,c_23747,c_23701,c_23665,c_23664,c_23610,c_23045,c_23044,c_23042,c_22735,c_22733,c_22732,c_22730,c_22254,c_22233,c_22208,c_15962,c_15961,c_15943,c_14949,c_14944,c_14913,c_14057,c_13930,c_12564,c_12032,c_12030,c_11633,c_11632,c_11628,c_11627,c_11625,c_11616,c_11611,c_10811,c_10709,c_10706,c_10704,c_10703,c_10629,c_10628,c_10626,c_9130,c_8838,c_8545,c_452,c_440,c_434,c_424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP275-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 14:20:29 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 10.40/2.19 % SZS status Started for theBenchmark.p
% 10.40/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 10.40/2.19
% 10.40/2.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.40/2.19
% 10.40/2.19 % ------ iProver source info
% 10.40/2.19
% 10.40/2.19 % git: date: 2026-07-19 20:42:38 +0200
% 10.40/2.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.40/2.19 % git: non_committed_changes: false
% 10.40/2.19
% 10.40/2.19 % ------ Parsing...% successful
% 10.40/2.19
% 10.40/2.19
% 10.40/2.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.40/2.19
% 10.40/2.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.40/2.19
% 10.40/2.19 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.40/2.19
% 10.40/2.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.40/2.19 % ------ Proving...
% 10.40/2.19 % ------ Problem Properties
% 10.40/2.19
% 10.40/2.19 %
% 10.40/2.19 % clauses 48
% 10.40/2.19 % conjectures 34
% 10.40/2.19 % EPR 31
% 10.40/2.19 % Horn 17
% 10.40/2.19 % unary 14
% 10.40/2.19 % binary 30
% 10.40/2.19 % lits 88
% 10.40/2.19 % lits eq 82
% 10.40/2.19 % fd_pure 0
% 10.40/2.19 % fd_pseudo 0
% 10.40/2.19 % fd_cond 0
% 10.40/2.19 % fd_pseudo_cond 0
% 10.40/2.19 % AC symbols 0
% 10.40/2.19
% 10.40/2.19 % ------ Schedule dynamic 5 is on
% 10.40/2.19
% 10.40/2.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.40/2.19
% 10.40/2.19
% 10.40/2.19 % ------
% 10.40/2.19 % Current options:
% 10.40/2.19 % ------
% 10.40/2.19
% 10.40/2.19
% 10.40/2.19 %
% 10.40/2.19
% 10.40/2.19 % ------ Proving...
% 10.40/2.19 %
% 10.40/2.19
% 10.40/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 10.40/2.19
% 10.40/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.40/2.19
% 10.40/2.19
%------------------------------------------------------------------------------