%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP245-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 01:32:27 PM UTC 2026
% Result : Unsatisfiable 7.77s 7.29s
% Output : CNFRefutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 248 ( 80 unt; 13 def)
% Number of atoms : 792 ( 448 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 431 ( 170 ~; 261 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 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 : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 75 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f5]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c6)
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c6)
| sk_c10 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f61,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f71,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = inverse(sk_c6)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f71]) ).
fof(f75,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X6,sk_c8)
| inverse(X5) != X6
| sk_c9 != multiply(X5,X6)
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != inverse(X4)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != multiply(inverse(X5),sk_c8)
| sk_c9 != multiply(X5,inverse(X5))
| sk_c9 != multiply(X4,sk_c8)
| sk_c9 != inverse(X4)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9)
| inverse(X0) != sk_c10
| sk_c9 != multiply(X0,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c9 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c4,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_133,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c4,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c9 )
| ( inverse(X4) != sk_c9 )
| ( inverse(X2) != sk_c10 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(X5,sk_c9) != sk_c8 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( multiply(X2,sk_c9) != sk_c10 )
| ( multiply(X1,sk_c9) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 )
| ( multiply(inverse(X3),sk_c8) != sk_c9 )
| ( multiply(X3,inverse(X3)) != sk_c9 ) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_537,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_140]) ).
tcf(c_538,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_539,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_140]) ).
tcf(c_540,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_541,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_140]) ).
tcf(c_542,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_543,definition,
iPr_def_15 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_544,definition,
iPr_def_16 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_545,definition,
iPr_def_17 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_546,definition,
iPr_def_18 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_547,definition,
iPr_def_19 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_548,definition,
iPr_def_20 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_549,definition,
iPr_def_21 = multiply(sk_c4,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_550,definition,
iPr_def_22 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_551,definition,
iPr_def_23 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_552,definition,
iPr_def_24 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_553,definition,
iPr_def_25 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_554,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_555,definition,
iPr_def_27 = multiply(sk_c1,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_556,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_542]) ).
tcf(c_557,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_558,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_540]) ).
tcf(c_559,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_539]) ).
tcf(c_560,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_538]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_537]) ).
tcf(c_568,negated_conjecture,
( ( iPr_def_21 = sk_c10 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_134,c_549]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_22 = sk_c10 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_133,c_550]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_23 = sk_c10 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_575,negated_conjecture,
( ( iPr_def_23 = sk_c10 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_576,negated_conjecture,
( ( iPr_def_23 = sk_c10 )
| ( iPr_def_22 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_580,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_581,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_587,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_588,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_592,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_597,negated_conjecture,
( ( iPr_def_26 = sk_c10 )
| ( iPr_def_22 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_599,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_600,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_604,negated_conjecture,
( ( iPr_def_27 = sk_c9 )
| ( iPr_def_22 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1127,plain,
( ( sk_c10 = iPr_def_23 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_571,c_546]) ).
tcf(c_1139,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_576,c_555]) ).
tcf(c_1140,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_575,c_555]) ).
tcf(c_1145,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_569,c_555]) ).
tcf(c_1146,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_568,c_555]) ).
tcf(c_1175,plain,
multiply(iPr_def_22,sk_c4) = identity,
inference(superposition,[status(thm)],[c_550,c_96]) ).
tcf(c_1176,plain,
multiply(iPr_def_20,sk_c5) = identity,
inference(superposition,[status(thm)],[c_548,c_96]) ).
tcf(c_1177,plain,
multiply(iPr_def_17,sk_c6) = identity,
inference(superposition,[status(thm)],[c_545,c_96]) ).
tcf(c_1178,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_554,c_96]) ).
tcf(c_1179,plain,
multiply(iPr_def_24,sk_c2) = identity,
inference(superposition,[status(thm)],[c_552,c_96]) ).
tcf(c_1203,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_579,c_553]) ).
tcf(c_1216,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_580,c_553]) ).
tcf(c_1239,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_553]) ).
tcf(c_1446,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_586,c_547]) ).
tcf(c_1447,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_586,c_543]) ).
tcf(c_1462,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_587,c_547]) ).
tcf(c_1463,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_587,c_543]) ).
tcf(c_1472,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_588,c_547]) ).
tcf(c_1595,plain,
( ( sk_c10 = iPr_def_26 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_592,c_546]) ).
tcf(c_1638,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_593,c_555]) ).
tcf(c_1990,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_599,c_546]) ).
tcf(c_2016,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_27) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_600,c_553]) ).
tcf(c_2305,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_604,c_555]) ).
tcf(c_2749,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( inverse(sk_c2) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_553,c_558]) ).
tcf(c_2751,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_558]) ).
tcf(c_2771,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2749,c_552]) ).
tcf(c_2915,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_27 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_555,c_559]) ).
tcf(c_2917,plain,
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_96,c_559]) ).
tcf(c_2944,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_27 )
| ( sk_c10 != iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_2915,c_554]) ).
tcf(c_3137,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_19 )
| ( inverse(sk_c5) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_547,c_560]) ).
tcf(c_3140,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c8)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_96,c_560]) ).
tcf(c_3153,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_20 )
| ( sk_c9 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3137,c_548]) ).
tcf(c_3234,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_549,c_562]) ).
tcf(c_3236,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_16 )
| ( inverse(sk_c3) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_544,c_562]) ).
tcf(c_3253,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_23 )
| ( sk_c10 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3236,c_551]) ).
tcf(c_3261,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_22 )
| ( sk_c10 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3234,c_550]) ).
tcf(c_3393,plain,
( ~ iPr_def_14
| ( inverse(identity) != sk_c9 )
| ( multiply(inverse(identity),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_557]) ).
tcf(c_3798,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_546,c_97]) ).
tcf(c_3803,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_3805,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1175,c_97]) ).
tcf(c_3806,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1176,c_97]) ).
tcf(c_3807,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1177,c_97]) ).
tcf(c_3808,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1178,c_97]) ).
tcf(c_3809,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1179,c_97]) ).
tcf(c_3818,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3809,c_95]) ).
tcf(c_3819,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3808,c_95]) ).
tcf(c_3820,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3807,c_95]) ).
tcf(c_3821,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3806,c_95]) ).
tcf(c_3822,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3805,c_95]) ).
tcf(c_5915,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_553,c_3818]) ).
tcf(c_6302,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c10,
inference(superposition,[status(thm)],[c_555,c_3819]) ).
tcf(c_6322,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_546,c_3820]) ).
tcf(c_6338,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_6322,c_97]) ).
tcf(c_6424,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_547,c_3821]) ).
tcf(c_6427,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_6424,c_97]) ).
tcf(c_6540,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1145,c_3819]) ).
tcf(c_6541,plain,
( ( sk_c10 = iPr_def_22 )
| ( sk_c10 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6540,c_6302]) ).
tcf(c_6552,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1146,c_3819]) ).
tcf(c_6553,plain,
( ( sk_c10 = iPr_def_21 )
| ( sk_c10 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6552,c_6302]) ).
tcf(c_7144,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1446,c_3821]) ).
tcf(c_7145,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_7144,c_6424]) ).
tcf(c_7184,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1462,c_3821]) ).
tcf(c_7185,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_7184,c_6424]) ).
tcf(c_7220,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1472,c_3821]) ).
tcf(c_7221,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_7220,c_6424]) ).
tcf(c_7947,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2016,c_3818]) ).
tcf(c_7948,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c9 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_7947,c_5915]) ).
tcf(c_8155,plain,
( ( sk_c9 = iPr_def_27 )
| ( multiply(iPr_def_26,iPr_def_27) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_2305,c_3819]) ).
tcf(c_8156,plain,
( ( sk_c9 = iPr_def_27 )
| ( sk_c10 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_8155,c_6302]) ).
tcf(c_9548,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_543,c_3798]) ).
tcf(c_11638,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3803,c_95]) ).
tcf(c_11649,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_543,c_11638]) ).
tcf(c_11652,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_11638]) ).
tcf(c_11653,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_11638]) ).
tcf(c_11686,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(inverse(sk_c1),iPr_def_27) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1140,c_11638]) ).
tcf(c_11687,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(inverse(sk_c1),iPr_def_27) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1139,c_11638]) ).
tcf(c_11716,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(inverse(sk_c7),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1463,c_11638]) ).
tcf(c_11717,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(inverse(sk_c7),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1447,c_11638]) ).
tcf(c_11796,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3822,c_11638]) ).
tcf(c_11797,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3821,c_11638]) ).
tcf(c_11798,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3820,c_11638]) ).
tcf(c_11799,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3819,c_11638]) ).
tcf(c_11800,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3818,c_11638]) ).
tcf(c_11818,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11638,c_11638]) ).
tcf(c_11939,plain,
( ( sk_c10 = iPr_def_23 )
| ( sk_c10 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_11687,c_554,c_6302]) ).
tcf(c_11942,plain,
( ( sk_c10 = iPr_def_23 )
| ( sk_c10 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_11686,c_554,c_6302]) ).
tcf(c_12358,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11653,c_11818]) ).
tcf(c_12375,plain,
multiply(sk_c8,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_12358,c_6427]) ).
tcf(c_12378,plain,
multiply(sk_c7,identity) = multiply(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_12358,c_6338]) ).
tcf(c_12388,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12358,c_11652]) ).
tcf(c_12392,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_12378,c_6322]) ).
tcf(c_12395,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12375,c_6424]) ).
tcf(c_12550,plain,
( ~ iPr_def_14
| ( multiply(identity,identity) != sk_c9 )
| ( multiply(inverse(identity),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_12388,c_557]) ).
tcf(c_12551,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_12388,c_96]) ).
tcf(c_12553,plain,
( ~ iPr_def_14
| ( multiply(identity,identity) != sk_c9 )
| ( multiply(identity,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_12550,c_12388]) ).
tcf(c_12615,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_581,c_2771]) ).
tcf(c_12616,plain,
( ( sk_c9 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_580,c_2771]) ).
tcf(c_12617,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_579,c_2771]) ).
tcf(c_12753,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12615,c_7221,c_12615]) ).
tcf(c_12779,plain,
( ( sk_c9 = iPr_def_19 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12616,c_7185,c_12616]) ).
tcf(c_12785,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12617,c_7145,c_12617]) ).
tcf(c_13051,plain,
( ( sk_c10 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_597,c_2944]) ).
tcf(c_13055,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c9 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_593,c_2944]) ).
tcf(c_13215,plain,
( ( sk_c10 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13051,c_8156,c_13051]) ).
tcf(c_13395,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13055,c_7948,c_13055]) ).
tcf(c_13690,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_3253,c_3261,c_3253,c_6541,c_6553]) ).
tcf(c_13692,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_13690,c_3261,c_11942,c_11939,c_13690]) ).
tcf(c_13694,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_556,c_13692]) ).
tcf(c_13777,plain,
multiply(sk_c4,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_11796,c_12358]) ).
tcf(c_13799,plain,
inverse(iPr_def_22) = sk_c4,
inference(demodulation,[status(thm)],[c_13777,c_12358]) ).
tcf(c_13886,plain,
multiply(sk_c5,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11797,c_96]) ).
tcf(c_13891,plain,
multiply(sk_c5,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_11797,c_12358]) ).
tcf(c_13910,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_13886,c_3821]) ).
tcf(c_13913,plain,
inverse(iPr_def_20) = sk_c5,
inference(demodulation,[status(thm)],[c_13891,c_12358]) ).
tcf(c_13916,plain,
( ~ iPr_def_14
| ( multiply(iPr_def_20,sk_c5) != sk_c9 )
| ( multiply(inverse(iPr_def_20),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13913,c_557]) ).
tcf(c_13918,plain,
( ~ iPr_def_14
| ( sk_c9 != iPr_def_19 )
| ( sk_c9 != identity ) ),
inference(light_normalisation,[status(thm)],[c_13916,c_547,c_1176,c_13913]) ).
tcf(c_13978,plain,
multiply(sk_c6,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_11798,c_96]) ).
tcf(c_13983,plain,
multiply(sk_c6,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_11798,c_12358]) ).
tcf(c_13996,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1990,c_13978]) ).
tcf(c_13997,plain,
( ( identity = iPr_def_18 )
| ( sk_c10 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1595,c_13978]) ).
tcf(c_14001,plain,
( ( identity = iPr_def_18 )
| ( sk_c10 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1127,c_13978]) ).
tcf(c_14019,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(superposition,[status(thm)],[c_13978,c_3820]) ).
tcf(c_14356,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_13997,c_555]) ).
tcf(c_14797,plain,
inverse(iPr_def_17) = sk_c6,
inference(demodulation,[status(thm)],[c_13983,c_12358]) ).
tcf(c_15106,plain,
( ( iPr_def_23 = iPr_def_26 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_14001,c_13997]) ).
tcf(c_15107,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_12
| ( iPr_def_23 != iPr_def_26 )
| ( sk_c9 != iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_14001,c_2944]) ).
tcf(c_15429,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_11799,c_96]) ).
tcf(c_15483,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_14356,c_15429]) ).
tcf(c_15488,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1638,c_15429]) ).
tcf(c_17793,plain,
multiply(sk_c2,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_11800,c_96]) ).
tcf(c_17797,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_11800,c_11638]) ).
tcf(c_17798,plain,
multiply(sk_c2,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_11800,c_12358]) ).
tcf(c_17814,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1239,c_17793]) ).
tcf(c_17815,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1216,c_17793]) ).
tcf(c_17816,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1203,c_17793]) ).
tcf(c_18199,plain,
inverse(iPr_def_24) = sk_c2,
inference(demodulation,[status(thm)],[c_17798,c_12358]) ).
tcf(c_18208,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1179,c_17797]) ).
tcf(c_18209,plain,
multiply(sk_c2,sk_c9) = iPr_def_25,
inference(superposition,[status(thm)],[c_5915,c_17797]) ).
tcf(c_19410,plain,
( ~ iPr_def_13
| ( sk_c9 != identity )
| ( sk_c9 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2751,c_12388]) ).
tcf(c_21118,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_25)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_588,c_3140]) ).
tcf(c_21119,plain,
( ( sk_c9 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_25)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_587,c_3140]) ).
tcf(c_21120,plain,
( ( sk_c9 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c9 != identity )
| ( inverse(inverse(iPr_def_25)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_586,c_3140]) ).
tcf(c_24909,plain,
( ~ iPr_def_14
| ( sk_c9 != identity )
| ( multiply(identity,sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3393,c_12388]) ).
tcf(c_27069,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_24909,c_21120,c_21119,c_21118,c_19410,c_18209,c_18208,c_18199,c_17816,c_17815,c_17814,c_15488,c_15483,c_15107,c_15106,c_14797,c_14019,c_13996,c_13978,c_13918,c_13910,c_13799,c_13694,c_13395,c_13215,c_12785,c_12779,c_12753,c_12553,c_12395,c_12392,c_12378,c_12375,c_11717,c_11716,c_11649,c_9548,c_7948,c_12551,c_3153,c_2917,c_1990,c_552,c_550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP245-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n003.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Wed Sep 23 14:16:56 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 7.77/7.29 % SZS status Started for theBenchmark.p
% 7.77/7.29 % SZS status Unsatisfiable for theBenchmark.p
% 7.77/7.29
% 7.77/7.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.77/7.29
% 7.77/7.29 % ------ iProver source info
% 7.77/7.29
% 7.77/7.29 % git: date: 2026-07-19 20:42:38 +0200
% 7.77/7.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.77/7.29 % git: non_committed_changes: false
% 7.77/7.29
% 7.77/7.29 % ------ Parsing...% successful
% 7.77/7.29
% 7.77/7.29
% 7.77/7.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.77/7.29
% 7.77/7.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.77/7.29
% 7.77/7.29 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.77/7.29
% 7.77/7.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.77/7.29 % ------ Proving...
% 7.77/7.29 % ------ Problem Properties
% 7.77/7.29
% 7.77/7.29 %
% 7.77/7.29 % clauses 64
% 7.77/7.29 % conjectures 48
% 7.77/7.29 % EPR 43
% 7.77/7.29 % Horn 21
% 7.77/7.29 % unary 16
% 7.77/7.29 % binary 42
% 7.77/7.29 % lits 120
% 7.77/7.29 % lits eq 110
% 7.77/7.29 % fd_pure 0
% 7.77/7.29 % fd_pseudo 0
% 7.77/7.29 % fd_cond 0
% 7.77/7.29 % fd_pseudo_cond 0
% 7.77/7.29 % AC symbols 0
% 7.77/7.29
% 7.77/7.29 % ------ Schedule dynamic 5 is on
% 7.77/7.29
% 7.77/7.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.77/7.29
% 7.77/7.29
% 7.77/7.29 % ------
% 7.77/7.29 % Current options:
% 7.77/7.29 % ------
% 7.77/7.29
% 7.77/7.29
% 7.77/7.29 %
% 7.77/7.29
% 7.77/7.29 % ------ Proving...
% 7.77/7.29 %
% 7.77/7.29
% 7.77/7.29 % SZS status Unsatisfiable for theBenchmark.p
% 7.77/7.29
% 7.77/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.77/7.29
% 7.77/7.29
%------------------------------------------------------------------------------