%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:38:10 PM UTC 2026
% Result : Unsatisfiable 95.83s 15.29s
% Output : CNFRefutation 95.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 11
% Syntax : Number of formulae : 161 ( 161 unt; 2 def)
% Number of atoms : 340 ( 160 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 145 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f3,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
fof(f6,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
fof(f7,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
fof(f8,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
fof(f9,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_x) ).
fof(f10,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
tcf(c_58,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(X0,multiply(X0,X0)) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_66,negated_conjecture,
multiply(a,b) != multiply(b,a),
inference(cnf_transformation,[],[f10]) ).
tcf(c_97,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_98,definition,
iPr_def_11 = multiply(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_99,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_66,c_98,c_97]) ).
tcf(c_156,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(superposition,[status(thm)],[c_58,c_63]) ).
tcf(c_169,plain,
additive_inverse(additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_156,c_59]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] : multiply(X0,add(multiply(X0,X0),X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_65,c_60]) ).
tcf(c_195,plain,
! [X0: $i] : add(iPr_def_10,multiply(a,X0)) = multiply(a,add(b,X0)),
inference(superposition,[status(thm)],[c_97,c_60]) ).
tcf(c_196,plain,
! [X0: $i] : add(iPr_def_11,multiply(b,X0)) = multiply(b,add(a,X0)),
inference(superposition,[status(thm)],[c_98,c_60]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_59,c_62]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_62,c_59]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_220,c_156]) ).
tcf(c_248,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_59,c_225]) ).
tcf(c_259,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_248,c_58]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_224,c_225]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_364,c_58]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,additive_inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_63,c_369]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_259,c_369]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_259,c_423]) ).
tcf(c_517,plain,
! [X0: $i] : add(iPr_def_10,multiply(X0,b)) = multiply(add(a,X0),b),
inference(superposition,[status(thm)],[c_97,c_61]) ).
tcf(c_518,plain,
! [X0: $i] : add(iPr_def_11,multiply(X0,a)) = multiply(add(b,X0),a),
inference(superposition,[status(thm)],[c_98,c_61]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X2,X0),X1),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),additive_inverse(multiply(X0,add(X2,X1)))) = additive_inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c_60,c_430]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),additive_inverse(multiply(add(X2,X0),X1))) = additive_inverse(multiply(X2,X1)),
inference(superposition,[status(thm)],[c_61,c_430]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),additive_inverse(multiply(X0,add(X1,X2)))) = additive_inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c_60,c_480]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),additive_inverse(multiply(add(X0,X2),X1))) = additive_inverse(multiply(X2,X1)),
inference(superposition,[status(thm)],[c_61,c_480]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(X0,X0),X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_65,c_64]) ).
tcf(c_1192,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_97,c_64]) ).
tcf(c_1193,plain,
! [X0: $i] : multiply(b,multiply(a,X0)) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_98,c_64]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_1191,c_64]) ).
tcf(c_1201,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_1199,c_64]) ).
tcf(c_1217,plain,
multiply(a,iPr_def_11) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_98,c_1192]) ).
tcf(c_1237,plain,
! [X0: $i] : multiply(multiply(iPr_def_10,a),X0) = multiply(a,multiply(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_1217,c_64]) ).
tcf(c_1242,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,X0)) = multiply(iPr_def_10,multiply(a,X0)),
inference(demodulation,[status(thm)],[c_1237,c_64]) ).
tcf(c_1283,plain,
multiply(b,iPr_def_10) = multiply(iPr_def_11,b),
inference(superposition,[status(thm)],[c_97,c_1193]) ).
tcf(c_1311,plain,
multiply(a,multiply(iPr_def_11,b)) = multiply(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_1283,c_1192]) ).
tcf(c_1371,plain,
! [X0: $i] : multiply(a,multiply(multiply(iPr_def_11,b),X0)) = multiply(multiply(iPr_def_10,iPr_def_10),X0),
inference(superposition,[status(thm)],[c_1311,c_64]) ).
tcf(c_1377,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_11,multiply(b,X0))) = multiply(iPr_def_10,multiply(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_1371,c_64]) ).
tcf(c_1955,plain,
! [X0: $i] : multiply(X0,multiply(X0,X0)) = add(X0,multiply(X0,additive_identity)),
inference(superposition,[status(thm)],[c_58,c_194]) ).
tcf(c_1956,plain,
! [X0: $i] : add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_59,c_194]) ).
tcf(c_1980,plain,
! [X0: $i] : add(X0,multiply(X0,additive_identity)) = X0,
inference(demodulation,[status(thm)],[c_1955,c_65]) ).
tcf(c_2008,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = multiply(additive_inverse(X0),additive_identity),
inference(superposition,[status(thm)],[c_1980,c_225]) ).
tcf(c_2009,plain,
! [X0: $i] : multiply(additive_inverse(X0),additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_2008,c_59]) ).
tcf(c_3173,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_259,c_2009]) ).
tcf(c_3198,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(additive_identity,X1)) = multiply(additive_identity,X1),
inference(superposition,[status(thm)],[c_3173,c_64]) ).
tcf(c_3206,plain,
multiply(a,add(b,additive_identity)) = add(iPr_def_10,additive_identity),
inference(superposition,[status(thm)],[c_3173,c_195]) ).
tcf(c_3209,plain,
multiply(b,add(a,additive_identity)) = add(iPr_def_11,additive_identity),
inference(superposition,[status(thm)],[c_3173,c_196]) ).
tcf(c_3211,plain,
multiply(b,a) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3209,c_58]) ).
tcf(c_3213,plain,
multiply(a,b) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3206,c_58]) ).
tcf(c_3414,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,multiply(additive_identity,X1)),multiply(additive_identity,X1)) = multiply(add(X0,X2),multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_3198,c_61]) ).
tcf(c_3428,plain,
! [X0: $i] : multiply(additive_identity,add(X0,X0)) = multiply(additive_identity,X0),
inference(demodulation,[status(thm)],[c_3414,c_60,c_63,c_3198]) ).
tcf(c_3853,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(multiply(add(a,X0),b))) = additive_inverse(multiply(X0,b)),
inference(superposition,[status(thm)],[c_517,c_480]) ).
tcf(c_4029,plain,
! [X0: $i] : add(iPr_def_11,additive_inverse(multiply(add(b,X0),a))) = additive_inverse(multiply(X0,a)),
inference(superposition,[status(thm)],[c_518,c_480]) ).
tcf(c_4533,plain,
multiply(a,multiply(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_3213,c_1200]) ).
tcf(c_4543,plain,
! [X0: $i] : multiply(a,multiply(a,multiply(iPr_def_10,X0))) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1192,c_1200]) ).
tcf(c_4544,plain,
! [X0: $i] : multiply(b,multiply(b,multiply(iPr_def_11,X0))) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_1193,c_1200]) ).
tcf(c_7685,plain,
! [X0: $i] : add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1956,c_3173]) ).
tcf(c_7691,plain,
! [X0: $i] : add(multiply(additive_identity,X0),multiply(multiply(additive_identity,X0),additive_inverse(multiply(additive_identity,X0)))) = additive_identity,
inference(superposition,[status(thm)],[c_3198,c_7685]) ).
tcf(c_7700,plain,
! [X0: $i] : add(multiply(X0,additive_inverse(multiply(X0,X0))),additive_inverse(additive_identity)) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_7685,c_430]) ).
tcf(c_7721,plain,
! [X0: $i] : add(additive_inverse(additive_identity),multiply(X0,additive_inverse(multiply(X0,X0)))) = additive_inverse(X0),
inference(demodulation,[status(thm)],[c_7700,c_63]) ).
tcf(c_7722,plain,
! [X0: $i] : add(additive_identity,multiply(X0,additive_inverse(multiply(X0,X0)))) = additive_inverse(X0),
inference(light_normalisation,[status(thm)],[c_7721,c_169]) ).
tcf(c_7723,plain,
! [X0: $i] : multiply(X0,additive_inverse(multiply(X0,X0))) = additive_inverse(X0),
inference(ac_demodulation,[status(thm)],[c_7722,c_58,c_62,c_63]) ).
tcf(c_7729,plain,
! [X0: $i] : multiply(additive_identity,add(X0,multiply(X0,additive_inverse(multiply(additive_identity,X0))))) = additive_identity,
inference(demodulation,[status(thm)],[c_7691,c_60,c_64]) ).
tcf(c_7957,plain,
multiply(a,multiply(a,additive_inverse(iPr_def_10))) = additive_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_7723,c_4543]) ).
tcf(c_7959,plain,
multiply(b,multiply(b,additive_inverse(iPr_def_11))) = additive_inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_7723,c_4544]) ).
tcf(c_8442,plain,
multiply(a,add(b,multiply(a,additive_inverse(iPr_def_10)))) = add(iPr_def_10,additive_inverse(iPr_def_10)),
inference(superposition,[status(thm)],[c_7957,c_195]) ).
tcf(c_8444,plain,
multiply(a,add(b,multiply(a,additive_inverse(iPr_def_10)))) = additive_identity,
inference(demodulation,[status(thm)],[c_8442,c_59]) ).
tcf(c_8464,plain,
multiply(b,add(a,multiply(b,additive_inverse(iPr_def_11)))) = add(iPr_def_11,additive_inverse(iPr_def_11)),
inference(superposition,[status(thm)],[c_7959,c_196]) ).
tcf(c_8466,plain,
multiply(b,add(a,multiply(b,additive_inverse(iPr_def_11)))) = additive_identity,
inference(demodulation,[status(thm)],[c_8464,c_59]) ).
tcf(c_15092,plain,
! [X0: $i] : add(multiply(additive_identity,X0),additive_inverse(multiply(additive_identity,X0))) = additive_inverse(multiply(additive_identity,X0)),
inference(superposition,[status(thm)],[c_3428,c_563]) ).
tcf(c_15103,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_inverse(X1)),additive_inverse(multiply(X0,additive_identity))) = additive_inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_59,c_563]) ).
tcf(c_15173,plain,
! [X0: $i] : additive_inverse(multiply(additive_identity,X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_15092,c_59]) ).
tcf(c_15177,plain,
! [X0: $i,X1: $i] : add(additive_inverse(additive_identity),multiply(X0,additive_inverse(X1))) = additive_inverse(multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_15103,c_63,c_3173]) ).
tcf(c_15178,plain,
! [X0: $i,X1: $i] : add(additive_identity,multiply(X0,additive_inverse(X1))) = additive_inverse(multiply(X0,X1)),
inference(light_normalisation,[status(thm)],[c_15177,c_169]) ).
tcf(c_15179,plain,
! [X0: $i,X1: $i] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(ac_demodulation,[status(thm)],[c_15178,c_58,c_62,c_63]) ).
tcf(c_15319,plain,
! [X0: $i] : multiply(additive_identity,add(X0,multiply(X0,additive_identity))) = additive_identity,
inference(demodulation,[status(thm)],[c_7729,c_15173]) ).
tcf(c_15320,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_15319,c_58,c_3173]) ).
tcf(c_15912,plain,
multiply(a,additive_inverse(add(b,multiply(a,additive_inverse(iPr_def_10))))) = additive_inverse(additive_identity),
inference(superposition,[status(thm)],[c_8444,c_15179]) ).
tcf(c_15914,plain,
multiply(b,additive_inverse(add(a,multiply(b,additive_inverse(iPr_def_11))))) = additive_inverse(additive_identity),
inference(superposition,[status(thm)],[c_8466,c_15179]) ).
tcf(c_15960,plain,
multiply(b,additive_inverse(add(a,multiply(b,additive_inverse(iPr_def_11))))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_15914,c_169]) ).
tcf(c_15961,plain,
multiply(a,additive_inverse(add(b,multiply(a,additive_inverse(iPr_def_10))))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_15912,c_169]) ).
tcf(c_16353,plain,
! [X0: $i,X1: $i] : add(multiply(additive_inverse(X0),X1),additive_inverse(multiply(additive_identity,X1))) = additive_inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_59,c_565]) ).
tcf(c_16429,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(demodulation,[status(thm)],[c_16353,c_58,c_15320,c_15179]) ).
tcf(c_20369,plain,
! [X0: $i] : multiply(b,multiply(additive_inverse(add(a,multiply(b,additive_inverse(iPr_def_11)))),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_15960,c_64]) ).
tcf(c_20387,plain,
! [X0: $i] : multiply(b,multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),additive_inverse(X0))) = additive_identity,
inference(demodulation,[status(thm)],[c_20369,c_15320,c_16429]) ).
tcf(c_20417,plain,
! [X0: $i] : multiply(a,multiply(additive_inverse(add(b,multiply(a,additive_inverse(iPr_def_10)))),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_15961,c_64]) ).
tcf(c_20437,plain,
! [X0: $i] : multiply(a,multiply(add(b,multiply(a,additive_inverse(iPr_def_10))),additive_inverse(X0))) = additive_identity,
inference(demodulation,[status(thm)],[c_20417,c_15320,c_16429]) ).
tcf(c_97183,plain,
! [X0: $i] : multiply(b,multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),X0)) = additive_identity,
inference(superposition,[status(thm)],[c_259,c_20387]) ).
tcf(c_97363,plain,
multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),additive_identity) = multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),b),
inference(superposition,[status(thm)],[c_97183,c_1201]) ).
tcf(c_97369,plain,
multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),b) = additive_identity,
inference(demodulation,[status(thm)],[c_97363,c_3173]) ).
tcf(c_97436,plain,
! [X0: $i] : multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),multiply(b,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_97369,c_64]) ).
tcf(c_97452,plain,
additive_inverse(multiply(multiply(b,additive_inverse(iPr_def_11)),b)) = add(iPr_def_10,additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_97369,c_3853]) ).
tcf(c_97457,plain,
multiply(b,multiply(iPr_def_11,b)) = add(iPr_def_10,additive_inverse(additive_identity)),
inference(demodulation,[status(thm)],[c_97452,c_64,c_259,c_15179,c_16429]) ).
tcf(c_97458,plain,
multiply(b,multiply(iPr_def_11,b)) = add(iPr_def_10,additive_identity),
inference(light_normalisation,[status(thm)],[c_97457,c_169]) ).
tcf(c_97459,plain,
multiply(b,multiply(iPr_def_11,b)) = iPr_def_10,
inference(ac_demodulation,[status(thm)],[c_97458,c_58,c_62,c_63]) ).
tcf(c_97473,plain,
! [X0: $i] : multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),multiply(b,X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_97436,c_15320]) ).
tcf(c_97522,plain,
! [X0: $i] : multiply(b,multiply(multiply(iPr_def_11,b),X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_97459,c_64]) ).
tcf(c_97563,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,multiply(b,X0))) = multiply(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_97522,c_64]) ).
tcf(c_98841,plain,
multiply(b,multiply(iPr_def_11,iPr_def_11)) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_3211,c_97563]) ).
tcf(c_99690,plain,
multiply(a,multiply(iPr_def_10,a)) = multiply(iPr_def_10,multiply(iPr_def_11,iPr_def_11)),
inference(superposition,[status(thm)],[c_98841,c_1192]) ).
tcf(c_103104,plain,
! [X0: $i] : multiply(add(a,multiply(b,additive_inverse(iPr_def_11))),multiply(iPr_def_11,X0)) = additive_identity,
inference(superposition,[status(thm)],[c_4544,c_97473]) ).
tcf(c_104794,plain,
multiply(iPr_def_11,add(a,multiply(b,additive_inverse(iPr_def_11)))) = multiply(iPr_def_11,additive_identity),
inference(superposition,[status(thm)],[c_103104,c_1201]) ).
tcf(c_104799,plain,
multiply(iPr_def_11,add(a,multiply(b,additive_inverse(iPr_def_11)))) = additive_identity,
inference(demodulation,[status(thm)],[c_104794,c_3173]) ).
tcf(c_104847,plain,
additive_inverse(multiply(iPr_def_11,multiply(b,additive_inverse(iPr_def_11)))) = add(multiply(iPr_def_11,a),additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_104799,c_619]) ).
tcf(c_104883,plain,
add(additive_inverse(additive_identity),multiply(iPr_def_11,a)) = multiply(iPr_def_11,multiply(b,iPr_def_11)),
inference(demodulation,[status(thm)],[c_104847,c_63,c_259,c_15179]) ).
tcf(c_104884,plain,
add(additive_identity,multiply(iPr_def_11,a)) = multiply(iPr_def_11,multiply(b,iPr_def_11)),
inference(light_normalisation,[status(thm)],[c_104883,c_169]) ).
tcf(c_104885,plain,
multiply(iPr_def_11,multiply(b,iPr_def_11)) = multiply(iPr_def_11,a),
inference(ac_demodulation,[status(thm)],[c_104884,c_58,c_62,c_63]) ).
tcf(c_104965,plain,
multiply(a,multiply(iPr_def_11,a)) = multiply(iPr_def_10,multiply(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_104885,c_1377]) ).
tcf(c_104967,plain,
multiply(iPr_def_10,multiply(a,a)) = multiply(iPr_def_10,multiply(iPr_def_10,iPr_def_11)),
inference(demodulation,[status(thm)],[c_104965,c_1242]) ).
tcf(c_111528,plain,
! [X0: $i] : multiply(a,multiply(add(b,multiply(a,additive_inverse(iPr_def_10))),X0)) = additive_identity,
inference(superposition,[status(thm)],[c_259,c_20437]) ).
tcf(c_111892,plain,
multiply(add(b,multiply(a,additive_inverse(iPr_def_10))),additive_identity) = multiply(add(b,multiply(a,additive_inverse(iPr_def_10))),a),
inference(superposition,[status(thm)],[c_111528,c_1201]) ).
tcf(c_111899,plain,
multiply(add(b,multiply(a,additive_inverse(iPr_def_10))),a) = additive_identity,
inference(demodulation,[status(thm)],[c_111892,c_3173]) ).
tcf(c_111981,plain,
additive_inverse(multiply(multiply(a,additive_inverse(iPr_def_10)),a)) = add(multiply(b,a),additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_111899,c_621]) ).
tcf(c_111988,plain,
additive_inverse(multiply(multiply(a,additive_inverse(iPr_def_10)),a)) = add(iPr_def_11,additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_111899,c_4029]) ).
tcf(c_111994,plain,
multiply(a,multiply(iPr_def_10,a)) = add(iPr_def_11,additive_inverse(additive_identity)),
inference(demodulation,[status(thm)],[c_111988,c_64,c_259,c_15179,c_16429]) ).
tcf(c_111995,plain,
multiply(a,multiply(iPr_def_10,a)) = add(iPr_def_11,additive_identity),
inference(light_normalisation,[status(thm)],[c_111994,c_169,c_99690]) ).
tcf(c_111996,plain,
multiply(a,multiply(iPr_def_10,a)) = iPr_def_11,
inference(ac_demodulation,[status(thm)],[c_111995,c_58,c_62,c_63]) ).
tcf(c_112006,plain,
add(additive_inverse(additive_identity),multiply(b,a)) = multiply(a,multiply(iPr_def_10,a)),
inference(demodulation,[status(thm)],[c_111981,c_63,c_64,c_259,c_15179,c_16429]) ).
tcf(c_112007,plain,
multiply(iPr_def_10,multiply(iPr_def_11,iPr_def_11)) = add(additive_identity,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_112006,c_169,c_3211,c_99690]) ).
tcf(c_112008,plain,
multiply(iPr_def_10,multiply(iPr_def_11,iPr_def_11)) = add(iPr_def_11,additive_identity),
inference(theory_normalisation,[status(thm)],[c_112007,c_62,c_63]) ).
tcf(c_112009,plain,
multiply(iPr_def_10,multiply(iPr_def_11,iPr_def_11)) = iPr_def_11,
inference(ac_demodulation,[status(thm)],[c_112008,c_58,c_62,c_63]) ).
tcf(c_112319,plain,
! [X0: $i] : multiply(a,multiply(multiply(iPr_def_10,a),X0)) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_111996,c_64]) ).
tcf(c_112363,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_10,multiply(a,X0))) = multiply(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_112319,c_64]) ).
tcf(c_112424,plain,
multiply(iPr_def_10,multiply(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_112009,c_1200]) ).
tcf(c_112480,plain,
multiply(iPr_def_10,multiply(a,a)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_104967,c_112424]) ).
tcf(c_117906,plain,
multiply(a,iPr_def_11) = multiply(iPr_def_11,a),
inference(superposition,[status(thm)],[c_112480,c_112363]) ).
tcf(c_118020,plain,
multiply(iPr_def_10,a) = multiply(iPr_def_11,a),
inference(light_normalisation,[status(thm)],[c_117906,c_1217]) ).
tcf(c_118497,plain,
! [X0: $i] : add(multiply(X0,a),multiply(iPr_def_10,a)) = multiply(add(iPr_def_11,X0),a),
inference(superposition,[status(thm)],[c_118020,c_524]) ).
tcf(c_118529,plain,
! [X0: $i] : multiply(add(iPr_def_10,X0),a) = multiply(add(iPr_def_11,X0),a),
inference(demodulation,[status(thm)],[c_118497,c_524]) ).
tcf(c_125707,plain,
multiply(add(iPr_def_10,additive_inverse(iPr_def_11)),a) = multiply(additive_identity,a),
inference(superposition,[status(thm)],[c_59,c_118529]) ).
tcf(c_125788,plain,
multiply(add(iPr_def_10,additive_inverse(iPr_def_11)),a) = additive_identity,
inference(demodulation,[status(thm)],[c_125707,c_15320]) ).
tcf(c_126036,plain,
! [X0: $i] : multiply(add(iPr_def_10,additive_inverse(iPr_def_11)),multiply(a,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_125788,c_64]) ).
tcf(c_126062,plain,
! [X0: $i] : multiply(add(iPr_def_10,additive_inverse(iPr_def_11)),multiply(a,X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_126036,c_15320]) ).
tcf(c_126750,plain,
multiply(a,add(iPr_def_10,additive_inverse(iPr_def_11))) = multiply(a,additive_identity),
inference(superposition,[status(thm)],[c_126062,c_1201]) ).
tcf(c_126755,plain,
multiply(a,add(iPr_def_10,additive_inverse(iPr_def_11))) = additive_identity,
inference(demodulation,[status(thm)],[c_126750,c_3173]) ).
tcf(c_128086,plain,
add(multiply(a,iPr_def_10),additive_inverse(additive_identity)) = additive_inverse(multiply(a,additive_inverse(iPr_def_11))),
inference(superposition,[status(thm)],[c_126755,c_619]) ).
tcf(c_128140,plain,
add(additive_inverse(additive_identity),multiply(a,iPr_def_10)) = multiply(a,iPr_def_11),
inference(demodulation,[status(thm)],[c_128086,c_63,c_259,c_15179]) ).
tcf(c_128141,plain,
add(additive_identity,multiply(a,iPr_def_10)) = multiply(iPr_def_10,a),
inference(light_normalisation,[status(thm)],[c_128140,c_169,c_1217]) ).
tcf(c_128142,plain,
multiply(a,iPr_def_10) = multiply(iPr_def_10,a),
inference(ac_demodulation,[status(thm)],[c_128141,c_58,c_62,c_63]) ).
tcf(c_128193,plain,
multiply(a,multiply(iPr_def_10,a)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4533,c_128142]) ).
tcf(c_128194,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_111996,c_128193]) ).
tcf(c_128195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_128194,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 07:39:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running UEQ theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 95.83/15.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 95.83/15.29 % SZS status Started for theBenchmark.p
% 95.83/15.29 % SZS status Unsatisfiable for theBenchmark.p
% 95.83/15.29
% 95.83/15.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 95.83/15.29
% 95.83/15.29 % ------ iProver source info
% 95.83/15.29
% 95.83/15.29 % git: date: 2026-07-19 20:42:38 +0200
% 95.83/15.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 95.83/15.29 % git: non_committed_changes: false
% 95.83/15.29
% 95.83/15.29 % ------ Parsing...% successful
% 95.83/15.29
% 95.83/15.29
% 95.83/15.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 95.83/15.29
% 95.83/15.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 95.83/15.29
% 95.83/15.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 95.83/15.29
% 95.83/15.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 95.83/15.29 % ------ Proving...
% 95.83/15.29 % ------ Problem Properties
% 95.83/15.29
% 95.83/15.29 %
% 95.83/15.29 % clauses 11
% 95.83/15.29 % conjectures 1
% 95.83/15.29 % EPR 1
% 95.83/15.29 % Horn 11
% 95.83/15.29 % unary 11
% 95.83/15.29 % binary 0
% 95.83/15.29 % lits 11
% 95.83/15.29 % lits eq 11
% 95.83/15.29 % fd_pure 0
% 95.83/15.29 % fd_pseudo 0
% 95.83/15.29 % fd_cond 0
% 95.83/15.29 % fd_pseudo_cond 0
% 95.83/15.29 % AC symbols 1
% 95.83/15.29
% 95.83/15.29 % ------ Input Options Time Limit: Unbounded
% 95.83/15.29
% 95.83/15.29
% 95.83/15.29 % ------
% 95.83/15.29 % Current options:
% 95.83/15.29 % ------
% 95.83/15.29
% 95.83/15.29
% 95.83/15.29 %
% 95.83/15.29
% 95.83/15.29 % ------ Proving...
% 95.83/15.29 %
% 95.83/15.29
% 95.83/15.29 % SZS status Unsatisfiable for theBenchmark.p
% 95.83/15.29
% 95.83/15.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 95.83/15.29
% 95.83/15.29
%------------------------------------------------------------------------------