TSTP Solution File: RNG009-5 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:57:14 EDT 2024
% Result : Unsatisfiable 255.86s 33.06s
% Output : CNFRefutation 255.86s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(c_50,plain,
add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
cnf(c_51,plain,
add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
cnf(c_52,plain,
add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
cnf(c_53,plain,
add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
cnf(c_54,plain,
add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
cnf(c_55,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
cnf(c_56,plain,
multiply(X0,multiply(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_x) ).
cnf(c_57,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_88,plain,
multiply(a,b) = sP0_iProver_def,
definition ).
cnf(c_89,plain,
multiply(b,a) = sP1_iProver_def,
definition ).
cnf(c_90,negated_conjecture,
sP0_iProver_def != sP1_iProver_def,
inference(demodulation,[status(thm)],[c_57,c_89,c_88]) ).
cnf(c_91,plain,
X0 = X0,
theory(equality) ).
cnf(c_92,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_139,plain,
add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_53,c_54]) ).
cnf(c_142,plain,
add(additive_identity,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_54]) ).
cnf(c_150,plain,
additive_inverse(additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_142,c_50]) ).
cnf(c_160,plain,
add(X0,add(X1,additive_inverse(X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_50,c_139]) ).
cnf(c_173,plain,
add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_53,c_50]) ).
cnf(c_177,plain,
multiply(X0,multiply(multiply(X0,X0),X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_56,c_55]) ).
cnf(c_178,plain,
multiply(a,multiply(b,X0)) = multiply(sP0_iProver_def,X0),
inference(superposition,[status(thm)],[c_88,c_55]) ).
cnf(c_179,plain,
multiply(b,multiply(a,X0)) = multiply(sP1_iProver_def,X0),
inference(superposition,[status(thm)],[c_89,c_55]) ).
cnf(c_180,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(X0,X1)))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
cnf(c_190,plain,
multiply(X0,add(multiply(X0,X0),X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_56,c_51]) ).
cnf(c_191,plain,
add(sP0_iProver_def,multiply(a,X0)) = multiply(a,add(b,X0)),
inference(superposition,[status(thm)],[c_88,c_51]) ).
cnf(c_192,plain,
add(sP1_iProver_def,multiply(b,X0)) = multiply(b,add(a,X0)),
inference(superposition,[status(thm)],[c_89,c_51]) ).
cnf(c_195,plain,
add(multiply(a,X0),sP0_iProver_def) = multiply(a,add(X0,b)),
inference(superposition,[status(thm)],[c_88,c_51]) ).
cnf(c_196,plain,
add(multiply(b,X0),sP1_iProver_def) = multiply(b,add(X0,a)),
inference(superposition,[status(thm)],[c_89,c_51]) ).
cnf(c_202,plain,
add(sP1_iProver_def,multiply(b,X0)) = multiply(b,add(X0,a)),
inference(theory_normalisation,[status(thm)],[c_196,c_53,c_54]) ).
cnf(c_203,plain,
add(sP0_iProver_def,multiply(a,X0)) = multiply(a,add(X0,b)),
inference(theory_normalisation,[status(thm)],[c_195,c_53,c_54]) ).
cnf(c_219,plain,
sP1_iProver_def = sP1_iProver_def,
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_234,plain,
multiply(sP0_iProver_def,multiply(b,b)) = multiply(a,b),
inference(superposition,[status(thm)],[c_56,c_178]) ).
cnf(c_235,plain,
multiply(a,sP1_iProver_def) = multiply(sP0_iProver_def,a),
inference(superposition,[status(thm)],[c_89,c_178]) ).
cnf(c_238,plain,
add(multiply(a,X0),multiply(sP0_iProver_def,X1)) = multiply(a,add(X0,multiply(b,X1))),
inference(superposition,[status(thm)],[c_178,c_51]) ).
cnf(c_239,plain,
multiply(sP0_iProver_def,multiply(b,b)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_234,c_88]) ).
cnf(c_250,plain,
multiply(sP0_iProver_def,add(multiply(b,b),X0)) = add(sP0_iProver_def,multiply(sP0_iProver_def,X0)),
inference(superposition,[status(thm)],[c_239,c_51]) ).
cnf(c_260,plain,
multiply(sP1_iProver_def,multiply(a,a)) = multiply(b,a),
inference(superposition,[status(thm)],[c_56,c_179]) ).
cnf(c_261,plain,
multiply(b,sP0_iProver_def) = multiply(sP1_iProver_def,b),
inference(superposition,[status(thm)],[c_88,c_179]) ).
cnf(c_262,plain,
multiply(b,multiply(sP0_iProver_def,X0)) = multiply(sP1_iProver_def,multiply(b,X0)),
inference(superposition,[status(thm)],[c_178,c_179]) ).
cnf(c_267,plain,
multiply(a,multiply(sP1_iProver_def,X0)) = multiply(sP0_iProver_def,multiply(a,X0)),
inference(superposition,[status(thm)],[c_179,c_178]) ).
cnf(c_268,plain,
multiply(sP1_iProver_def,multiply(a,a)) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_260,c_89]) ).
cnf(c_285,plain,
multiply(a,multiply(sP1_iProver_def,b)) = multiply(sP0_iProver_def,sP0_iProver_def),
inference(superposition,[status(thm)],[c_261,c_178]) ).
cnf(c_299,plain,
multiply(sP1_iProver_def,add(multiply(a,a),X0)) = add(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_268,c_51]) ).
cnf(c_318,plain,
add(X0,add(X1,additive_inverse(X0))) = X1,
inference(demodulation,[status(thm)],[c_160,c_49]) ).
cnf(c_326,plain,
add(X0,add(additive_inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_54,c_318]) ).
cnf(c_359,plain,
multiply(X0,multiply(X0,multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_177,c_55]) ).
cnf(c_361,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(multiply(X0,X1),X2)))) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c_55,c_359]) ).
cnf(c_375,plain,
multiply(sP0_iProver_def,multiply(b,multiply(b,X0))) = multiply(a,multiply(b,X0)),
inference(superposition,[status(thm)],[c_359,c_178]) ).
cnf(c_376,plain,
multiply(sP1_iProver_def,multiply(a,multiply(a,X0))) = multiply(b,multiply(a,X0)),
inference(superposition,[status(thm)],[c_359,c_179]) ).
cnf(c_377,plain,
multiply(sP1_iProver_def,multiply(a,multiply(a,X0))) = multiply(sP1_iProver_def,X0),
inference(light_normalisation,[status(thm)],[c_376,c_179]) ).
cnf(c_378,plain,
multiply(sP0_iProver_def,multiply(b,multiply(b,X0))) = multiply(sP0_iProver_def,X0),
inference(light_normalisation,[status(thm)],[c_375,c_178]) ).
cnf(c_416,plain,
add(multiply(X0,multiply(X1,X2)),multiply(X3,X2)) = multiply(add(multiply(X0,X1),X3),X2),
inference(superposition,[status(thm)],[c_55,c_52]) ).
cnf(c_418,plain,
add(sP0_iProver_def,multiply(X0,b)) = multiply(add(a,X0),b),
inference(superposition,[status(thm)],[c_88,c_52]) ).
cnf(c_419,plain,
add(sP1_iProver_def,multiply(X0,a)) = multiply(add(b,X0),a),
inference(superposition,[status(thm)],[c_89,c_52]) ).
cnf(c_429,plain,
add(multiply(X0,b),sP0_iProver_def) = multiply(add(X0,a),b),
inference(superposition,[status(thm)],[c_88,c_52]) ).
cnf(c_430,plain,
add(multiply(X0,a),sP1_iProver_def) = multiply(add(X0,b),a),
inference(superposition,[status(thm)],[c_89,c_52]) ).
cnf(c_439,plain,
multiply(add(X0,X0),X1) = multiply(X0,add(X1,X1)),
inference(superposition,[status(thm)],[c_52,c_51]) ).
cnf(c_444,plain,
add(sP1_iProver_def,multiply(X0,a)) = multiply(add(X0,b),a),
inference(theory_normalisation,[status(thm)],[c_430,c_53,c_54]) ).
cnf(c_445,plain,
add(sP0_iProver_def,multiply(X0,b)) = multiply(add(X0,a),b),
inference(theory_normalisation,[status(thm)],[c_429,c_53,c_54]) ).
cnf(c_537,plain,
sP0_iProver_def = sP0_iProver_def,
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_538,plain,
( X0 != X1
| sP0_iProver_def != X1
| sP0_iProver_def = X0 ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_604,plain,
add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_50,c_326]) ).
cnf(c_621,plain,
additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_604,c_49]) ).
cnf(c_708,plain,
add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_173,c_326]) ).
cnf(c_748,plain,
multiply(a,add(b,b)) = add(sP0_iProver_def,sP0_iProver_def),
inference(superposition,[status(thm)],[c_88,c_191]) ).
cnf(c_749,plain,
multiply(a,add(b,multiply(b,X0))) = add(sP0_iProver_def,multiply(sP0_iProver_def,X0)),
inference(superposition,[status(thm)],[c_178,c_191]) ).
cnf(c_756,plain,
add(X0,multiply(a,add(b,X1))) = add(sP0_iProver_def,add(X0,multiply(a,X1))),
inference(superposition,[status(thm)],[c_191,c_139]) ).
cnf(c_823,plain,
multiply(a,multiply(add(b,b),X0)) = multiply(add(sP0_iProver_def,sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_748,c_55]) ).
cnf(c_846,plain,
multiply(b,add(a,multiply(a,X0))) = add(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_179,c_192]) ).
cnf(c_877,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_180,c_55]) ).
cnf(c_921,plain,
multiply(sP1_iProver_def,multiply(X0,multiply(a,multiply(X0,multiply(a,X0))))) = multiply(b,multiply(a,X0)),
inference(superposition,[status(thm)],[c_877,c_179]) ).
cnf(c_941,plain,
multiply(sP1_iProver_def,multiply(X0,multiply(a,multiply(X0,multiply(a,X0))))) = multiply(sP1_iProver_def,X0),
inference(light_normalisation,[status(thm)],[c_921,c_179]) ).
cnf(c_1554,plain,
multiply(a,multiply(add(b,b),X0)) = multiply(sP0_iProver_def,add(X0,X0)),
inference(superposition,[status(thm)],[c_439,c_178]) ).
cnf(c_1764,plain,
add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_708,c_49]) ).
cnf(c_1771,plain,
add(X0,additive_inverse(add(X0,additive_inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_54,c_1764]) ).
cnf(c_1778,plain,
add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_621,c_1764]) ).
cnf(c_1824,plain,
( X0 != sP0_iProver_def
| sP0_iProver_def != sP0_iProver_def
| sP0_iProver_def = X0 ),
inference(instantiation,[status(thm)],[c_538]) ).
cnf(c_1846,plain,
add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_621,c_1771]) ).
cnf(c_1873,plain,
add(multiply(X0,X1),additive_inverse(multiply(add(X2,X0),X1))) = additive_inverse(multiply(X2,X1)),
inference(superposition,[status(thm)],[c_52,c_1778]) ).
cnf(c_2005,plain,
add(multiply(X0,X1),additive_inverse(multiply(X0,add(X1,X2)))) = additive_inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c_51,c_1846]) ).
cnf(c_2015,plain,
add(sP0_iProver_def,additive_inverse(multiply(a,add(X0,b)))) = additive_inverse(multiply(a,X0)),
inference(superposition,[status(thm)],[c_203,c_1846]) ).
cnf(c_2016,plain,
add(sP0_iProver_def,additive_inverse(multiply(a,add(b,X0)))) = additive_inverse(multiply(a,X0)),
inference(superposition,[status(thm)],[c_191,c_1846]) ).
cnf(c_2017,plain,
add(sP1_iProver_def,additive_inverse(multiply(b,add(X0,a)))) = additive_inverse(multiply(b,X0)),
inference(superposition,[status(thm)],[c_202,c_1846]) ).
cnf(c_2018,plain,
add(sP1_iProver_def,additive_inverse(multiply(b,add(a,X0)))) = additive_inverse(multiply(b,X0)),
inference(superposition,[status(thm)],[c_192,c_1846]) ).
cnf(c_2019,plain,
add(sP0_iProver_def,additive_inverse(multiply(add(X0,a),b))) = additive_inverse(multiply(X0,b)),
inference(superposition,[status(thm)],[c_445,c_1846]) ).
cnf(c_2020,plain,
add(sP0_iProver_def,additive_inverse(multiply(add(a,X0),b))) = additive_inverse(multiply(X0,b)),
inference(superposition,[status(thm)],[c_418,c_1846]) ).
cnf(c_2021,plain,
add(sP1_iProver_def,additive_inverse(multiply(add(X0,b),a))) = additive_inverse(multiply(X0,a)),
inference(superposition,[status(thm)],[c_444,c_1846]) ).
cnf(c_2022,plain,
add(sP1_iProver_def,additive_inverse(multiply(add(b,X0),a))) = additive_inverse(multiply(X0,a)),
inference(superposition,[status(thm)],[c_419,c_1846]) ).
cnf(c_2351,plain,
multiply(X0,multiply(X0,X0)) = add(X0,multiply(X0,additive_identity)),
inference(superposition,[status(thm)],[c_49,c_190]) ).
cnf(c_2352,plain,
add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_50,c_190]) ).
cnf(c_2355,plain,
add(X0,multiply(X0,multiply(X1,X0))) = multiply(X0,multiply(add(X0,X1),X0)),
inference(superposition,[status(thm)],[c_52,c_190]) ).
cnf(c_2386,plain,
add(X0,multiply(X0,additive_identity)) = X0,
inference(light_normalisation,[status(thm)],[c_2351,c_56]) ).
cnf(c_2509,plain,
add(X0,add(multiply(X0,additive_identity),X1)) = add(X0,X1),
inference(superposition,[status(thm)],[c_2386,c_53]) ).
cnf(c_2516,plain,
add(X0,additive_inverse(X0)) = multiply(additive_inverse(X0),additive_identity),
inference(superposition,[status(thm)],[c_2386,c_326]) ).
cnf(c_2518,plain,
multiply(additive_inverse(X0),additive_identity) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2516,c_50]) ).
cnf(c_2568,plain,
add(X0,additive_inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_2509,c_318]) ).
cnf(c_2573,plain,
multiply(X0,additive_identity) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2568,c_50]) ).
cnf(c_2650,plain,
add(additive_identity,multiply(X0,X1)) = multiply(X0,add(additive_identity,X1)),
inference(superposition,[status(thm)],[c_2573,c_51]) ).
cnf(c_2660,plain,
multiply(a,additive_identity) = multiply(sP0_iProver_def,additive_identity),
inference(superposition,[status(thm)],[c_2573,c_178]) ).
cnf(c_2664,plain,
multiply(a,add(b,additive_identity)) = add(sP0_iProver_def,additive_identity),
inference(superposition,[status(thm)],[c_2573,c_191]) ).
cnf(c_2665,plain,
multiply(b,additive_identity) = multiply(sP1_iProver_def,additive_identity),
inference(superposition,[status(thm)],[c_2573,c_179]) ).
cnf(c_2667,plain,
multiply(a,add(additive_identity,b)) = add(sP0_iProver_def,additive_identity),
inference(theory_normalisation,[status(thm)],[c_2664,c_53,c_54]) ).
cnf(c_3586,plain,
add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2352,c_2573]) ).
cnf(c_3594,plain,
additive_inverse(multiply(X0,additive_inverse(multiply(X0,X0)))) = add(X0,additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_3586,c_1846]) ).
cnf(c_3610,plain,
additive_inverse(multiply(X0,additive_inverse(multiply(X0,X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_3594,c_49,c_150]) ).
cnf(c_3661,plain,
multiply(X0,additive_inverse(multiply(X0,X0))) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_3610,c_621]) ).
cnf(c_3722,plain,
multiply(X0,multiply(X0,additive_inverse(X0))) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_3661,c_359]) ).
cnf(c_3724,plain,
multiply(X0,multiply(additive_inverse(multiply(X0,X0)),X1)) = multiply(additive_inverse(X0),X1),
inference(superposition,[status(thm)],[c_3661,c_55]) ).
cnf(c_3731,plain,
multiply(sP0_iProver_def,additive_inverse(multiply(b,b))) = multiply(sP0_iProver_def,multiply(b,additive_inverse(b))),
inference(superposition,[status(thm)],[c_3661,c_378]) ).
cnf(c_3734,plain,
multiply(sP0_iProver_def,additive_inverse(multiply(b,b))) = multiply(a,additive_inverse(b)),
inference(superposition,[status(thm)],[c_3661,c_178]) ).
cnf(c_3737,plain,
multiply(sP1_iProver_def,additive_inverse(multiply(a,a))) = multiply(sP1_iProver_def,multiply(a,additive_inverse(a))),
inference(superposition,[status(thm)],[c_3661,c_377]) ).
cnf(c_3838,plain,
multiply(additive_inverse(X0),multiply(additive_inverse(X0),X0)) = X0,
inference(superposition,[status(thm)],[c_621,c_3722]) ).
cnf(c_3855,plain,
multiply(sP0_iProver_def,multiply(b,additive_inverse(b))) = multiply(a,additive_inverse(b)),
inference(superposition,[status(thm)],[c_3722,c_178]) ).
cnf(c_3860,plain,
multiply(sP1_iProver_def,multiply(a,additive_inverse(a))) = multiply(b,additive_inverse(a)),
inference(superposition,[status(thm)],[c_3722,c_179]) ).
cnf(c_5437,plain,
add(sP0_iProver_def,multiply(sP0_iProver_def,additive_identity)) = multiply(sP0_iProver_def,multiply(b,b)),
inference(superposition,[status(thm)],[c_49,c_250]) ).
cnf(c_5438,plain,
add(sP0_iProver_def,multiply(sP0_iProver_def,additive_inverse(multiply(b,b)))) = multiply(sP0_iProver_def,additive_identity),
inference(superposition,[status(thm)],[c_50,c_250]) ).
cnf(c_5468,plain,
add(sP0_iProver_def,multiply(sP0_iProver_def,additive_identity)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_5437,c_239]) ).
cnf(c_5469,plain,
add(sP0_iProver_def,multiply(a,additive_inverse(b))) = multiply(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_5438,c_3731,c_3855]) ).
cnf(c_6071,plain,
multiply(a,add(X0,multiply(b,multiply(sP0_iProver_def,sP0_iProver_def)))) = add(multiply(a,X0),sP0_iProver_def),
inference(superposition,[status(thm)],[c_56,c_238]) ).
cnf(c_6109,plain,
multiply(a,add(X0,multiply(b,multiply(sP0_iProver_def,sP0_iProver_def)))) = add(sP0_iProver_def,multiply(a,X0)),
inference(theory_normalisation,[status(thm)],[c_6071,c_53,c_54]) ).
cnf(c_6110,plain,
multiply(a,add(X0,multiply(b,multiply(sP0_iProver_def,sP0_iProver_def)))) = multiply(a,add(b,X0)),
inference(light_normalisation,[status(thm)],[c_6109,c_191]) ).
cnf(c_6202,plain,
( add(sP0_iProver_def,additive_identity) != sP0_iProver_def
| sP0_iProver_def != sP0_iProver_def
| sP0_iProver_def = add(sP0_iProver_def,additive_identity) ),
inference(instantiation,[status(thm)],[c_1824]) ).
cnf(c_6203,plain,
add(sP0_iProver_def,additive_identity) = sP0_iProver_def,
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_6442,plain,
add(sP1_iProver_def,multiply(sP1_iProver_def,additive_identity)) = multiply(sP1_iProver_def,multiply(a,a)),
inference(superposition,[status(thm)],[c_49,c_299]) ).
cnf(c_6443,plain,
add(sP1_iProver_def,multiply(sP1_iProver_def,additive_inverse(multiply(a,a)))) = multiply(sP1_iProver_def,additive_identity),
inference(superposition,[status(thm)],[c_50,c_299]) ).
cnf(c_6474,plain,
add(sP1_iProver_def,multiply(sP1_iProver_def,additive_identity)) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_6442,c_268]) ).
cnf(c_6475,plain,
add(sP1_iProver_def,multiply(b,additive_inverse(a))) = multiply(sP1_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_6443,c_3737,c_3860]) ).
cnf(c_8695,plain,
add(sP0_iProver_def,multiply(sP0_iProver_def,multiply(b,additive_inverse(b)))) = multiply(a,add(b,additive_inverse(b))),
inference(superposition,[status(thm)],[c_3722,c_749]) ).
cnf(c_8725,plain,
multiply(a,add(b,additive_inverse(b))) = multiply(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_8695,c_3855,c_5469]) ).
cnf(c_8795,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))))) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_361,c_55]) ).
cnf(c_8825,plain,
multiply(sP0_iProver_def,multiply(b,multiply(sP0_iProver_def,multiply(b,sP0_iProver_def)))) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_239,c_8795]) ).
cnf(c_8827,plain,
multiply(sP1_iProver_def,multiply(a,multiply(sP1_iProver_def,multiply(a,sP1_iProver_def)))) = sP1_iProver_def,
inference(superposition,[status(thm)],[c_268,c_8795]) ).
cnf(c_8957,plain,
multiply(sP1_iProver_def,multiply(a,multiply(sP1_iProver_def,multiply(sP0_iProver_def,a)))) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_8827,c_235]) ).
cnf(c_8958,plain,
multiply(sP0_iProver_def,multiply(b,multiply(sP0_iProver_def,multiply(sP1_iProver_def,b)))) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_8825,c_261]) ).
cnf(c_9847,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,multiply(a,multiply(sP0_iProver_def,a)))) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_8957,c_267]) ).
cnf(c_9887,plain,
multiply(sP0_iProver_def,multiply(sP1_iProver_def,multiply(b,multiply(sP1_iProver_def,b)))) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_8958,c_262]) ).
cnf(c_9901,plain,
multiply(sP0_iProver_def,multiply(sP1_iProver_def,multiply(sP0_iProver_def,multiply(sP1_iProver_def,sP0_iProver_def)))) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_9887,c_8795]) ).
cnf(c_10200,plain,
add(sP1_iProver_def,multiply(sP1_iProver_def,multiply(a,additive_inverse(a)))) = multiply(b,add(a,additive_inverse(a))),
inference(superposition,[status(thm)],[c_3722,c_846]) ).
cnf(c_10233,plain,
multiply(b,add(a,additive_inverse(a))) = multiply(sP1_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_10200,c_3860,c_6475]) ).
cnf(c_10856,plain,
multiply(sP0_iProver_def,add(X0,X0)) = multiply(add(sP0_iProver_def,sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_1554,c_823]) ).
cnf(c_11684,plain,
multiply(sP0_iProver_def,add(additive_identity,additive_identity)) = additive_identity,
inference(superposition,[status(thm)],[c_10856,c_2573]) ).
cnf(c_13847,plain,
add(sP0_iProver_def,additive_inverse(multiply(a,b))) = additive_inverse(multiply(a,additive_identity)),
inference(superposition,[status(thm)],[c_142,c_2015]) ).
cnf(c_13862,plain,
add(sP0_iProver_def,additive_inverse(sP0_iProver_def)) = additive_inverse(multiply(sP0_iProver_def,additive_identity)),
inference(light_normalisation,[status(thm)],[c_13847,c_88,c_2660]) ).
cnf(c_13909,plain,
add(sP0_iProver_def,additive_inverse(multiply(a,additive_identity))) = additive_inverse(multiply(a,additive_inverse(b))),
inference(superposition,[status(thm)],[c_50,c_2016]) ).
cnf(c_13942,plain,
add(sP0_iProver_def,add(sP0_iProver_def,additive_inverse(sP0_iProver_def))) = additive_inverse(multiply(a,additive_inverse(b))),
inference(light_normalisation,[status(thm)],[c_13909,c_2660,c_13862]) ).
cnf(c_14650,plain,
additive_inverse(multiply(a,additive_inverse(b))) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_13942,c_318]) ).
cnf(c_14657,plain,
multiply(a,additive_inverse(b)) = additive_inverse(sP0_iProver_def),
inference(superposition,[status(thm)],[c_14650,c_621]) ).
cnf(c_14673,plain,
multiply(sP0_iProver_def,additive_inverse(multiply(b,b))) = additive_inverse(sP0_iProver_def),
inference(demodulation,[status(thm)],[c_3734,c_14657]) ).
cnf(c_14740,plain,
multiply(a,multiply(additive_inverse(b),X0)) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_14657,c_55]) ).
cnf(c_14751,plain,
multiply(a,add(b,additive_inverse(b))) = add(sP0_iProver_def,additive_inverse(sP0_iProver_def)),
inference(superposition,[status(thm)],[c_14657,c_191]) ).
cnf(c_14755,plain,
add(sP0_iProver_def,additive_inverse(sP0_iProver_def)) = multiply(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_14751,c_8725]) ).
cnf(c_14828,plain,
multiply(sP0_iProver_def,multiply(additive_inverse(multiply(b,b)),X0)) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_14673,c_55]) ).
cnf(c_15016,plain,
multiply(additive_inverse(sP0_iProver_def),multiply(additive_inverse(b),b)) = multiply(a,b),
inference(superposition,[status(thm)],[c_3838,c_14740]) ).
cnf(c_15039,plain,
multiply(b,multiply(additive_inverse(sP0_iProver_def),X0)) = multiply(sP1_iProver_def,multiply(additive_inverse(b),X0)),
inference(superposition,[status(thm)],[c_14740,c_179]) ).
cnf(c_15051,plain,
multiply(additive_inverse(sP0_iProver_def),multiply(additive_inverse(b),b)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_15016,c_88]) ).
cnf(c_15183,plain,
multiply(add(multiply(X0,X0),X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_56,c_416]) ).
cnf(c_15188,plain,
multiply(add(multiply(sP1_iProver_def,a),X0),a) = add(sP1_iProver_def,multiply(X0,a)),
inference(superposition,[status(thm)],[c_268,c_416]) ).
cnf(c_15449,plain,
multiply(add(multiply(sP1_iProver_def,a),X0),a) = multiply(add(b,X0),a),
inference(light_normalisation,[status(thm)],[c_15188,c_419]) ).
cnf(c_21199,plain,
add(sP1_iProver_def,additive_inverse(multiply(b,a))) = additive_inverse(multiply(b,additive_identity)),
inference(superposition,[status(thm)],[c_142,c_2017]) ).
cnf(c_21215,plain,
add(sP1_iProver_def,additive_inverse(sP1_iProver_def)) = additive_inverse(multiply(sP1_iProver_def,additive_identity)),
inference(light_normalisation,[status(thm)],[c_21199,c_89,c_2665]) ).
cnf(c_21291,plain,
add(sP1_iProver_def,additive_inverse(multiply(b,additive_identity))) = additive_inverse(multiply(b,additive_inverse(a))),
inference(superposition,[status(thm)],[c_50,c_2018]) ).
cnf(c_21327,plain,
add(sP1_iProver_def,add(sP1_iProver_def,additive_inverse(sP1_iProver_def))) = additive_inverse(multiply(b,additive_inverse(a))),
inference(light_normalisation,[status(thm)],[c_21291,c_2665,c_21215]) ).
cnf(c_22955,plain,
additive_inverse(multiply(b,additive_inverse(a))) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_21327,c_318]) ).
cnf(c_22963,plain,
multiply(b,additive_inverse(a)) = additive_inverse(sP1_iProver_def),
inference(superposition,[status(thm)],[c_22955,c_621]) ).
cnf(c_22996,plain,
multiply(b,multiply(additive_inverse(a),X0)) = multiply(additive_inverse(sP1_iProver_def),X0),
inference(superposition,[status(thm)],[c_22963,c_55]) ).
cnf(c_23009,plain,
multiply(b,add(a,additive_inverse(a))) = add(sP1_iProver_def,additive_inverse(sP1_iProver_def)),
inference(superposition,[status(thm)],[c_22963,c_192]) ).
cnf(c_23014,plain,
add(sP1_iProver_def,additive_inverse(sP1_iProver_def)) = multiply(sP1_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_23009,c_10233]) ).
cnf(c_25317,plain,
multiply(multiply(X0,X0),X0) = add(X0,multiply(additive_identity,X0)),
inference(superposition,[status(thm)],[c_49,c_15183]) ).
cnf(c_25318,plain,
add(X0,multiply(additive_inverse(multiply(X0,X0)),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_50,c_15183]) ).
cnf(c_25589,plain,
add(X0,multiply(additive_identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_25317,c_55,c_56]) ).
cnf(c_25614,plain,
add(X0,additive_inverse(X0)) = additive_inverse(multiply(additive_identity,X0)),
inference(superposition,[status(thm)],[c_25589,c_1846]) ).
cnf(c_25628,plain,
add(X0,additive_inverse(X0)) = multiply(additive_identity,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_25589,c_326]) ).
cnf(c_25645,plain,
multiply(additive_identity,additive_inverse(X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_25628,c_50]) ).
cnf(c_25647,plain,
additive_inverse(multiply(additive_identity,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_25614,c_50]) ).
cnf(c_25754,plain,
multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_621,c_25645]) ).
cnf(c_25815,plain,
add(multiply(X0,X1),additive_identity) = multiply(add(X0,additive_identity),X1),
inference(superposition,[status(thm)],[c_25754,c_52]) ).
cnf(c_25879,plain,
add(additive_identity,multiply(X0,X1)) = multiply(add(X0,additive_identity),X1),
inference(theory_normalisation,[status(thm)],[c_25815,c_53,c_54]) ).
cnf(c_25880,plain,
multiply(X0,add(additive_identity,X1)) = multiply(X0,X1),
inference(light_normalisation,[status(thm)],[c_25879,c_49,c_2650]) ).
cnf(c_27539,plain,
add(X0,multiply(additive_inverse(multiply(X0,X0)),X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_25318,c_25754]) ).
cnf(c_27549,plain,
additive_inverse(multiply(additive_inverse(multiply(X0,X0)),X0)) = add(X0,additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_27539,c_1846]) ).
cnf(c_27584,plain,
additive_inverse(multiply(additive_inverse(multiply(X0,X0)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_27549,c_49,c_150]) ).
cnf(c_27674,plain,
multiply(additive_inverse(multiply(X0,X0)),X0) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_27584,c_621]) ).
cnf(c_27744,plain,
multiply(additive_inverse(multiply(X0,X0)),multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(superposition,[status(thm)],[c_27674,c_55]) ).
cnf(c_27766,plain,
multiply(additive_inverse(X0),X0) = multiply(X0,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_27674,c_3724]) ).
cnf(c_27777,plain,
multiply(additive_inverse(X0),multiply(X0,additive_inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_3838,c_27766]) ).
cnf(c_27779,plain,
multiply(additive_inverse(sP0_iProver_def),multiply(b,additive_inverse(b))) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_15051,c_27766]) ).
cnf(c_27954,plain,
multiply(multiply(X0,additive_inverse(X0)),X1) = multiply(additive_inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c_27766,c_55]) ).
cnf(c_33178,plain,
add(sP0_iProver_def,additive_inverse(multiply(a,b))) = additive_inverse(multiply(additive_identity,b)),
inference(superposition,[status(thm)],[c_142,c_2019]) ).
cnf(c_33197,plain,
additive_inverse(multiply(additive_identity,b)) = multiply(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_33178,c_88,c_14755]) ).
cnf(c_33245,plain,
add(sP0_iProver_def,additive_inverse(multiply(additive_identity,b))) = additive_inverse(multiply(additive_inverse(a),b)),
inference(superposition,[status(thm)],[c_50,c_2020]) ).
cnf(c_33286,plain,
additive_inverse(multiply(additive_inverse(a),b)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_33245,c_5468,c_33197]) ).
cnf(c_33371,plain,
multiply(additive_inverse(a),b) = additive_inverse(sP0_iProver_def),
inference(superposition,[status(thm)],[c_33286,c_621]) ).
cnf(c_33419,plain,
multiply(additive_inverse(a),multiply(b,X0)) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_33371,c_55]) ).
cnf(c_33614,plain,
multiply(additive_inverse(sP0_iProver_def),multiply(b,additive_inverse(b))) = multiply(additive_inverse(a),additive_inverse(b)),
inference(superposition,[status(thm)],[c_3722,c_33419]) ).
cnf(c_33665,plain,
multiply(additive_inverse(a),additive_inverse(b)) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_33614,c_27779]) ).
cnf(c_34010,plain,
multiply(additive_inverse(sP1_iProver_def),additive_inverse(b)) = multiply(b,sP0_iProver_def),
inference(superposition,[status(thm)],[c_33665,c_22996]) ).
cnf(c_34011,plain,
multiply(additive_inverse(sP1_iProver_def),additive_inverse(b)) = multiply(sP1_iProver_def,b),
inference(light_normalisation,[status(thm)],[c_34010,c_261]) ).
cnf(c_35313,plain,
multiply(additive_inverse(multiply(b,b)),sP1_iProver_def) = multiply(additive_inverse(b),a),
inference(superposition,[status(thm)],[c_89,c_27744]) ).
cnf(c_35378,plain,
multiply(additive_inverse(multiply(X0,X0)),additive_inverse(X0)) = multiply(additive_inverse(X0),multiply(X0,additive_inverse(X0))),
inference(superposition,[status(thm)],[c_3722,c_27744]) ).
cnf(c_35486,plain,
multiply(additive_inverse(X0),multiply(X0,X1)) = multiply(X0,multiply(additive_inverse(X0),X1)),
inference(superposition,[status(thm)],[c_27744,c_3724]) ).
cnf(c_35510,plain,
multiply(additive_inverse(multiply(X0,X0)),additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_35378,c_27777]) ).
cnf(c_35980,plain,
multiply(sP0_iProver_def,multiply(additive_inverse(b),a)) = multiply(additive_inverse(sP0_iProver_def),sP1_iProver_def),
inference(superposition,[status(thm)],[c_35313,c_14828]) ).
cnf(c_36484,plain,
multiply(additive_inverse(X0),additive_inverse(X0)) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_35510,c_3724]) ).
cnf(c_38391,plain,
add(sP1_iProver_def,additive_inverse(multiply(b,a))) = additive_inverse(multiply(additive_identity,a)),
inference(superposition,[status(thm)],[c_142,c_2021]) ).
cnf(c_38410,plain,
additive_inverse(multiply(additive_identity,a)) = multiply(sP1_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_38391,c_89,c_23014]) ).
cnf(c_38440,plain,
add(sP1_iProver_def,additive_inverse(multiply(additive_identity,a))) = additive_inverse(multiply(additive_inverse(b),a)),
inference(superposition,[status(thm)],[c_50,c_2022]) ).
cnf(c_38482,plain,
additive_inverse(multiply(additive_inverse(b),a)) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_38440,c_6474,c_38410]) ).
cnf(c_38659,plain,
multiply(additive_inverse(b),a) = additive_inverse(sP1_iProver_def),
inference(superposition,[status(thm)],[c_38482,c_621]) ).
cnf(c_38674,plain,
multiply(additive_inverse(sP0_iProver_def),sP1_iProver_def) = multiply(sP0_iProver_def,additive_inverse(sP1_iProver_def)),
inference(demodulation,[status(thm)],[c_35980,c_38659]) ).
cnf(c_38699,plain,
multiply(additive_inverse(b),multiply(a,X0)) = multiply(additive_inverse(sP1_iProver_def),X0),
inference(superposition,[status(thm)],[c_38659,c_55]) ).
cnf(c_38857,plain,
multiply(additive_inverse(b),additive_inverse(sP0_iProver_def)) = multiply(additive_inverse(sP1_iProver_def),additive_inverse(b)),
inference(superposition,[status(thm)],[c_14657,c_38699]) ).
cnf(c_38907,plain,
multiply(additive_inverse(b),additive_inverse(sP0_iProver_def)) = multiply(sP1_iProver_def,b),
inference(light_normalisation,[status(thm)],[c_38857,c_34011]) ).
cnf(c_70858,plain,
multiply(sP1_iProver_def,multiply(additive_inverse(b),additive_inverse(sP0_iProver_def))) = multiply(b,multiply(sP0_iProver_def,sP0_iProver_def)),
inference(superposition,[status(thm)],[c_36484,c_15039]) ).
cnf(c_70933,plain,
multiply(b,multiply(sP0_iProver_def,sP0_iProver_def)) = multiply(sP1_iProver_def,multiply(sP1_iProver_def,b)),
inference(light_normalisation,[status(thm)],[c_70858,c_38907]) ).
cnf(c_76721,plain,
multiply(add(b,additive_inverse(multiply(sP1_iProver_def,a))),a) = multiply(additive_identity,a),
inference(superposition,[status(thm)],[c_50,c_15449]) ).
cnf(c_76966,plain,
multiply(add(b,additive_inverse(multiply(sP1_iProver_def,a))),a) = additive_identity,
inference(demodulation,[status(thm)],[c_76721,c_25754]) ).
cnf(c_76978,plain,
multiply(add(b,additive_inverse(multiply(sP1_iProver_def,a))),multiply(a,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_76966,c_55]) ).
cnf(c_77005,plain,
multiply(add(b,additive_inverse(multiply(sP1_iProver_def,a))),multiply(a,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_76978,c_25754]) ).
cnf(c_77609,plain,
multiply(a,add(b,additive_inverse(multiply(sP1_iProver_def,a)))) = multiply(a,additive_identity),
inference(superposition,[status(thm)],[c_77005,c_877]) ).
cnf(c_77619,plain,
multiply(a,add(b,additive_inverse(multiply(sP1_iProver_def,a)))) = multiply(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_77609,c_2660]) ).
cnf(c_82028,plain,
add(multiply(additive_inverse(X0),X1),additive_inverse(multiply(additive_identity,X1))) = additive_inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_50,c_1873]) ).
cnf(c_83616,plain,
additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(demodulation,[status(thm)],[c_82028,c_49,c_25647]) ).
cnf(c_83792,plain,
additive_inverse(multiply(X0,additive_inverse(X0))) = multiply(additive_inverse(additive_inverse(X0)),X0),
inference(superposition,[status(thm)],[c_27766,c_83616]) ).
cnf(c_83924,plain,
additive_inverse(multiply(X0,additive_inverse(X0))) = multiply(X0,X0),
inference(light_normalisation,[status(thm)],[c_83792,c_621]) ).
cnf(c_101292,plain,
add(multiply(X0,X1),multiply(additive_inverse(X0),add(X1,X2))) = multiply(additive_inverse(X0),X2),
inference(demodulation,[status(thm)],[c_2005,c_83616]) ).
cnf(c_101521,plain,
add(multiply(X0,X1),multiply(additive_inverse(X0),additive_identity)) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(superposition,[status(thm)],[c_50,c_101292]) ).
cnf(c_101648,plain,
add(multiply(X0,X1),additive_identity) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(light_normalisation,[status(thm)],[c_101521,c_2518]) ).
cnf(c_101649,plain,
add(additive_identity,multiply(X0,X1)) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(theory_normalisation,[status(thm)],[c_101648,c_53,c_54]) ).
cnf(c_101650,plain,
multiply(additive_inverse(X0),additive_inverse(X1)) = multiply(X0,X1),
inference(light_normalisation,[status(thm)],[c_101649,c_2650,c_25880]) ).
cnf(c_104212,plain,
add(sP1_iProver_def,multiply(sP1_iProver_def,multiply(sP0_iProver_def,additive_inverse(sP1_iProver_def)))) = multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def)),
inference(superposition,[status(thm)],[c_38674,c_2355]) ).
cnf(c_105210,plain,
multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(superposition,[status(thm)],[c_621,c_101650]) ).
cnf(c_105286,plain,
additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(demodulation,[status(thm)],[c_83616,c_105210]) ).
cnf(c_105298,plain,
multiply(a,additive_inverse(multiply(b,X0))) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(demodulation,[status(thm)],[c_33419,c_105210]) ).
cnf(c_105310,plain,
multiply(b,additive_inverse(multiply(a,X0))) = multiply(additive_inverse(sP1_iProver_def),X0),
inference(demodulation,[status(thm)],[c_38699,c_105210]) ).
cnf(c_105404,plain,
add(multiply(X0,X1),multiply(X2,additive_inverse(X1))) = multiply(add(X0,additive_inverse(X2)),X1),
inference(superposition,[status(thm)],[c_105210,c_52]) ).
cnf(c_105795,plain,
multiply(a,additive_inverse(multiply(b,X0))) = additive_inverse(multiply(sP0_iProver_def,X0)),
inference(superposition,[status(thm)],[c_178,c_105286]) ).
cnf(c_105796,plain,
multiply(b,additive_inverse(multiply(a,X0))) = additive_inverse(multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_179,c_105286]) ).
cnf(c_105962,plain,
additive_inverse(multiply(sP1_iProver_def,X0)) = multiply(additive_inverse(sP1_iProver_def),X0),
inference(light_normalisation,[status(thm)],[c_105796,c_105310]) ).
cnf(c_105963,plain,
additive_inverse(multiply(sP0_iProver_def,X0)) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(light_normalisation,[status(thm)],[c_105795,c_105298]) ).
cnf(c_111588,plain,
multiply(a,add(b,multiply(sP1_iProver_def,additive_inverse(a)))) = additive_identity,
inference(demodulation,[status(thm)],[c_77619,c_2573,c_105210,c_105962]) ).
cnf(c_111630,plain,
add(sP0_iProver_def,add(X0,multiply(a,multiply(sP1_iProver_def,additive_inverse(a))))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_111588,c_756]) ).
cnf(c_111636,plain,
add(sP0_iProver_def,add(X0,multiply(a,multiply(sP1_iProver_def,additive_inverse(a))))) = X0,
inference(light_normalisation,[status(thm)],[c_111630,c_49]) ).
cnf(c_113740,plain,
add(sP0_iProver_def,add(X0,multiply(sP0_iProver_def,multiply(a,additive_inverse(a))))) = X0,
inference(demodulation,[status(thm)],[c_111636,c_267]) ).
cnf(c_113785,plain,
multiply(sP0_iProver_def,multiply(a,additive_inverse(a))) = additive_inverse(sP0_iProver_def),
inference(superposition,[status(thm)],[c_113740,c_326]) ).
cnf(c_113949,plain,
multiply(sP0_iProver_def,additive_inverse(multiply(a,additive_inverse(a)))) = additive_inverse(additive_inverse(sP0_iProver_def)),
inference(superposition,[status(thm)],[c_113785,c_105286]) ).
cnf(c_113961,plain,
multiply(sP0_iProver_def,multiply(multiply(a,additive_inverse(a)),X0)) = multiply(additive_inverse(sP0_iProver_def),X0),
inference(superposition,[status(thm)],[c_113785,c_55]) ).
cnf(c_114035,plain,
multiply(sP0_iProver_def,multiply(a,multiply(a,additive_inverse(X0)))) = multiply(sP0_iProver_def,additive_inverse(X0)),
inference(demodulation,[status(thm)],[c_113961,c_27954,c_35486,c_105210]) ).
cnf(c_114041,plain,
multiply(sP0_iProver_def,multiply(a,multiply(a,X0))) = multiply(sP0_iProver_def,X0),
inference(superposition,[status(thm)],[c_621,c_114035]) ).
cnf(c_114094,plain,
multiply(sP0_iProver_def,multiply(a,a)) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_113949,c_621,c_83924]) ).
cnf(c_114128,plain,
multiply(sP1_iProver_def,multiply(b,multiply(a,a))) = multiply(b,sP0_iProver_def),
inference(superposition,[status(thm)],[c_114094,c_262]) ).
cnf(c_114144,plain,
multiply(sP1_iProver_def,multiply(b,multiply(a,a))) = multiply(sP1_iProver_def,b),
inference(light_normalisation,[status(thm)],[c_114128,c_261]) ).
cnf(c_114399,plain,
multiply(sP0_iProver_def,multiply(a,multiply(sP0_iProver_def,X0))) = multiply(sP0_iProver_def,multiply(b,X0)),
inference(superposition,[status(thm)],[c_178,c_114041]) ).
cnf(c_114514,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,multiply(b,a))) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_9847,c_114399]) ).
cnf(c_114517,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,sP1_iProver_def)) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_114514,c_89]) ).
cnf(c_114577,plain,
multiply(sP1_iProver_def,additive_inverse(multiply(sP0_iProver_def,sP1_iProver_def))) = additive_inverse(sP1_iProver_def),
inference(superposition,[status(thm)],[c_114517,c_105286]) ).
cnf(c_114589,plain,
multiply(sP1_iProver_def,multiply(multiply(sP0_iProver_def,sP1_iProver_def),X0)) = multiply(sP1_iProver_def,X0),
inference(superposition,[status(thm)],[c_114517,c_55]) ).
cnf(c_114592,plain,
multiply(sP1_iProver_def,add(X0,multiply(sP0_iProver_def,sP1_iProver_def))) = add(multiply(sP1_iProver_def,X0),sP1_iProver_def),
inference(superposition,[status(thm)],[c_114517,c_51]) ).
cnf(c_114621,plain,
multiply(sP1_iProver_def,add(X0,multiply(sP0_iProver_def,sP1_iProver_def))) = add(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(theory_normalisation,[status(thm)],[c_114592,c_53,c_54]) ).
cnf(c_115406,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,additive_inverse(sP1_iProver_def))) = additive_inverse(sP1_iProver_def),
inference(demodulation,[status(thm)],[c_114577,c_105210,c_105963]) ).
cnf(c_115419,plain,
multiply(sP1_iProver_def,add(multiply(sP0_iProver_def,additive_inverse(sP1_iProver_def)),X0)) = add(additive_inverse(sP1_iProver_def),multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_115406,c_51]) ).
cnf(c_118486,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,multiply(sP1_iProver_def,X0))) = multiply(sP1_iProver_def,X0),
inference(demodulation,[status(thm)],[c_114589,c_55]) ).
cnf(c_118487,plain,
multiply(sP0_iProver_def,multiply(sP1_iProver_def,sP0_iProver_def)) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_9901,c_118486]) ).
cnf(c_122018,plain,
( sP0_iProver_def != X0
| sP1_iProver_def != X0
| sP0_iProver_def = sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_175732,plain,
multiply(sP0_iProver_def,multiply(multiply(sP1_iProver_def,sP0_iProver_def),X0)) = multiply(sP0_iProver_def,X0),
inference(superposition,[status(thm)],[c_118487,c_55]) ).
cnf(c_179468,plain,
( sP0_iProver_def != add(sP0_iProver_def,additive_identity)
| sP1_iProver_def != add(sP0_iProver_def,additive_identity)
| sP0_iProver_def = sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_122018]) ).
cnf(c_184737,plain,
multiply(sP1_iProver_def,multiply(sP1_iProver_def,a)) = multiply(sP1_iProver_def,b),
inference(demodulation,[status(thm)],[c_114144,c_179]) ).
cnf(c_184775,plain,
multiply(sP1_iProver_def,multiply(sP1_iProver_def,b)) = multiply(sP1_iProver_def,a),
inference(superposition,[status(thm)],[c_184737,c_359]) ).
cnf(c_184861,plain,
multiply(sP0_iProver_def,multiply(a,multiply(sP1_iProver_def,b))) = multiply(a,multiply(sP1_iProver_def,a)),
inference(superposition,[status(thm)],[c_184775,c_267]) ).
cnf(c_184878,plain,
multiply(a,multiply(sP1_iProver_def,a)) = multiply(sP0_iProver_def,multiply(sP0_iProver_def,sP0_iProver_def)),
inference(light_normalisation,[status(thm)],[c_184861,c_285]) ).
cnf(c_185460,plain,
multiply(sP0_iProver_def,multiply(sP1_iProver_def,multiply(sP0_iProver_def,X0))) = multiply(sP0_iProver_def,X0),
inference(demodulation,[status(thm)],[c_175732,c_55]) ).
cnf(c_191888,plain,
multiply(a,add(X0,multiply(sP1_iProver_def,a))) = multiply(a,add(b,X0)),
inference(light_normalisation,[status(thm)],[c_6110,c_70933,c_184775]) ).
cnf(c_191902,plain,
multiply(a,add(b,additive_identity)) = multiply(a,multiply(sP1_iProver_def,a)),
inference(superposition,[status(thm)],[c_142,c_191888]) ).
cnf(c_191971,plain,
multiply(a,add(additive_identity,b)) = multiply(a,multiply(sP1_iProver_def,a)),
inference(theory_normalisation,[status(thm)],[c_191902,c_53,c_54]) ).
cnf(c_191972,plain,
multiply(sP0_iProver_def,multiply(sP0_iProver_def,sP0_iProver_def)) = add(sP0_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_191971,c_2667,c_184878]) ).
cnf(c_276659,plain,
( add(sP0_iProver_def,additive_identity) != X0
| sP1_iProver_def != X0
| sP1_iProver_def = add(sP0_iProver_def,additive_identity) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_283415,plain,
( add(sP0_iProver_def,additive_identity) != sP1_iProver_def
| sP1_iProver_def != sP1_iProver_def
| sP1_iProver_def = add(sP0_iProver_def,additive_identity) ),
inference(instantiation,[status(thm)],[c_276659]) ).
cnf(c_391326,plain,
multiply(add(X0,additive_inverse(X1)),additive_identity) = add(additive_identity,multiply(X1,additive_inverse(additive_identity))),
inference(superposition,[status(thm)],[c_2573,c_105404]) ).
cnf(c_391605,plain,
multiply(add(X0,additive_inverse(X1)),additive_identity) = add(additive_identity,multiply(X1,additive_identity)),
inference(light_normalisation,[status(thm)],[c_391326,c_150]) ).
cnf(c_400655,plain,
add(additive_inverse(sP1_iProver_def),multiply(sP1_iProver_def,multiply(sP0_iProver_def,sP1_iProver_def))) = add(sP1_iProver_def,multiply(sP1_iProver_def,multiply(sP0_iProver_def,additive_inverse(sP1_iProver_def)))),
inference(superposition,[status(thm)],[c_115419,c_114621]) ).
cnf(c_400660,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def)) = add(additive_inverse(sP1_iProver_def),sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_400655,c_104212,c_114517]) ).
cnf(c_400661,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def)) = add(sP1_iProver_def,additive_inverse(sP1_iProver_def)),
inference(theory_normalisation,[status(thm)],[c_400660,c_53,c_54]) ).
cnf(c_400662,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def)) = multiply(sP1_iProver_def,additive_identity),
inference(light_normalisation,[status(thm)],[c_400661,c_23014]) ).
cnf(c_403523,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def)) = additive_identity,
inference(demodulation,[status(thm)],[c_400662,c_2573]) ).
cnf(c_403542,plain,
multiply(sP1_iProver_def,multiply(multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_403523,c_55]) ).
cnf(c_403588,plain,
multiply(sP1_iProver_def,multiply(multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def),X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_403542,c_25754]) ).
cnf(c_404100,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),multiply(sP1_iProver_def,X0))) = additive_identity,
inference(demodulation,[status(thm)],[c_403588,c_55]) ).
cnf(c_404259,plain,
multiply(sP1_iProver_def,multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),X0)) = additive_identity,
inference(superposition,[status(thm)],[c_404100,c_8795]) ).
cnf(c_404357,plain,
multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),additive_identity) = multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def),
inference(superposition,[status(thm)],[c_404259,c_877]) ).
cnf(c_404367,plain,
multiply(sP1_iProver_def,add(sP1_iProver_def,additive_inverse(sP0_iProver_def))) = additive_identity,
inference(superposition,[status(thm)],[c_404259,c_941]) ).
cnf(c_405624,plain,
multiply(sP1_iProver_def,add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def)))) = add(multiply(sP1_iProver_def,X0),additive_identity),
inference(superposition,[status(thm)],[c_404367,c_51]) ).
cnf(c_405657,plain,
multiply(sP1_iProver_def,add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def)))) = add(additive_identity,multiply(sP1_iProver_def,X0)),
inference(theory_normalisation,[status(thm)],[c_405624,c_53,c_54]) ).
cnf(c_406112,plain,
multiply(sP1_iProver_def,add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def)))) = multiply(sP1_iProver_def,X0),
inference(demodulation,[status(thm)],[c_405657,c_2650,c_25880]) ).
cnf(c_406130,plain,
multiply(sP1_iProver_def,sP0_iProver_def) = multiply(sP1_iProver_def,sP1_iProver_def),
inference(superposition,[status(thm)],[c_318,c_406112]) ).
cnf(c_408721,plain,
multiply(multiply(sP1_iProver_def,sP0_iProver_def),X0) = multiply(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_406130,c_55]) ).
cnf(c_408740,plain,
multiply(sP1_iProver_def,multiply(sP1_iProver_def,sP0_iProver_def)) = sP1_iProver_def,
inference(superposition,[status(thm)],[c_406130,c_56]) ).
cnf(c_413864,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,X0)) = multiply(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(demodulation,[status(thm)],[c_408721,c_55]) ).
cnf(c_413868,plain,
multiply(sP1_iProver_def,multiply(sP0_iProver_def,sP0_iProver_def)) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_408740,c_413864]) ).
cnf(c_414885,plain,
multiply(sP0_iProver_def,sP0_iProver_def) = multiply(sP0_iProver_def,sP1_iProver_def),
inference(superposition,[status(thm)],[c_413868,c_185460]) ).
cnf(c_581697,plain,
multiply(add(sP1_iProver_def,additive_inverse(sP0_iProver_def)),sP1_iProver_def) = additive_identity,
inference(demodulation,[status(thm)],[c_404357,c_2650,c_11684,c_391605]) ).
cnf(c_581732,plain,
multiply(add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def))),sP1_iProver_def) = add(multiply(X0,sP1_iProver_def),additive_identity),
inference(superposition,[status(thm)],[c_581697,c_52]) ).
cnf(c_581772,plain,
multiply(add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def))),sP1_iProver_def) = add(additive_identity,multiply(X0,sP1_iProver_def)),
inference(theory_normalisation,[status(thm)],[c_581732,c_53,c_54]) ).
cnf(c_585296,plain,
multiply(add(X0,add(sP1_iProver_def,additive_inverse(sP0_iProver_def))),sP1_iProver_def) = multiply(X0,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_581772,c_2650,c_25880]) ).
cnf(c_585311,plain,
multiply(sP0_iProver_def,sP1_iProver_def) = multiply(sP1_iProver_def,sP1_iProver_def),
inference(superposition,[status(thm)],[c_318,c_585296]) ).
cnf(c_585390,plain,
multiply(sP0_iProver_def,sP0_iProver_def) = multiply(sP1_iProver_def,sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_585311,c_406130,c_414885]) ).
cnf(c_586003,plain,
multiply(multiply(sP0_iProver_def,sP0_iProver_def),X0) = multiply(sP1_iProver_def,multiply(sP1_iProver_def,X0)),
inference(superposition,[status(thm)],[c_585390,c_55]) ).
cnf(c_586059,plain,
multiply(multiply(sP0_iProver_def,sP0_iProver_def),X0) = multiply(sP1_iProver_def,multiply(sP0_iProver_def,X0)),
inference(light_normalisation,[status(thm)],[c_586003,c_413864]) ).
cnf(c_588531,plain,
multiply(sP0_iProver_def,multiply(sP0_iProver_def,X0)) = multiply(sP1_iProver_def,multiply(sP0_iProver_def,X0)),
inference(demodulation,[status(thm)],[c_586059,c_55]) ).
cnf(c_588538,plain,
multiply(sP0_iProver_def,multiply(sP0_iProver_def,sP0_iProver_def)) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_413868,c_588531]) ).
cnf(c_588546,plain,
add(sP0_iProver_def,additive_identity) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_588538,c_191972]) ).
cnf(c_588595,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_588546,c_283415,c_179468,c_6203,c_6202,c_537,c_219,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover %s %d THM
% 0.07/0.25 % Computer : n011.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Thu May 2 21:25:33 EDT 2024
% 0.07/0.25 % CPUTime :
% 0.11/0.33 Running UEQ theorem proving
% 0.11/0.33 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule casc_24_ueq --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 255.86/33.06 % SZS status Started for theBenchmark.p
% 255.86/33.06 % SZS status Unsatisfiable for theBenchmark.p
% 255.86/33.06
% 255.86/33.06 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 255.86/33.06
% 255.86/33.06 ------ iProver source info
% 255.86/33.06
% 255.86/33.06 git: date: 2024-05-02 19:28:25 +0000
% 255.86/33.06 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 255.86/33.06 git: non_committed_changes: false
% 255.86/33.06
% 255.86/33.06 ------ Parsing...successful
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06 ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e
% 255.86/33.06
% 255.86/33.06 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 255.86/33.06
% 255.86/33.06 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 255.86/33.06 ------ Proving...
% 255.86/33.06 ------ Problem Properties
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06 clauses 11
% 255.86/33.06 conjectures 1
% 255.86/33.06 EPR 1
% 255.86/33.06 Horn 11
% 255.86/33.06 unary 11
% 255.86/33.06 binary 0
% 255.86/33.06 lits 11
% 255.86/33.06 lits eq 11
% 255.86/33.06 fd_pure 0
% 255.86/33.06 fd_pseudo 0
% 255.86/33.06 fd_cond 0
% 255.86/33.06 fd_pseudo_cond 0
% 255.86/33.06 AC symbols 1
% 255.86/33.06
% 255.86/33.06 ------ Input Options Time Limit: Unbounded
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06 ------
% 255.86/33.06 Current options:
% 255.86/33.06 ------
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06 ------ Proving...
% 255.86/33.06
% 255.86/33.06
% 255.86/33.06 % SZS status Unsatisfiable for theBenchmark.p
% 255.86/33.06
% 255.86/33.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 255.86/33.06
% 255.86/33.06
%------------------------------------------------------------------------------