%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO014-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 06:55:05 AM UTC 2026
% Result : Unsatisfiable 0.14s 15.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 14
% Syntax : Number of formulae : 152 ( 152 unt; 0 def)
% Number of atoms : 152 ( 151 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 284 ( 32 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_2,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(multiply(VAR_0,VAR_1),VAR_2) = multiply(add(VAR_0,VAR_2),add(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_4,plain,
multiply(add(A,B),add(C,B)) = add(multiply(A,C),B),
inference(copy,[status(thm)],[c_3]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),VAR_2) = add(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity3) ).
cnf(c_7,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distributivity3]) ).
fof(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity4) ).
cnf(c_8,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_9,plain,
add(A,inverse(A)) = multiplicative_identity,
inference(clausify,[status(thm)],[additive_inverse1]) ).
fof(multiplicative_inverse1,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_11,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(multiplicative_id1,axiom,
! [VAR_0] : multiply(VAR_0,multiplicative_identity) = VAR_0,
file('theBenchmark.p',multiplicative_id1) ).
cnf(c_13,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
fof(multiplicative_id2,axiom,
! [VAR_0] : multiply(multiplicative_identity,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_id2) ).
cnf(c_14,plain,
multiply(multiplicative_identity,A) = A,
inference(clausify,[status(thm)],[multiplicative_id2]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_15,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(additive_id2,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',additive_id2) ).
cnf(c_16,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[additive_id2]) ).
fof(a_plus_b_is_c,axiom,
add(a,b) = c,
file('theBenchmark.p',a_plus_b_is_c) ).
cnf(c_17,plain,
add(a,b) = c,
inference(clausify,[status(thm)],[a_plus_b_is_c]) ).
cnf(c_18,plain,
c = add(a,b),
inference(copy,[status(thm)],[c_17]) ).
fof(a_inverse_times_b_inverse_is_d,axiom,
multiply(inverse(a),inverse(b)) = d,
file('theBenchmark.p',a_inverse_times_b_inverse_is_d) ).
cnf(c_19,plain,
multiply(inverse(a),inverse(b)) = d,
inference(clausify,[status(thm)],[a_inverse_times_b_inverse_is_d]) ).
cnf(c_20,plain,
d = multiply(inverse(a),inverse(b)),
inference(copy,[status(thm)],[c_19]) ).
fof(prove_c_inverse_is_d,axiom,
inverse(c) != d,
file('theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_21,plain,
inverse(c) != d,
inference(clausify,[status(thm)],[prove_c_inverse_is_d]) ).
cnf(c_426,plain,
inverse(add(a,b)) != d,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_22,plain,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_20,c_426]) ).
cnf(c_427,plain,
add(multiply(add(A,B),C),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_428,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_7,c_427]) ).
cnf(c_429,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(B,add(A,B))) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_2,c_428]) ).
cnf(c_24,plain,
add(add(multiply(A,B),multiply(C,B)),add(multiply(C,A),multiply(C,C))) = add(multiply(A,B),C),
inference(paramod,[status(thm)],[c_8,c_429]) ).
cnf(c_430,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_431,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_430]) ).
cnf(c_25,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_431]) ).
cnf(c_432,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_433,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_432]) ).
cnf(c_26,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_433]) ).
cnf(c_434,plain,
additive_identity = add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_27,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = additive_identity,
inference(copy,[status(thm)],[c_434]) ).
cnf(c_33,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_47,plain,
add(multiply(A,B),multiply(inverse(B),A)) = A,
inference(paramod,[status(thm)],[c_2,c_25]) ).
cnf(c_435,plain,
multiply(A,B) = add(multiply(multiply(C,A),B),multiply(multiply(inverse(C),A),B)),
inference(paramod,[status(thm)],[c_25,c_7]) ).
cnf(c_49,plain,
add(multiply(multiply(A,B),C),multiply(multiply(inverse(A),B),C)) = multiply(B,C),
inference(copy,[status(thm)],[c_435]) ).
cnf(c_436,plain,
add(additive_identity,multiply(inverse(A),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_11,c_25]) ).
cnf(c_52,plain,
multiply(inverse(A),inverse(A)) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_436]) ).
cnf(c_437,plain,
add(multiply(A,inverse(inverse(A))),additive_identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_11,c_25]) ).
cnf(c_438,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1,c_437]) ).
cnf(c_53,plain,
multiply(A,inverse(inverse(A))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_16,c_438]) ).
cnf(c_439,plain,
add(A,add(multiply(inverse(B),B),multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_440,plain,
add(A,add(multiply(B,inverse(B)),multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_2,c_439]) ).
cnf(c_441,plain,
add(A,add(additive_identity,multiply(inverse(B),inverse(B)))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_11,c_440]) ).
cnf(c_442,plain,
add(A,add(additive_identity,inverse(B))) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_52,c_441]) ).
cnf(c_443,plain,
add(A,inverse(B)) = add(multiply(B,A),inverse(B)),
inference(paramod,[status(thm)],[c_16,c_442]) ).
cnf(c_55,plain,
add(multiply(A,B),inverse(A)) = add(B,inverse(A)),
inference(copy,[status(thm)],[c_443]) ).
cnf(c_444,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_11,c_26]) ).
cnf(c_445,plain,
add(additive_identity,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_53,c_444]) ).
cnf(c_59,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_16,c_445]) ).
cnf(c_446,plain,
add(multiply(A,inverse(A)),multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_27]) ).
cnf(c_447,plain,
add(additive_identity,multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_446]) ).
cnf(c_448,plain,
add(additive_identity,multiply(additive_identity,inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_447]) ).
cnf(c_78,plain,
multiply(additive_identity,inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_448]) ).
cnf(c_449,plain,
add(additive_identity,multiply(additive_identity,inverse(inverse(A)))) = additive_identity,
inference(paramod,[status(thm)],[c_78,c_26]) ).
cnf(c_450,plain,
add(additive_identity,multiply(additive_identity,A)) = additive_identity,
inference(paramod,[status(thm)],[c_59,c_449]) ).
cnf(c_83,plain,
multiply(additive_identity,A) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_450]) ).
cnf(c_451,plain,
add(A,inverse(B)) = add(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_85,plain,
add(inverse(A),multiply(A,B)) = add(B,inverse(A)),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,plain,
multiply(add(A,inverse(B)),C) = add(multiply(multiply(B,A),C),multiply(inverse(B),C)),
inference(paramod,[status(thm)],[c_55,c_7]) ).
cnf(c_453,plain,
add(multiply(A,C),multiply(inverse(B),C)) = add(multiply(multiply(B,A),C),multiply(inverse(B),C)),
inference(paramod,[status(thm)],[c_7,c_452]) ).
cnf(c_87,plain,
add(multiply(multiply(A,B),C),multiply(inverse(A),C)) = add(multiply(B,C),multiply(inverse(A),C)),
inference(copy,[status(thm)],[c_453]) ).
cnf(c_454,plain,
multiply(A,add(B,inverse(C))) = add(multiply(A,multiply(C,B)),multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_55,c_8]) ).
cnf(c_455,plain,
add(multiply(A,B),multiply(A,inverse(C))) = add(multiply(A,multiply(C,B)),multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_8,c_454]) ).
cnf(c_89,plain,
add(multiply(A,multiply(B,C)),multiply(A,inverse(B))) = add(multiply(A,C),multiply(A,inverse(B))),
inference(copy,[status(thm)],[c_455]) ).
cnf(c_456,plain,
add(multiply(additive_identity,A),multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_33,c_55]) ).
cnf(c_457,plain,
add(additive_identity,multiplicative_identity) = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_83,c_456]) ).
cnf(c_458,plain,
multiplicative_identity = add(A,inverse(additive_identity)),
inference(paramod,[status(thm)],[c_16,c_457]) ).
cnf(c_459,plain,
multiplicative_identity = add(A,multiplicative_identity),
inference(paramod,[status(thm)],[c_33,c_458]) ).
cnf(c_93,plain,
add(A,multiplicative_identity) = multiplicative_identity,
inference(copy,[status(thm)],[c_459]) ).
cnf(c_460,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_93,c_7]) ).
cnf(c_461,plain,
A = add(multiply(B,A),multiply(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_14,c_460]) ).
cnf(c_462,plain,
A = add(multiply(B,A),A),
inference(paramod,[status(thm)],[c_14,c_461]) ).
cnf(c_463,plain,
A = add(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_462]) ).
cnf(c_96,plain,
add(A,multiply(B,A)) = A,
inference(copy,[status(thm)],[c_463]) ).
cnf(c_464,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,multiplicative_identity)),
inference(paramod,[status(thm)],[c_93,c_8]) ).
cnf(c_465,plain,
A = add(multiply(A,B),multiply(A,multiplicative_identity)),
inference(paramod,[status(thm)],[c_13,c_464]) ).
cnf(c_466,plain,
A = add(multiply(A,B),A),
inference(paramod,[status(thm)],[c_13,c_465]) ).
cnf(c_467,plain,
A = add(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_466]) ).
cnf(c_97,plain,
add(A,multiply(A,B)) = A,
inference(copy,[status(thm)],[c_467]) ).
cnf(c_468,plain,
multiply(A,B) = add(multiply(A,multiply(B,C)),multiply(A,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_47,c_8]) ).
cnf(c_103,plain,
add(multiply(A,multiply(B,C)),multiply(A,multiply(inverse(C),B))) = multiply(A,B),
inference(copy,[status(thm)],[c_468]) ).
cnf(c_469,plain,
add(multiply(A,inverse(A)),multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_96,c_27]) ).
cnf(c_470,plain,
add(additive_identity,multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_469]) ).
cnf(c_471,plain,
add(additive_identity,multiply(multiply(B,A),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_96,c_470]) ).
cnf(c_114,plain,
multiply(multiply(A,B),inverse(B)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_471]) ).
cnf(c_472,plain,
add(multiply(A,inverse(A)),multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_97,c_27]) ).
cnf(c_473,plain,
add(additive_identity,multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_472]) ).
cnf(c_474,plain,
add(additive_identity,multiply(multiply(A,B),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_97,c_473]) ).
cnf(c_119,plain,
multiply(multiply(A,B),inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_474]) ).
cnf(c_475,plain,
add(additive_identity,multiply(inverse(multiply(A,B)),inverse(B))) = inverse(B),
inference(paramod,[status(thm)],[c_114,c_25]) ).
cnf(c_476,plain,
add(additive_identity,multiply(inverse(B),inverse(multiply(A,B)))) = inverse(B),
inference(paramod,[status(thm)],[c_2,c_475]) ).
cnf(c_121,plain,
multiply(inverse(A),inverse(multiply(B,A))) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_476]) ).
cnf(c_477,plain,
add(additive_identity,inverse(multiply(A,B))) = add(inverse(B),inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_114,c_55]) ).
cnf(c_478,plain,
inverse(multiply(A,B)) = add(inverse(B),inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_16,c_477]) ).
cnf(c_124,plain,
add(inverse(A),inverse(multiply(B,A))) = inverse(multiply(B,A)),
inference(copy,[status(thm)],[c_478]) ).
cnf(c_479,plain,
add(additive_identity,multiply(multiply(inverse(A),B),inverse(multiply(A,B)))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_11,c_49]) ).
cnf(c_127,plain,
multiply(multiply(inverse(A),B),inverse(multiply(A,B))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_16,c_479]) ).
cnf(c_480,plain,
additive_identity = multiply(inverse(A),multiply(A,B)),
inference(paramod,[status(thm)],[c_119,c_2]) ).
cnf(c_136,plain,
multiply(inverse(A),multiply(A,B)) = additive_identity,
inference(copy,[status(thm)],[c_480]) ).
cnf(c_481,plain,
add(additive_identity,multiply(inverse(multiply(A,B)),inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_119,c_25]) ).
cnf(c_482,plain,
add(additive_identity,multiply(inverse(A),inverse(multiply(A,B)))) = inverse(A),
inference(paramod,[status(thm)],[c_2,c_481]) ).
cnf(c_137,plain,
multiply(inverse(A),inverse(multiply(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_16,c_482]) ).
cnf(c_143,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_85,c_1]) ).
cnf(c_483,plain,
add(multiply(multiply(A,B),multiply(A,C)),additive_identity) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_136,c_87]) ).
cnf(c_484,plain,
add(additive_identity,multiply(multiply(A,B),multiply(A,C))) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_483]) ).
cnf(c_485,plain,
multiply(multiply(A,B),multiply(A,C)) = add(multiply(B,multiply(A,C)),multiply(inverse(A),multiply(A,C))),
inference(paramod,[status(thm)],[c_16,c_484]) ).
cnf(c_486,plain,
multiply(multiply(A,B),multiply(A,C)) = add(multiply(B,multiply(A,C)),additive_identity),
inference(paramod,[status(thm)],[c_136,c_485]) ).
cnf(c_487,plain,
multiply(multiply(A,B),multiply(A,C)) = add(additive_identity,multiply(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_486]) ).
cnf(c_228,plain,
multiply(multiply(A,B),multiply(A,C)) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_16,c_487]) ).
cnf(c_488,plain,
add(multiply(multiply(A,B),multiply(A,C)),additive_identity) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_119,c_89]) ).
cnf(c_489,plain,
add(multiply(B,multiply(A,C)),additive_identity) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_228,c_488]) ).
cnf(c_490,plain,
add(additive_identity,multiply(B,multiply(A,C))) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_1,c_489]) ).
cnf(c_491,plain,
multiply(B,multiply(A,C)) = add(multiply(multiply(A,B),C),multiply(multiply(A,B),inverse(A))),
inference(paramod,[status(thm)],[c_16,c_490]) ).
cnf(c_492,plain,
multiply(B,multiply(A,C)) = add(multiply(multiply(A,B),C),additive_identity),
inference(paramod,[status(thm)],[c_119,c_491]) ).
cnf(c_493,plain,
multiply(B,multiply(A,C)) = add(additive_identity,multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_1,c_492]) ).
cnf(c_494,plain,
multiply(B,multiply(A,C)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_16,c_493]) ).
cnf(c_256,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_494]) ).
cnf(c_495,plain,
multiply(B,multiply(inverse(A),inverse(multiply(A,B)))) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_256,c_127]) ).
cnf(c_496,plain,
multiply(B,inverse(A)) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_137,c_495]) ).
cnf(c_276,plain,
multiply(A,inverse(multiply(B,A))) = multiply(A,inverse(B)),
inference(copy,[status(thm)],[c_496]) ).
cnf(c_497,plain,
add(multiply(A,multiply(inverse(multiply(B,C)),C)),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_121,c_103]) ).
cnf(c_498,plain,
add(multiply(A,multiply(C,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_2,c_497]) ).
cnf(c_499,plain,
add(multiply(A,multiply(C,inverse(B))),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_276,c_498]) ).
cnf(c_500,plain,
add(multiply(A,inverse(B)),multiply(A,inverse(C))) = multiply(A,inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_89,c_499]) ).
cnf(c_325,plain,
multiply(A,inverse(multiply(B,C))) = add(multiply(A,inverse(B)),multiply(A,inverse(C))),
inference(copy,[status(thm)],[c_500]) ).
cnf(c_501,plain,
add(inverse(A),multiply(A,inverse(multiply(B,A)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_124,c_143]) ).
cnf(c_502,plain,
add(inverse(A),add(multiply(A,inverse(B)),multiply(A,inverse(A)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_325,c_501]) ).
cnf(c_503,plain,
add(inverse(A),add(multiply(A,inverse(B)),additive_identity)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_11,c_502]) ).
cnf(c_504,plain,
add(inverse(A),add(additive_identity,multiply(A,inverse(B)))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_503]) ).
cnf(c_505,plain,
add(inverse(A),multiply(A,inverse(B))) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_16,c_504]) ).
cnf(c_506,plain,
add(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_143,c_505]) ).
cnf(c_365,plain,
inverse(multiply(A,B)) = add(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_506]) ).
cnf(c_384,plain,
inverse(add(inverse(A),inverse(B))) = multiply(B,A),
inference(paramod,[status(thm)],[c_365,c_59]) ).
cnf(c_398,plain,
inverse(add(A,inverse(B))) = multiply(B,inverse(A)),
inference(paramod,[status(thm)],[c_59,c_384]) ).
cnf(c_414,plain,
inverse(add(A,B)) = multiply(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_59,c_398]) ).
cnf(c_507,plain,
multiply(inverse(b),inverse(a)) != multiply(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_414,c_22]) ).
cnf(c_508,plain,
multiply(inverse(a),inverse(b)) != multiply(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_2,c_507]) ).
cnf(c_425,plain,
$false,
inference(copy,[status(thm)],[c_508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.39 % Computer : n017.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Sat Sep 26 22:31:49 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/15.39 % Process 1817773 was started by sandbox2 on n017,
% 0.10/15.39 % Sat Sep 26 22:31:49 2026
% 0.10/15.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/15.40
% 0.10/15.40 % From the command line: assign(max_seconds, 300).
% 0.14/15.57
% 0.14/15.57 % SZS status Unsatisfiable for theBenchmark
% 0.14/15.57
% 0.14/15.57 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.14/15.57 % Length of proof is 55.
% 0.14/15.57 % Level of proof is 17.
% 0.14/15.57 % Maximum clause weight is 33.000.
% 0.14/15.57 % Given clauses 88.
% 0.14/15.57
% 0.14/15.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------