%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:00:16 PM UTC 2026
% Result : Unsatisfiable 3.38s 2.76s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 10
% Syntax : Number of formulae : 139 ( 139 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 166 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f2,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
fof(f4,axiom,
! [X0] : multiply(X0,inverse(X0)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
fof(f5,axiom,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
fof(f7,axiom,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X0),multiply(inverse(X1),X0))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
fof(f8,axiom,
! [X0,X1] : multiply(add(X0,inverse(X0)),multiply(add(X0,X1),add(inverse(X0),X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1_dual) ).
fof(f9,axiom,
! [X0,X1] : multiply(add(X0,inverse(X1)),multiply(add(X0,X1),add(inverse(X1),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2_dual) ).
fof(f10,axiom,
! [X0,X1] : multiply(add(X0,inverse(X1)),multiply(add(X0,X0),add(inverse(X1),X0))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3_dual) ).
fof(f11,negated_conjecture,
multiply(add(a,b),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add) ).
fof(f12,plain,
b != multiply(add(a,b),b),
inference(reorient_equations,[],[f11]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(X1,add(X0,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i] : add(X0,inverse(X0)) = n1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(X1,multiply(X0,X2)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = n0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : add(multiply(X0,inverse(X1)),add(multiply(X0,X0),multiply(inverse(X1),X0))) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : multiply(add(X0,inverse(X0)),multiply(add(X0,X1),add(inverse(X0),X1))) = X1,
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : multiply(add(X0,inverse(X1)),multiply(add(X0,X1),add(inverse(X1),X1))) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : multiply(add(X0,inverse(X1)),multiply(add(X0,X0),add(inverse(X1),X0))) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
multiply(add(a,b),b) != b,
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X0,X1)) = add(n0,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_63,c_60]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X1,X0)) = add(multiply(X1,inverse(X0)),n0),
inference(superposition,[status(thm)],[c_63,c_60]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X2,X0))) = add(multiply(X2,X0),multiply(multiply(X1,X0),X3)),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X0,X1)) = multiply(n1,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(add(X0,multiply(X1,X2)),multiply(X2,add(X3,X1))) = add(multiply(X1,X2),multiply(X0,multiply(X3,X2))),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X1,X0)) = multiply(add(X1,inverse(X0)),n1),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(multiply(X0,X1),multiply(inverse(X0),X1)),multiply(multiply(X0,inverse(X0)),X2)) = multiply(X1,add(X2,add(multiply(X0,X1),multiply(inverse(X0),X1)))),
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_102,plain,
! [X0: $i] : add(n0,add(multiply(X0,X0),multiply(inverse(X0),X0))) = X0,
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(add(X0,X1),add(inverse(X0),X1)),add(add(X0,inverse(X0)),X2)) = add(X1,multiply(X2,multiply(add(X0,X1),add(inverse(X0),X1)))),
inference(superposition,[status(thm)],[c_67,c_60]) ).
tcf(c_123,plain,
! [X0: $i] : multiply(add(X0,inverse(inverse(X0))),multiply(n1,add(inverse(inverse(X0)),inverse(X0)))) = X0,
inference(superposition,[status(thm)],[c_61,c_68]) ).
tcf(c_131,plain,
! [X0: $i] : multiply(n1,multiply(add(X0,X0),add(inverse(X0),X0))) = X0,
inference(superposition,[status(thm)],[c_61,c_69]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : multiply(add(X0,inverse(X1)),add(X0,multiply(X0,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_62,c_69]) ).
tcf(c_139,plain,
! [X0: $i] : multiply(n1,add(X0,n0)) = X0,
inference(demodulation,[status(thm)],[c_131,c_62,c_63]) ).
tcf(c_141,plain,
! [X0: $i] : add(n0,multiply(X0,n1)) = X0,
inference(demodulation,[status(thm)],[c_102,c_60,c_61]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,add(X0,n0))) = multiply(add(X0,n0),add(n1,X1)),
inference(demodulation,[status(thm)],[c_118,c_61,c_62,c_63]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,multiply(X0,n1))) = add(multiply(X0,n1),multiply(n0,X1)),
inference(demodulation,[status(thm)],[c_94,c_60,c_61,c_63]) ).
tcf(c_328,plain,
! [X0: $i] : add(n0,multiply(inverse(X0),inverse(X0))) = multiply(inverse(X0),n1),
inference(superposition,[status(thm)],[c_61,c_81]) ).
tcf(c_342,plain,
! [X0: $i] : add(multiply(X0,inverse(inverse(X0))),n0) = multiply(inverse(inverse(X0)),n1),
inference(superposition,[status(thm)],[c_61,c_82]) ).
tcf(c_356,plain,
! [X0: $i] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),n0),
inference(superposition,[status(thm)],[c_63,c_84]) ).
tcf(c_378,plain,
! [X0: $i] : multiply(add(X0,inverse(inverse(X0))),n1) = add(inverse(inverse(X0)),n0),
inference(superposition,[status(thm)],[c_63,c_86]) ).
tcf(c_387,plain,
! [X0: $i] : add(inverse(X0),multiply(X0,X0)) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_61,c_86]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] : add(n0,add(inverse(X0),multiply(X1,X0))) = add(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_86,c_141]) ).
tcf(c_490,plain,
! [X0: $i] : multiply(add(X0,n0),add(n1,n1)) = add(X0,X0),
inference(superposition,[status(thm)],[c_139,c_156]) ).
tcf(c_510,plain,
! [X0: $i] : add(X0,multiply(n0,add(X0,n0))) = add(n0,multiply(X0,n1)),
inference(superposition,[status(thm)],[c_156,c_62]) ).
tcf(c_540,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(n0,n0)) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_141,c_162]) ).
tcf(c_553,plain,
! [X0: $i] : add(X0,multiply(multiply(add(X0,n0),n1),add(X0,n0))) = add(multiply(add(X0,n0),n1),multiply(n0,n1)),
inference(superposition,[status(thm)],[c_162,c_156]) ).
tcf(c_567,plain,
! [X0: $i] : add(X0,multiply(n0,add(X0,n0))) = X0,
inference(demodulation,[status(thm)],[c_510,c_141]) ).
tcf(c_570,plain,
! [X0: $i] : add(X0,multiply(multiply(add(X0,n0),n1),add(X0,n0))) = add(X0,n0),
inference(demodulation,[status(thm)],[c_553,c_60,c_139]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i] : add(inverse(add(X0,X1)),add(X1,multiply(X0,X0))) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_62,c_387]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i] : multiply(add(multiply(X0,X1),n0),add(n1,n1)) = multiply(X1,add(X0,X0)),
inference(superposition,[status(thm)],[c_490,c_60]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i] : add(multiply(add(X0,X1),n1),multiply(n0,n0)) = add(X1,multiply(X0,X0)),
inference(superposition,[status(thm)],[c_540,c_62]) ).
tcf(c_1225,plain,
! [X0: $i] : add(multiply(X0,inverse(inverse(X0))),multiply(X0,inverse(inverse(X0)))) = multiply(multiply(inverse(inverse(X0)),n1),add(n1,n1)),
inference(superposition,[status(thm)],[c_342,c_490]) ).
tcf(c_1242,plain,
! [X0: $i] : add(n0,add(inverse(inverse(X0)),n0)) = add(X0,inverse(inverse(X0))),
inference(superposition,[status(thm)],[c_63,c_402]) ).
tcf(c_1325,plain,
! [X0: $i,X1: $i] : add(multiply(n0,n1),multiply(multiply(X0,n1),X1)) = multiply(X0,add(X1,multiply(n0,n1))),
inference(superposition,[status(thm)],[c_139,c_83]) ).
tcf(c_1411,plain,
! [X0: $i] : multiply(multiply(inverse(inverse(X0)),n1),add(n1,n1)) = multiply(inverse(inverse(X0)),add(X0,X0)),
inference(demodulation,[status(thm)],[c_1225,c_60]) ).
tcf(c_2745,plain,
! [X0: $i,X1: $i] : multiply(add(n0,add(inverse(inverse(X0)),n0)),add(X1,inverse(inverse(X0)))) = add(inverse(inverse(X0)),multiply(X0,X1)),
inference(superposition,[status(thm)],[c_1242,c_62]) ).
tcf(c_2748,plain,
! [X0: $i] : multiply(add(n0,add(inverse(inverse(X0)),n0)),add(X0,multiply(X0,inverse(inverse(X0))))) = X0,
inference(superposition,[status(thm)],[c_1242,c_132]) ).
tcf(c_2787,plain,
! [X0: $i,X1: $i] : add(inverse(add(X0,multiply(X1,X0))),multiply(X0,add(X1,X0))) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_60,c_1116]) ).
tcf(c_2942,plain,
! [X0: $i] : add(X0,multiply(multiply(multiply(add(n1,n0),n1),add(n1,n0)),add(X0,n0))) = multiply(add(X0,n0),add(n1,n0)),
inference(superposition,[status(thm)],[c_570,c_156]) ).
tcf(c_2956,plain,
! [X0: $i] : add(X0,multiply(multiply(multiply(add(n1,n0),n1),add(n1,n0)),add(X0,n0))) = X0,
inference(demodulation,[status(thm)],[c_2942,c_62,c_141]) ).
tcf(c_3656,plain,
! [X0: $i,X1: $i] : multiply(add(multiply(X0,X1),n0),add(n1,n1)) = multiply(X1,multiply(add(X0,n0),add(n1,n1))),
inference(superposition,[status(thm)],[c_490,c_1141]) ).
tcf(c_3701,plain,
! [X0: $i] : add(add(inverse(inverse(X0)),n0),multiply(n0,n0)) = add(inverse(inverse(X0)),multiply(X0,X0)),
inference(superposition,[status(thm)],[c_378,c_1177]) ).
tcf(c_3769,plain,
! [X0: $i,X1: $i] : add(multiply(add(X0,multiply(X1,X0)),n1),multiply(n0,n0)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c_1177,c_60]) ).
tcf(c_3783,plain,
! [X0: $i] : add(multiply(add(X0,multiply(X0,X0)),n1),multiply(n0,n0)) = multiply(add(multiply(X0,X0),n0),add(n1,n1)),
inference(superposition,[status(thm)],[c_1177,c_490]) ).
tcf(c_3828,plain,
! [X0: $i] : multiply(X0,multiply(add(X0,n0),add(n1,n1))) = multiply(X0,add(X0,X0)),
inference(demodulation,[status(thm)],[c_3783,c_3656,c_3769]) ).
tcf(c_8647,plain,
! [X0: $i] : multiply(X0,add(n1,multiply(n0,n1))) = multiply(n1,add(n0,multiply(X0,n1))),
inference(superposition,[status(thm)],[c_1325,c_60]) ).
tcf(c_8669,plain,
! [X0: $i] : add(inverse(multiply(X0,add(multiply(n0,n1),multiply(n0,n1)))),multiply(multiply(n0,n1),add(multiply(X0,n1),multiply(n0,n1)))) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_1325,c_2787]) ).
tcf(c_8825,plain,
! [X0: $i] : multiply(X0,add(n1,multiply(n0,n1))) = multiply(n1,X0),
inference(demodulation,[status(thm)],[c_8647,c_141]) ).
tcf(c_8852,plain,
! [X0: $i] : add(inverse(multiply(X0,n0)),multiply(multiply(n0,n1),X0)) = multiply(n1,n1),
inference(demodulation,[status(thm)],[c_8669,c_60,c_139]) ).
tcf(c_9510,plain,
! [X0: $i] : add(multiply(n0,n1),multiply(X0,n1)) = multiply(n1,add(X0,multiply(n0,n1))),
inference(superposition,[status(thm)],[c_8825,c_62]) ).
tcf(c_9528,plain,
add(multiply(n0,n1),multiply(n0,n1)) = multiply(n1,n0),
inference(superposition,[status(thm)],[c_8825,c_162]) ).
tcf(c_9543,plain,
add(inverse(multiply(inverse(multiply(n0,n1)),n0)),n0) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_63,c_8852]) ).
tcf(c_9771,plain,
multiply(n1,n0) = n0,
inference(demodulation,[status(thm)],[c_9528,c_60,c_139]) ).
tcf(c_9774,plain,
! [X0: $i] : multiply(n1,add(X0,multiply(n0,n1))) = multiply(n1,add(n0,X0)),
inference(demodulation,[status(thm)],[c_9510,c_60]) ).
tcf(c_10531,plain,
! [X0: $i] : add(n0,multiply(X0,n0)) = multiply(n0,add(n1,X0)),
inference(superposition,[status(thm)],[c_9771,c_60]) ).
tcf(c_11171,plain,
add(n0,multiply(multiply(n0,n1),n0)) = multiply(n1,n0),
inference(superposition,[status(thm)],[c_10531,c_8825]) ).
tcf(c_11223,plain,
inverse(multiply(inverse(multiply(n0,n1)),n0)) = multiply(n1,multiply(n1,n1)),
inference(superposition,[status(thm)],[c_9543,c_139]) ).
tcf(c_11252,plain,
multiply(n1,add(n0,n1)) = multiply(n1,n1),
inference(superposition,[status(thm)],[c_9774,c_8825]) ).
tcf(c_11330,plain,
add(n0,multiply(multiply(n0,n1),n0)) = n0,
inference(light_normalisation,[status(thm)],[c_11171,c_9771]) ).
tcf(c_11442,plain,
add(multiply(n1,multiply(n1,n1)),n0) = multiply(n1,n1),
inference(demodulation,[status(thm)],[c_9543,c_11223]) ).
tcf(c_16552,plain,
multiply(add(multiply(n1,n1),n0),add(n1,n1)) = multiply(add(n0,n1),add(n1,n1)),
inference(superposition,[status(thm)],[c_11252,c_1141]) ).
tcf(c_16571,plain,
add(multiply(multiply(n0,n1),n0),multiply(n0,n0)) = add(multiply(n0,n1),multiply(n0,n0)),
inference(superposition,[status(thm)],[c_11330,c_1177]) ).
tcf(c_16800,plain,
multiply(n0,add(multiply(n0,n1),n0)) = multiply(n0,n0),
inference(demodulation,[status(thm)],[c_16571,c_60,c_540]) ).
tcf(c_16803,plain,
add(n1,multiply(n0,n1)) = multiply(n1,add(n1,n1)),
inference(demodulation,[status(thm)],[c_16552,c_62,c_3656,c_3828]) ).
tcf(c_17035,plain,
add(multiply(n0,n1),multiply(n0,n0)) = multiply(n0,n1),
inference(superposition,[status(thm)],[c_16800,c_567]) ).
tcf(c_17270,plain,
multiply(n0,n1) = multiply(n0,n0),
inference(demodulation,[status(thm)],[c_17035,c_540]) ).
tcf(c_17455,plain,
! [X0: $i] : add(add(inverse(inverse(X0)),n0),multiply(n0,n1)) = add(inverse(inverse(X0)),multiply(X0,X0)),
inference(demodulation,[status(thm)],[c_3701,c_17270]) ).
tcf(c_17461,plain,
! [X0: $i] : add(multiply(X0,n1),multiply(n0,n1)) = multiply(X0,X0),
inference(demodulation,[status(thm)],[c_540,c_17270]) ).
tcf(c_17462,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_17461,c_60,c_139]) ).
tcf(c_17467,plain,
! [X0: $i] : add(inverse(X0),X0) = multiply(n1,n1),
inference(demodulation,[status(thm)],[c_387,c_17462]) ).
tcf(c_17469,plain,
! [X0: $i] : add(n0,inverse(X0)) = multiply(inverse(X0),n1),
inference(demodulation,[status(thm)],[c_328,c_17462]) ).
tcf(c_17480,plain,
inverse(multiply(inverse(multiply(n0,n1)),n0)) = multiply(n1,n1),
inference(demodulation,[status(thm)],[c_11223,c_17462]) ).
tcf(c_17481,plain,
add(multiply(n1,n1),n0) = n1,
inference(demodulation,[status(thm)],[c_11442,c_17462]) ).
tcf(c_17520,plain,
add(n1,n0) = n1,
inference(demodulation,[status(thm)],[c_17481,c_17462]) ).
tcf(c_17523,plain,
! [X0: $i] : add(X0,multiply(multiply(multiply(n1,n1),n1),add(X0,n0))) = X0,
inference(demodulation,[status(thm)],[c_2956,c_17520]) ).
tcf(c_17533,plain,
! [X0: $i] : add(X0,multiply(n1,add(X0,n0))) = X0,
inference(demodulation,[status(thm)],[c_17523,c_17462]) ).
tcf(c_17534,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_17533,c_139]) ).
tcf(c_17535,plain,
! [X0: $i] : multiply(multiply(inverse(inverse(X0)),n1),add(n1,n1)) = multiply(inverse(inverse(X0)),X0),
inference(demodulation,[status(thm)],[c_1411,c_17534]) ).
tcf(c_17537,plain,
! [X0: $i,X1: $i] : multiply(add(multiply(X0,X1),n0),add(n1,n1)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_1141,c_17534]) ).
tcf(c_17540,plain,
! [X0: $i] : add(inverse(X0),n0) = multiply(n1,inverse(X0)),
inference(demodulation,[status(thm)],[c_356,c_17534]) ).
tcf(c_17541,plain,
add(n1,multiply(n0,n1)) = multiply(n1,n1),
inference(demodulation,[status(thm)],[c_16803,c_17534]) ).
tcf(c_17544,plain,
add(n1,multiply(n0,n1)) = n1,
inference(demodulation,[status(thm)],[c_17541,c_17462]) ).
tcf(c_17545,plain,
! [X0: $i] : multiply(X0,n1) = multiply(n1,X0),
inference(demodulation,[status(thm)],[c_8825,c_17544]) ).
tcf(c_17560,plain,
! [X0: $i] : multiply(n1,add(X0,inverse(inverse(X0)))) = add(inverse(inverse(X0)),n0),
inference(demodulation,[status(thm)],[c_378,c_17545]) ).
tcf(c_17580,plain,
! [X0: $i,X1: $i] : multiply(n1,add(multiply(X0,X1),n0)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_17537,c_17534,c_17545]) ).
tcf(c_17581,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_17580,c_139]) ).
tcf(c_17585,plain,
multiply(b,add(a,b)) != b,
inference(demodulation,[status(thm)],[c_70,c_17581]) ).
tcf(c_17602,plain,
! [X0: $i] : multiply(n1,add(inverse(inverse(X0)),n0)) = multiply(X0,inverse(inverse(X0))),
inference(demodulation,[status(thm)],[c_17535,c_17534,c_17540,c_17545,c_17581]) ).
tcf(c_17603,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[c_17602,c_139]) ).
tcf(c_17605,plain,
! [X0: $i] : multiply(add(n0,add(inverse(inverse(X0)),n0)),add(X0,inverse(inverse(X0)))) = X0,
inference(demodulation,[status(thm)],[c_2748,c_17603]) ).
tcf(c_17606,plain,
! [X0: $i] : add(inverse(inverse(X0)),multiply(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_17605,c_2745]) ).
tcf(c_17609,plain,
inverse(multiply(n0,inverse(multiply(n1,n0)))) = n1,
inference(demodulation,[status(thm)],[c_17480,c_17462,c_17545,c_17581]) ).
tcf(c_17610,plain,
inverse(multiply(n0,inverse(n0))) = n1,
inference(light_normalisation,[status(thm)],[c_17609,c_9771]) ).
tcf(c_17611,plain,
inverse(n0) = n1,
inference(demodulation,[status(thm)],[c_17610,c_63]) ).
tcf(c_17638,plain,
! [X0: $i] : add(inverse(X0),n0) = add(n0,inverse(X0)),
inference(demodulation,[status(thm)],[c_17469,c_17540,c_17545]) ).
tcf(c_17641,plain,
! [X0: $i] : add(inverse(X0),X0) = n1,
inference(demodulation,[status(thm)],[c_17467,c_17462]) ).
tcf(c_17643,plain,
! [X0: $i] : multiply(add(X0,inverse(inverse(X0))),multiply(n1,n1)) = X0,
inference(demodulation,[status(thm)],[c_123,c_17641]) ).
tcf(c_17644,plain,
! [X0: $i] : add(n0,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_17643,c_17462,c_17560,c_17581,c_17638]) ).
tcf(c_17659,plain,
! [X0: $i] : add(X0,multiply(n1,n0)) = X0,
inference(demodulation,[status(thm)],[c_17455,c_17545,c_17606,c_17638,c_17644]) ).
tcf(c_17660,plain,
! [X0: $i] : add(X0,n0) = X0,
inference(light_normalisation,[status(thm)],[c_17659,c_9771]) ).
tcf(c_17669,plain,
! [X0: $i] : multiply(n1,X0) = X0,
inference(demodulation,[status(thm)],[c_139,c_17660]) ).
tcf(c_18458,plain,
! [X0: $i] : add(n0,multiply(X0,n1)) = multiply(n1,add(n0,X0)),
inference(superposition,[status(thm)],[c_17611,c_81]) ).
tcf(c_18490,plain,
! [X0: $i] : add(n0,multiply(n1,X0)) = multiply(n1,add(X0,n0)),
inference(superposition,[status(thm)],[c_17520,c_62]) ).
tcf(c_18492,plain,
! [X0: $i,X1: $i] : add(multiply(n0,X0),multiply(X1,multiply(n1,X0))) = multiply(add(X1,multiply(n0,X0)),multiply(X0,n1)),
inference(superposition,[status(thm)],[c_17520,c_85]) ).
tcf(c_18501,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[c_17534,c_62]) ).
tcf(c_18525,plain,
! [X0: $i] : add(n0,X0) = X0,
inference(demodulation,[status(thm)],[c_18490,c_17660,c_17669]) ).
tcf(c_18534,plain,
! [X0: $i] : multiply(X0,n1) = multiply(n1,X0),
inference(demodulation,[status(thm)],[c_18458,c_18525]) ).
tcf(c_18535,plain,
! [X0: $i] : multiply(X0,n1) = X0,
inference(demodulation,[status(thm)],[c_18534,c_17669]) ).
tcf(c_18572,plain,
! [X0: $i,X1: $i] : add(multiply(n0,X0),multiply(X1,multiply(n1,X0))) = multiply(add(X1,multiply(n0,X0)),X0),
inference(demodulation,[status(thm)],[c_18492,c_18535]) ).
tcf(c_18573,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,multiply(n0,X0))) = multiply(X0,add(n0,X1)),
inference(demodulation,[status(thm)],[c_18572,c_60,c_17581,c_17669]) ).
tcf(c_19093,plain,
! [X0: $i,X1: $i] : multiply(add(X0,inverse(inverse(X1))),X1) = add(inverse(inverse(X1)),multiply(X0,n0)),
inference(superposition,[status(thm)],[c_17644,c_62]) ).
tcf(c_19094,plain,
! [X0: $i] : multiply(X0,add(n0,multiply(n0,inverse(inverse(X0))))) = n0,
inference(superposition,[status(thm)],[c_17644,c_132]) ).
tcf(c_19098,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_17644,c_18525]) ).
tcf(c_19100,plain,
! [X0: $i] : multiply(X0,add(n0,multiply(n0,X0))) = n0,
inference(demodulation,[status(thm)],[c_19094,c_19098]) ).
tcf(c_19101,plain,
! [X0: $i] : multiply(X0,n0) = n0,
inference(demodulation,[status(thm)],[c_19100,c_18525,c_18573]) ).
tcf(c_19104,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(X1,n0),
inference(demodulation,[status(thm)],[c_19093,c_19098,c_19101]) ).
tcf(c_19105,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_19104,c_17581,c_17660,c_18501]) ).
tcf(c_19363,plain,
$false,
inference(ground_joinability,[status(thm)],[c_17585,c_18501,c_19105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 06:38:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.39 Running UEQ theorem proving
% 0.08/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.38/2.76 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.38/2.76 % SZS status Started for theBenchmark.p
% 3.38/2.76 % SZS status Unsatisfiable for theBenchmark.p
% 3.38/2.76
% 3.38/2.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.38/2.76
% 3.38/2.76 % ------ iProver source info
% 3.38/2.76
% 3.38/2.76 % git: date: 2026-07-19 20:42:38 +0200
% 3.38/2.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.38/2.76 % git: non_committed_changes: false
% 3.38/2.76
% 3.38/2.76 % ------ Parsing...% successful
% 3.38/2.76
% 3.38/2.76
% 3.38/2.76 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.38/2.76 % ------ Proving...
% 3.38/2.76 % ------ Problem Properties
% 3.38/2.76
% 3.38/2.76 %
% 3.38/2.76 % clauses 11
% 3.38/2.76 % conjectures 1
% 3.38/2.76 % EPR 0
% 3.38/2.76 % Horn 11
% 3.38/2.76 % unary 11
% 3.38/2.76 % binary 0
% 3.38/2.76 % lits 11
% 3.38/2.76 % lits eq 11
% 3.38/2.76 % fd_pure 0
% 3.38/2.76 % fd_pseudo 0
% 3.38/2.76 % fd_cond 0
% 3.38/2.76 % fd_pseudo_cond 0
% 3.38/2.76 % AC symbols 0
% 3.38/2.76
% 3.38/2.76 % ------ Input Options Time Limit: Unbounded
% 3.38/2.76
% 3.38/2.76
% 3.38/2.76 % ------
% 3.38/2.76 % Current options:
% 3.38/2.76 % ------
% 3.38/2.76
% 3.38/2.76
% 3.38/2.76 %
% 3.38/2.76
% 3.38/2.76 % ------ Proving...
% 3.38/2.76 %
% 3.38/2.76
% 3.38/2.76 % SZS status Unsatisfiable for theBenchmark.p
% 3.38/2.76
% 3.38/2.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.38/2.76
% 3.38/2.76
%------------------------------------------------------------------------------