%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:38:17 PM UTC 2026
% Result : Unsatisfiable 33.67s 7.96s
% Output : CNFRefutation 33.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 124 ( 48 unt; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 240 ( 122 ~; 118 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 205 ( 0 sgn 205 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X3,X0,X1] :
( sum(X2,X1,X3)
| ~ sum(X2,X0,X3)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( sum(X2,X3,X1)
| ~ sum(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( product(X1,X2,X3)
| ~ product(X0,X2,X3)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( product(X2,X1,X3)
| ~ product(X2,X0,X3)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
fof(f12,axiom,
! [X2,X0,X1] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f13,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f15,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f19,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f20,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f21,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f26,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f27,axiom,
! [X0] : product(X0,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f30,axiom,
! [X2,X3,X0,X1] :
( equalish(X3,X0)
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_left_cancellation) ).
fof(f31,axiom,
! [X2,X3,X0,X1] :
( equalish(X3,X1)
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_right_concellation) ).
fof(f34,axiom,
! [X0] : sum(X0,X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
fof(f37,axiom,
! [X0] : equalish(multiply(X0,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
fof(f41,axiom,
product(a,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
fof(f43,axiom,
product(c,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
fof(f45,axiom,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
fof(f46,axiom,
! [X0,X1] : product(a,multiply(b,X0),multiply(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
fof(f48,axiom,
product(a,multiply(b,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
fof(f55,axiom,
! [X0] : product(multiply(X0,a),b,multiply(X0,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
fof(f71,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f72,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f73,negated_conjecture,
product(b,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).
fof(f74,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X0,X3,X2)
| ~ equalish(X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X2)
| ~ equalish(X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,X2)
| ~ equalish(X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_135,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_148,plain,
! [X0: $i] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_149,plain,
! [X0: $i] : product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[],[f27]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X3,X0)
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X3,X1)
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_156,plain,
! [X0: $i] : sum(X0,X0,additive_identity),
inference(cnf_transformation,[],[f34]) ).
tcf(c_159,plain,
! [X0: $i] : equalish(multiply(X0,X0),X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_163,plain,
product(a,c,c),
inference(cnf_transformation,[],[f41]) ).
tcf(c_165,plain,
product(c,b,c),
inference(cnf_transformation,[],[f43]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : product(X0,multiply(X0,X1),multiply(X0,X1)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] : product(a,multiply(b,X0),multiply(X1,X0)),
inference(cnf_transformation,[],[f46]) ).
tcf(c_170,plain,
product(a,multiply(b,c),c),
inference(cnf_transformation,[],[f48]) ).
tcf(c_177,plain,
! [X0: $i] : product(multiply(X0,a),b,multiply(X0,c)),
inference(cnf_transformation,[],[f55]) ).
tcf(c_193,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f71]) ).
tcf(c_194,negated_conjecture,
product(a,b,c),
inference(cnf_transformation,[],[f72]) ).
tcf(c_195,negated_conjecture,
product(b,a,d),
inference(cnf_transformation,[],[f73]) ).
tcf(c_196,negated_conjecture,
~ equalish(c,d),
inference(cnf_transformation,[],[f74]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X0,X1)
| ~ equalish(X0,X1)
| ~ sum(additive_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i] :
( sum(X0,X1,additive_identity)
| ~ equalish(X0,X1)
| ~ sum(X0,X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_495,plain,
! [X0: $i,X1: $i] :
( equalish(c,d)
| ~ sum(d,X0,X1)
| ~ sum(c,X0,X1) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_619,plain,
sum(additive_identity,d,d),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] :
( sum(X0,additive_identity,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_810,plain,
! [X0: $i] :
( equalish(c,d)
| ~ sum(d,additive_identity,X0)
| ~ sum(c,additive_identity,X0) ),
inference(instantiation,[status(thm)],[c_495]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,additive_identity)
| ~ equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_148,c_130]) ).
tcf(c_861,plain,
! [X0: $i] :
( product(X0,b,c)
| ~ equalish(c,X0) ),
inference(superposition,[status(thm)],[c_165,c_130]) ).
tcf(c_890,plain,
! [X0: $i] :
( product(X0,b,c)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_194,c_130]) ).
tcf(c_891,plain,
! [X0: $i] :
( product(X0,a,d)
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_195,c_130]) ).
tcf(c_1764,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,additive_identity)
| ~ equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_149,c_131]) ).
tcf(c_1795,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_131]) ).
tcf(c_1796,plain,
! [X0: $i] :
( product(a,X0,c)
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_194,c_131]) ).
tcf(c_2173,plain,
! [X0: $i] :
( product(a,b,X0)
| ~ equalish(c,X0) ),
inference(superposition,[status(thm)],[c_194,c_132]) ).
tcf(c_2799,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_135,c_126]) ).
tcf(c_3235,plain,
! [X0: $i,X1: $i] :
( product(a,b,X1)
| ~ equalish(c,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_2173,c_132]) ).
tcf(c_3718,plain,
! [X0: $i] :
( product(a,b,X0)
| ~ equalish(c,multiply(X0,X0)) ),
inference(superposition,[status(thm)],[c_159,c_3235]) ).
tcf(c_3818,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_135,c_150]) ).
tcf(c_3864,plain,
( equalish(c,d)
| ~ sum(d,additive_identity,additive_identity)
| ~ sum(c,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_3865,plain,
( sum(c,additive_identity,additive_identity)
| ~ equalish(c,additive_identity)
| ~ sum(c,c,additive_identity) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_3951,plain,
sum(c,c,additive_identity),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_3979,plain,
! [X0: $i,X1: $i] :
( equalish(additive_identity,X1)
| ~ product(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_148,c_151]) ).
tcf(c_3981,plain,
! [X0: $i] :
( equalish(c,X0)
| ~ product(a,c,X0) ),
inference(superposition,[status(thm)],[c_163,c_151]) ).
tcf(c_3988,plain,
! [X0: $i] :
( equalish(c,X0)
| ~ product(a,multiply(b,c),X0) ),
inference(superposition,[status(thm)],[c_170,c_151]) ).
tcf(c_4019,plain,
! [X0: $i,X1: $i] :
( equalish(c,X1)
| ~ equalish(a,X0)
| ~ product(X0,b,X1) ),
inference(superposition,[status(thm)],[c_890,c_151]) ).
tcf(c_4026,plain,
! [X0: $i,X1: $i] :
( equalish(c,X1)
| ~ equalish(b,X0)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_1796,c_151]) ).
tcf(c_6325,plain,
! [X0: $i] : equalish(c,multiply(X0,c)),
inference(superposition,[status(thm)],[c_168,c_3988]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,d)
| ~ product(X1,a,X2)
| ~ product(X0,X1,b) ),
inference(resolution,[status(thm)],[c_142,c_195]) ).
tcf(c_8247,plain,
! [X0: $i] :
( product(X0,d,d)
| ~ product(X0,b,b) ),
inference(resolution,[status(thm)],[c_6943,c_195]) ).
tcf(c_8248,plain,
( product(a,d,d)
| ~ product(a,b,b) ),
inference(instantiation,[status(thm)],[c_8247]) ).
tcf(c_11830,plain,
! [X0: $i,X1: $i] :
( equalish(c,multiply(X1,X0))
| ~ equalish(b,multiply(b,X0)) ),
inference(superposition,[status(thm)],[c_168,c_4026]) ).
tcf(c_13844,plain,
( sum(additive_identity,d,additive_identity)
| ~ equalish(d,additive_identity)
| ~ sum(additive_identity,d,d) ),
inference(instantiation,[status(thm)],[c_482]) ).
tcf(c_14347,plain,
( sum(d,additive_identity,additive_identity)
| ~ sum(additive_identity,d,additive_identity) ),
inference(instantiation,[status(thm)],[c_742]) ).
tcf(c_24421,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_2799,c_3818]) ).
tcf(c_26038,plain,
! [X0: $i] : equalish(X0,multiply(X0,X0)),
inference(superposition,[status(thm)],[c_159,c_24421]) ).
tcf(c_26188,plain,
! [X0: $i] : equalish(c,multiply(X0,b)),
inference(superposition,[status(thm)],[c_26038,c_11830]) ).
tcf(c_27064,plain,
( equalish(additive_identity,c)
| ~ equalish(c,additive_identity) ),
inference(superposition,[status(thm)],[c_861,c_3979]) ).
tcf(c_27847,plain,
( equalish(c,additive_identity)
| ~ equalish(additive_identity,c) ),
inference(superposition,[status(thm)],[c_1764,c_3981]) ).
tcf(c_31014,plain,
! [X0: $i] :
( equalish(c,multiply(X0,b))
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_137,c_4019]) ).
tcf(c_31051,plain,
! [X0: $i] : equalish(c,multiply(X0,b)),
inference(global_subsumption_just,[status(thm)],[c_31014,c_26188]) ).
tcf(c_31406,plain,
product(a,b,b),
inference(superposition,[status(thm)],[c_31051,c_3718]) ).
tcf(c_31414,plain,
! [X0: $i] :
( equalish(c,multiply(X0,c))
| ~ equalish(a,multiply(X0,a)) ),
inference(superposition,[status(thm)],[c_177,c_4019]) ).
tcf(c_31417,plain,
! [X0: $i] : equalish(c,multiply(X0,c)),
inference(global_subsumption_just,[status(thm)],[c_31414,c_6325]) ).
tcf(c_31719,plain,
! [X0: $i,X1: $i] :
( equalish(c,X1)
| ~ equalish(multiply(X0,c),X1) ),
inference(superposition,[status(thm)],[c_31417,c_134]) ).
tcf(c_32493,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ sum(X0,X1,additive_identity) ),
inference(superposition,[status(thm)],[c_156,c_153]) ).
tcf(c_32669,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,X1,X2)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(superposition,[status(thm)],[c_194,c_142]) ).
tcf(c_32752,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(c,X2,X1)
| ~ product(b,X2,X0)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_194,c_143]) ).
tcf(c_32753,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(d,X0,X2)
| ~ product(b,X1,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_143]) ).
tcf(c_32882,plain,
! [X0: $i] :
( product(a,additive_identity,X0)
| ~ product(c,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_149,c_32669]) ).
tcf(c_32893,plain,
! [X0: $i] :
( product(a,d,X0)
| ~ product(c,a,X0) ),
inference(superposition,[status(thm)],[c_195,c_32669]) ).
tcf(c_32914,plain,
( product(a,d,d)
| ~ equalish(b,c) ),
inference(superposition,[status(thm)],[c_891,c_32893]) ).
tcf(c_33015,plain,
! [X0: $i] :
( product(d,b,X0)
| ~ product(b,c,X0) ),
inference(superposition,[status(thm)],[c_194,c_32753]) ).
tcf(c_33215,plain,
product(a,d,d),
inference(global_subsumption_just,[status(thm)],[c_32914,c_8248,c_31406]) ).
tcf(c_33224,plain,
! [X0: $i] :
( product(c,X0,d)
| ~ product(b,X0,d) ),
inference(superposition,[status(thm)],[c_33215,c_32752]) ).
tcf(c_33814,plain,
product(c,a,d),
inference(superposition,[status(thm)],[c_195,c_33224]) ).
tcf(c_33829,plain,
! [X0: $i] :
( equalish(d,X0)
| ~ product(c,a,X0) ),
inference(superposition,[status(thm)],[c_33814,c_151]) ).
tcf(c_33911,plain,
( equalish(d,additive_identity)
| ~ equalish(additive_identity,c) ),
inference(superposition,[status(thm)],[c_857,c_33829]) ).
tcf(c_34679,plain,
( product(d,b,additive_identity)
| ~ equalish(additive_identity,c) ),
inference(superposition,[status(thm)],[c_1764,c_33015]) ).
tcf(c_34781,plain,
~ equalish(additive_identity,c),
inference(global_subsumption_just,[status(thm)],[c_34679,c_196,c_619,c_3864,c_3865,c_3951,c_13844,c_14347,c_27847,c_33911]) ).
tcf(c_34933,plain,
( product(a,additive_identity,c)
| ~ equalish(c,additive_identity) ),
inference(superposition,[status(thm)],[c_1795,c_32882]) ).
tcf(c_35342,plain,
! [X0: $i] :
( equalish(X0,additive_identity)
| ~ equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_2799,c_32493]) ).
tcf(c_35508,plain,
~ equalish(c,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_34933,c_27064,c_34781]) ).
tcf(c_36418,plain,
! [X0: $i] : equalish(additive_identity,multiply(additive_identity,X0)),
inference(superposition,[status(thm)],[c_167,c_3979]) ).
tcf(c_36445,plain,
! [X0: $i] : equalish(multiply(additive_identity,X0),additive_identity),
inference(superposition,[status(thm)],[c_36418,c_35342]) ).
tcf(c_36454,plain,
equalish(c,additive_identity),
inference(superposition,[status(thm)],[c_36445,c_31719]) ).
tcf(c_36455,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_36454,c_35508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:58:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 33.67/7.96 % SZS status Started for theBenchmark.p
% 33.67/7.96 % SZS status Unsatisfiable for theBenchmark.p
% 33.67/7.96
% 33.67/7.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.67/7.96
% 33.67/7.96 % ------ iProver source info
% 33.67/7.96
% 33.67/7.96 % git: date: 2026-07-19 20:42:38 +0200
% 33.67/7.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.67/7.96 % git: non_committed_changes: false
% 33.67/7.96
% 33.67/7.96 % ------ Parsing...% successful
% 33.67/7.96
% 33.67/7.96
% 33.67/7.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.67/7.96
% 33.67/7.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 33.67/7.96
% 33.67/7.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 33.67/7.96 % ------ Proving...
% 33.67/7.96 % ------ Problem Properties
% 33.67/7.96
% 33.67/7.96 %
% 33.67/7.96 % clauses 74
% 33.67/7.96 % conjectures 3
% 33.67/7.96 % EPR 34
% 33.67/7.96 % Horn 74
% 33.67/7.96 % unary 50
% 33.67/7.96 % binary 5
% 33.67/7.96 % lits 129
% 33.67/7.96 % lits eq 0
% 33.67/7.96 % fd_pure 0
% 33.67/7.96 % fd_pseudo 0
% 33.67/7.97 % fd_cond 0
% 33.67/7.97 % fd_pseudo_cond 0
% 33.67/7.97 % AC symbols 0
% 33.67/7.97
% 33.67/7.97 % ------ Input Options Time Limit: Unbounded
% 33.67/7.97
% 33.67/7.97
% 33.67/7.97 % ------
% 33.67/7.97 % Current options:
% 33.67/7.97 % ------
% 33.67/7.97
% 33.67/7.97
% 33.67/7.97 %
% 33.67/7.97
% 33.67/7.97 % ------ Proving...
% 33.67/7.97 %
% 33.67/7.97
% 33.67/7.97 % SZS status Unsatisfiable for theBenchmark.p
% 33.67/7.97
% 33.67/7.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.67/7.97
% 33.67/7.97
%------------------------------------------------------------------------------