%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:38:07 PM UTC 2026
% Result : Unsatisfiable 141.71s 22.96s
% Output : CNFRefutation 141.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 190 ( 96 ~; 94 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 161 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X3,X0,X1] :
( sum(X2,X1,X3)
| ~ sum(X2,X0,X3)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
fof(f13,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f14,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f15,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f16,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f17,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f20,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f25,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f30,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X0,X3,X2)
| ~ equalish(X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_91,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_95,plain,
! [X0: $i] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_106,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_107,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_108,negated_conjecture,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_110,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X1,X5,X3)
| ~ product(X1,X4,X0)
| ~ sum(X4,X2,X5)
| ~ product(X1,X2,multiply(X1,X2))
| ~ sum(X0,multiply(X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equalish(multiply(X2,X3),X4)
| ~ sum(X0,X1,X4)
| ~ sum(X0,X1,multiply(X2,X3)) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X4,X3)
| ~ sum(X1,X2,X4)
| ~ product(X0,X2,multiply(X0,X2))
| ~ product(X0,X1,multiply(X0,X1))
| ~ sum(multiply(X0,X1),multiply(X0,X2),X3) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( equalish(X4,multiply(X2,X3))
| ~ product(X0,X1,X4)
| ~ product(X0,X1,multiply(X2,X3)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,add(multiply(X0,X1),multiply(X0,X2)))
| ~ sum(X1,X2,X3)
| ~ product(X0,X2,multiply(X0,X2))
| ~ product(X0,X1,multiply(X0,X1))
| ~ sum(multiply(X0,X1),multiply(X0,X2),add(multiply(X0,X1),multiply(X0,X2))) ),
inference(instantiation,[status(thm)],[c_221]) ).
tcf(c_709,plain,
! [X0: $i,X1: $i,X2: $i] : sum(multiply(X0,X1),multiply(X0,X2),add(multiply(X0,X1),multiply(X0,X2))),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X1),X2)
| ~ sum(additive_identity,multiply(X0,X1),X2)
| ~ sum(additive_identity,multiply(X0,X1),multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_200]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i] : sum(additive_identity,multiply(X0,X1),multiply(X0,X1)),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_3507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(add(multiply(X0,X2),multiply(X0,X3)),multiply(X4,X5))
| ~ product(X0,X1,multiply(X4,X5))
| ~ product(X0,X1,add(multiply(X0,X2),multiply(X0,X3))) ),
inference(instantiation,[status(thm)],[c_513]) ).
tcf(c_21014,plain,
( product(a,additive_identity,additive_identity)
| ~ equalish(multiply(a,additive_identity),additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_21421,plain,
( equalish(multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_21602,plain,
! [X0: $i,X1: $i] :
( product(a,additive_identity,add(multiply(a,X0),multiply(a,X1)))
| ~ sum(X0,X1,additive_identity)
| ~ product(a,X1,multiply(a,X1))
| ~ product(a,X0,multiply(a,X0))
| ~ sum(multiply(a,X0),multiply(a,X1),add(multiply(a,X0),multiply(a,X1))) ),
inference(instantiation,[status(thm)],[c_708]) ).
tcf(c_21604,plain,
( product(a,additive_identity,add(multiply(a,additive_identity),multiply(a,additive_identity)))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),add(multiply(a,additive_identity),multiply(a,additive_identity))) ),
inference(instantiation,[status(thm)],[c_21602]) ).
tcf(c_21723,plain,
! [X0: $i] : product(a,X0,multiply(a,X0)),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_21725,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(instantiation,[status(thm)],[c_21723]) ).
tcf(c_36200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(add(multiply(a,X1),multiply(a,X2)),multiply(X3,additive_identity))
| ~ product(a,X0,multiply(X3,additive_identity))
| ~ product(a,X0,add(multiply(a,X1),multiply(a,X2))) ),
inference(instantiation,[status(thm)],[c_3507]) ).
tcf(c_39382,plain,
! [X0: $i,X1: $i] : sum(multiply(a,X0),multiply(a,X1),add(multiply(a,X0),multiply(a,X1))),
inference(instantiation,[status(thm)],[c_709]) ).
tcf(c_39383,plain,
sum(multiply(a,additive_identity),multiply(a,additive_identity),add(multiply(a,additive_identity),multiply(a,additive_identity))),
inference(instantiation,[status(thm)],[c_39382]) ).
tcf(c_39388,plain,
! [X0: $i] : sum(additive_identity,multiply(a,X0),multiply(a,X0)),
inference(instantiation,[status(thm)],[c_894]) ).
tcf(c_39389,plain,
sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)),
inference(instantiation,[status(thm)],[c_39388]) ).
tcf(c_47746,plain,
! [X0: $i,X1: $i] : sum(additive_inverse(add(multiply(a,X0),multiply(a,X1))),add(multiply(a,X0),multiply(a,X1)),additive_identity),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_47748,plain,
sum(additive_inverse(add(multiply(a,additive_identity),multiply(a,additive_identity))),add(multiply(a,additive_identity),multiply(a,additive_identity)),additive_identity),
inference(instantiation,[status(thm)],[c_47746]) ).
tcf(c_58361,plain,
! [X0: $i,X1: $i] :
( equalish(add(multiply(a,X0),multiply(a,X1)),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,add(multiply(a,X0),multiply(a,X1))) ),
inference(instantiation,[status(thm)],[c_36200]) ).
tcf(c_58362,plain,
( equalish(add(multiply(a,additive_identity),multiply(a,additive_identity)),multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,add(multiply(a,additive_identity),multiply(a,additive_identity))) ),
inference(instantiation,[status(thm)],[c_58361]) ).
tcf(c_162761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X3,multiply(X1,X2),X4)
| ~ sum(X3,X0,X4)
| ~ equalish(X0,multiply(X1,X2)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_162771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X5,multiply(X1,X2),X6)
| ~ sum(X4,X3,X6)
| ~ sum(X4,X0,X5)
| ~ sum(X0,multiply(X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_163391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X5,multiply(X1,X2),X4)
| ~ sum(X3,X0,X5)
| ~ sum(X3,add(X0,multiply(X1,X2)),X4)
| ~ sum(X0,multiply(X1,X2),add(X0,multiply(X1,X2))) ),
inference(instantiation,[status(thm)],[c_162771]) ).
tcf(c_228800,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(a,X1),additive_identity)
| ~ sum(X2,X0,additive_identity)
| ~ equalish(X0,multiply(a,X1)) ),
inference(instantiation,[status(thm)],[c_162761]) ).
tcf(c_235722,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(a,X1),additive_identity)
| ~ sum(X2,add(X0,multiply(a,X1)),additive_identity)
| ~ equalish(add(X0,multiply(a,X1)),multiply(a,X1)) ),
inference(instantiation,[status(thm)],[c_228800]) ).
tcf(c_327910,plain,
! [X0: $i,X1: $i] :
( sum(additive_inverse(add(multiply(a,X0),multiply(a,X1))),multiply(a,X1),additive_identity)
| ~ equalish(add(multiply(a,X0),multiply(a,X1)),multiply(a,X1))
| ~ sum(additive_inverse(add(multiply(a,X0),multiply(a,X1))),add(multiply(a,X0),multiply(a,X1)),additive_identity) ),
inference(instantiation,[status(thm)],[c_235722]) ).
tcf(c_327911,plain,
( sum(additive_inverse(add(multiply(a,additive_identity),multiply(a,additive_identity))),multiply(a,additive_identity),additive_identity)
| ~ equalish(add(multiply(a,additive_identity),multiply(a,additive_identity)),multiply(a,additive_identity))
| ~ sum(additive_inverse(add(multiply(a,additive_identity),multiply(a,additive_identity))),add(multiply(a,additive_identity),multiply(a,additive_identity)),additive_identity) ),
inference(instantiation,[status(thm)],[c_327910]) ).
tcf(c_329591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X3,multiply(a,X1),additive_identity)
| ~ sum(X2,X0,X3)
| ~ sum(X2,add(X0,multiply(a,X1)),additive_identity)
| ~ sum(X0,multiply(a,X1),add(X0,multiply(a,X1))) ),
inference(instantiation,[status(thm)],[c_163391]) ).
tcf(c_338303,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(a,X1),additive_identity)
| ~ sum(additive_inverse(add(multiply(a,X0),multiply(a,X1))),multiply(a,X0),X2)
| ~ sum(multiply(a,X0),multiply(a,X1),add(multiply(a,X0),multiply(a,X1)))
| ~ sum(additive_inverse(add(multiply(a,X0),multiply(a,X1))),add(multiply(a,X0),multiply(a,X1)),additive_identity) ),
inference(instantiation,[status(thm)],[c_329591]) ).
tcf(c_338304,plain,
( sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(add(multiply(a,additive_identity),multiply(a,additive_identity))),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),add(multiply(a,additive_identity),multiply(a,additive_identity)))
| ~ sum(additive_inverse(add(multiply(a,additive_identity),multiply(a,additive_identity))),add(multiply(a,additive_identity),multiply(a,additive_identity)),additive_identity) ),
inference(instantiation,[status(thm)],[c_338303]) ).
tcf(c_338305,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_338304,c_327911,c_58362,c_47748,c_39389,c_39383,c_21725,c_21604,c_21421,c_21014,c_108,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 07:42:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 141.71/22.96 % SZS status Started for theBenchmark.p
% 141.71/22.96 % SZS status Unsatisfiable for theBenchmark.p
% 141.71/22.96
% 141.71/22.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 141.71/22.96
% 141.71/22.96 % ------ iProver source info
% 141.71/22.96
% 141.71/22.96 % git: date: 2026-07-19 20:42:38 +0200
% 141.71/22.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 141.71/22.96 % git: non_committed_changes: false
% 141.71/22.96
% 141.71/22.96 % ------ Parsing...% successful
% 141.71/22.96
% 141.71/22.96
% 141.71/22.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 141.71/22.96
% 141.71/22.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 141.71/22.96
% 141.71/22.96 % ------ Preprocessing...
% 141.71/22.96 % ------ Proving...
% 141.71/22.96 % ------ Problem Properties
% 141.71/22.96
% 141.71/22.96 %
% 141.71/22.96 % clauses 30
% 141.71/22.96 % conjectures 1
% 141.71/22.96 % EPR 23
% 141.71/22.96 % Horn 30
% 141.71/22.96 % unary 8
% 141.71/22.96 % binary 5
% 141.71/22.96 % lits 81
% 141.71/22.96 % lits eq 0
% 141.71/22.96 % fd_pure 0
% 141.71/22.96 % fd_pseudo 0
% 141.71/22.96 % fd_cond 0
% 141.71/22.96 % fd_pseudo_cond 0
% 141.71/22.96 % AC symbols 0
% 141.71/22.96
% 141.71/22.96 % ------ Input Options Time Limit: Unbounded
% 141.71/22.96
% 141.71/22.96
% 141.71/22.96 % ------
% 141.71/22.96 % Current options:
% 141.71/22.96 % ------
% 141.71/22.96
% 141.71/22.96
% 141.71/22.96 %
% 141.71/22.96
% 141.71/22.96 % ------ Proving...
% 141.71/22.96 %
% 141.71/22.96
% 141.71/22.96 % SZS status Unsatisfiable for theBenchmark.p
% 141.71/22.96
% 141.71/22.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 141.71/22.96
% 141.71/22.96
%------------------------------------------------------------------------------