%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG001-2 : 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 : n014.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 7.21s 1.76s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 144 ( 73 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f4,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f6,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f14,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/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f18,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem) ).
tcf(c_69,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,plain,
! [X0: $i] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,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,[],[f9]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X4,X5,X6)
| ~ product(X3,X2,X6)
| ~ product(X3,X1,X5)
| ~ product(X3,X0,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,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,[],[f14]) ).
tcf(c_84,negated_conjecture,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_85,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(a,additive_identity,additive_identity)
| ~ product(a,X1,X3)
| ~ product(a,X0,X2)
| ~ sum(X2,X3,additive_identity)
| ~ sum(X0,X1,additive_identity) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,additive_identity,additive_identity)
| ~ product(a,X2,X0)
| ~ sum(X2,X1,additive_identity)
| ~ product(a,X1,multiply(a,X1))
| ~ sum(X0,multiply(a,X1),additive_identity) ),
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] :
( product(a,additive_identity,additive_identity)
| ~ sum(X0,X1,additive_identity)
| ~ product(a,X1,multiply(a,X1))
| ~ product(a,X0,multiply(a,X0))
| ~ sum(multiply(a,X0),multiply(a,X1),additive_identity) ),
inference(instantiation,[status(thm)],[c_216]) ).
tcf(c_249,plain,
( product(a,additive_identity,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),additive_identity) ),
inference(instantiation,[status(thm)],[c_248]) ).
tcf(c_291,plain,
! [X0: $i] : product(a,X0,multiply(a,X0)),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_292,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(multiply(a,X2),multiply(a,X3),additive_identity)
| ~ sum(X0,X4,additive_identity)
| ~ sum(X1,multiply(a,X3),X4)
| ~ sum(X0,X1,multiply(a,X2)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(multiply(a,X2),multiply(a,X4),X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,multiply(a,X4))
| ~ product(X0,X1,multiply(a,X2)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_553,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_75]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,multiply(a,additive_identity))
| ~ sum(X0,X1,multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(multiply(a,X1),multiply(a,X3),multiply(a,additive_identity))
| ~ sum(X0,X2,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,X2,multiply(a,X3))
| ~ product(a,X0,multiply(a,X1)) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_1011,plain,
( sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_1818,plain,
sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1923,plain,
sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2201,plain,
( sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| ~ sum(multiply(a,additive_identity),additive_identity,multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_762]) ).
tcf(c_3510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X3,multiply(a,X1),X4)
| ~ sum(X2,multiply(a,additive_identity),X4)
| ~ sum(X2,multiply(a,X0),X3)
| ~ sum(multiply(a,X0),multiply(a,X1),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_553]) ).
tcf(c_3538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(multiply(a,X3),multiply(a,X1),additive_identity)
| ~ sum(X2,multiply(a,additive_identity),additive_identity)
| ~ sum(X2,multiply(a,X0),multiply(a,X3))
| ~ sum(multiply(a,X0),multiply(a,X1),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_418]) ).
tcf(c_3539,plain,
( sum(multiply(a,additive_identity),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))
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_3538]) ).
tcf(c_9393,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(a,X1),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,X0),X2)
| ~ sum(multiply(a,X0),multiply(a,X1),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_3510]) ).
tcf(c_9394,plain,
( sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(instantiation,[status(thm)],[c_9393]) ).
tcf(c_9395,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9394,c_3539,c_2201,c_1923,c_1818,c_1011,c_292,c_249,c_84,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 07:40:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 7.21/1.76 % SZS status Started for theBenchmark.p
% 7.21/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 7.21/1.76
% 7.21/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.21/1.76
% 7.21/1.76 % ------ iProver source info
% 7.21/1.76
% 7.21/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 7.21/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.21/1.76 % git: non_committed_changes: false
% 7.21/1.76
% 7.21/1.76 % ------ Parsing...% successful
% 7.21/1.76
% 7.21/1.76
% 7.21/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.21/1.76
% 7.21/1.76 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.21/1.76
% 7.21/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.21/1.76 % ------ Proving...
% 7.21/1.76 % ------ Problem Properties
% 7.21/1.76
% 7.21/1.76 %
% 7.21/1.76 % clauses 18
% 7.21/1.76 % conjectures 1
% 7.21/1.76 % EPR 14
% 7.21/1.76 % Horn 18
% 7.21/1.76 % unary 7
% 7.21/1.76 % binary 1
% 7.21/1.76 % lits 51
% 7.21/1.76 % lits eq 0
% 7.21/1.76 % fd_pure 0
% 7.21/1.76 % fd_pseudo 0
% 7.21/1.76 % fd_cond 0
% 7.21/1.76 % fd_pseudo_cond 0
% 7.21/1.76 % AC symbols 0
% 7.21/1.76
% 7.21/1.76 % ------ Input Options Time Limit: Unbounded
% 7.21/1.76
% 7.21/1.76
% 7.21/1.76 % ------
% 7.21/1.76 % Current options:
% 7.21/1.76 % ------
% 7.21/1.76
% 7.21/1.76
% 7.21/1.76 %
% 7.21/1.76
% 7.21/1.76 % ------ Proving...
% 7.21/1.76 %
% 7.21/1.76
% 7.21/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 7.21/1.76
% 7.21/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.21/1.76
% 7.21/1.76
%------------------------------------------------------------------------------