%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI302_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 12:58:07 PM UTC 2026
% Result : Theorem 0.24s 6.05s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 28 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 132 ( 10 atm; 52 fun; 25 num; 45 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_1,type,
$bool: $tType ).
tff(f1,conjecture,
$product(1/20,0/1) = 0/1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_product_problem_19) ).
tff(f2,negated_conjecture,
( ( ~ $product(1/20,0/1) ) = 0/1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f4,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f5,plain,
! [X0: $rat] : ( $sum(X0,0/1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f6,plain,
! [X0: $rat,X1: $rat] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f7,plain,
! [X0: $rat] : ( 0/1 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f8,plain,
! [X0: $rat] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f9,plain,
! [X2: $rat,X0: $rat,X1: $rat] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f10,plain,
! [X0: $rat,X1: $rat] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f11,plain,
! [X2: $rat,X0: $rat,X1: $rat] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f12,plain,
! [X0: $rat,X1: $rat] :
( $less(X1,$sum(X0,1/1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f13,plain,
! [X0: $rat] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f14,plain,
! [X0: $rat,X1: $rat] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f15,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f16,plain,
! [X0: $rat] : ( $product(X0,1/1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f17,plain,
! [X0: $rat] : ( 0/1 = $product(X0,0/1) ),
introduced(definition,[],[tha_times_zero]) ).
tff(f18,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(definition,[],[tha_distributivity]) ).
tff(f19,plain,
! [X2: $rat,X3: $rat,X0: $rat,X1: $rat] :
( ( X2 = X3 )
| ( $product(X0,X3) != X1 )
| ( $product(X0,X2) != X1 )
| ( 0/1 = X0 ) ),
introduced(definition,[],[tha_divisibility]) ).
tff(f20,plain,
0/1 != $product(1/20,0/1),
inference(flattening,[],[f2]) ).
tff(f21,plain,
0/1 != $product(1/20,0/1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_53,plain,
! [X0_rat: $rat,X1_rat: $rat,X2_rat: $rat] : $product($product(X0_rat,X1_rat),X2_rat) = $product(X0_rat,$product(X1_rat,X2_rat)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_54,plain,
! [X0_rat: $rat,X1_rat: $rat] : $product(X0_rat,X1_rat) = $product(X1_rat,X0_rat),
inference(cnf_transformation,[],[f14]) ).
tcf(c_64,plain,
! [X0_rat: $rat,X1_rat: $rat,X2_rat: $rat] : $sum($sum(X0_rat,X1_rat),X2_rat) = $sum(X0_rat,$sum(X1_rat,X2_rat)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0_rat: $rat,X1_rat: $rat] : $sum(X0_rat,X1_rat) = $sum(X1_rat,X0_rat),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,negated_conjecture,
$product(1/20,0/1) != 0/1,
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
$product(0/1,1/20) != 0/1,
inference(theory_normalisation,[status(thm)],[c_66,c_53,c_54,c_64,c_65]) ).
tcf(c_135,plain,
$false,
inference(smt_theory_normalisation,[status(thm)],[c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI302_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 06:08:52 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.39 Running TFA theorem proving
% 0.09/5.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.41 % Detected problem language: tptp
% 0.13/5.42 % Proving...
% 0.24/6.05 % SZS status Started for theBenchmark.p
% 0.24/6.05 % SZS status Theorem for theBenchmark.p
% 0.24/6.05
% 0.24/6.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.24/6.05
% 0.24/6.05 % ------ iProver source info
% 0.24/6.05
% 0.24/6.05 % git: date: 2026-07-19 20:42:38 +0200
% 0.24/6.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.24/6.05 % git: non_committed_changes: false
% 0.24/6.05
% 0.24/6.05 % ------ Parsing...
% 0.24/6.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.24/6.05
% 0.24/6.05 % ------ Preprocessing...%
% 0.24/6.05
% 0.24/6.05 % SZS status Theorem for theBenchmark.p
% 0.24/6.05
% 0.24/6.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.24/6.05
% 0.24/6.05
%------------------------------------------------------------------------------