%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:23:16 PM UTC 2026
% Result : Unsatisfiable 1.61s 1.29s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 28 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
fof(f13,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_preserved_over_times) ).
fof(f14,axiom,
! [X0,X1] :
( ~ equalish(X0,X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_and_equal) ).
fof(f15,axiom,
! [X0,X1] :
( less(X1,X0)
| equalish(X1,X0)
| less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
fof(f16,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_not_less_than_itself) ).
fof(f18,axiom,
! [X2,X0,X1] :
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_lemma) ).
fof(f19,axiom,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_less_than_a) ).
fof(f20,axiom,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
fof(f21,negated_conjecture,
~ equalish(c,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_0) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ~ less(X0,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| less(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_85,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f16]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,n0)
| less(multiply(X0,X2),multiply(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
~ less(b,a),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
less(multiply(b,c),multiply(a,c)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
~ equalish(c,n0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_234,plain,
( ~ less(multiply(b,c),multiply(a,c))
| ~ equalish(multiply(b,c),multiply(a,c)) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] :
( equalish(c,n0)
| less(multiply(X0,c),multiply(X1,c))
| ~ less(X0,X1) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_264,plain,
! [X0: $i] :
( less(X0,multiply(a,c))
| ~ less(X0,multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_299,plain,
( equalish(multiply(b,c),multiply(a,c))
| ~ equalish(b,a) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_317,plain,
( less(multiply(a,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(instantiation,[status(thm)],[c_264]) ).
tcf(c_318,plain,
~ less(multiply(a,c),multiply(a,c)),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_589,plain,
( less(a,b)
| equalish(b,a) ),
inference(superposition,[status(thm)],[c_84,c_88]) ).
tcf(c_2827,plain,
( equalish(c,n0)
| less(multiply(a,c),multiply(b,c))
| ~ less(a,b) ),
inference(instantiation,[status(thm)],[c_261]) ).
tcf(c_2831,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2827,c_589,c_318,c_317,c_299,c_234,c_89,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.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 02:45:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.61/1.29 % SZS status Started for theBenchmark.p
% 1.61/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.29
% 1.61/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.29
% 1.61/1.29 % ------ iProver source info
% 1.61/1.29
% 1.61/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.29 % git: non_committed_changes: false
% 1.61/1.29
% 1.61/1.29 % ------ Parsing...% successful
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.29
% 1.61/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.61/1.29
% 1.61/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.61/1.29 % ------ Proving...
% 1.61/1.29 % ------ Problem Properties
% 1.61/1.29
% 1.61/1.29 %
% 1.61/1.29 % clauses 21
% 1.61/1.29 % conjectures 1
% 1.61/1.29 % EPR 9
% 1.61/1.29 % Horn 19
% 1.61/1.29 % unary 10
% 1.61/1.29 % binary 7
% 1.61/1.29 % lits 36
% 1.61/1.29 % lits eq 0
% 1.61/1.29 % fd_pure 0
% 1.61/1.29 % fd_pseudo 0
% 1.61/1.29 % fd_cond 0
% 1.61/1.29 % fd_pseudo_cond 0
% 1.61/1.29 % AC symbols 0
% 1.61/1.29
% 1.61/1.29 % ------ Schedule dynamic 5 is on
% 1.61/1.29
% 1.61/1.29 % ------ no equalities: superposition off
% 1.61/1.29
% 1.61/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 % ------
% 1.61/1.29 % Current options:
% 1.61/1.29 % ------
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 %
% 1.61/1.29
% 1.61/1.29 % ------ Proving...
% 1.61/1.29 %
% 1.61/1.29
% 1.61/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.29
% 1.61/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.29
% 1.61/1.29
%------------------------------------------------------------------------------