%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN008-4 : 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 : n009.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 01:37:23 PM UTC 2026
% Result : Unsatisfiable 2.12s 1.08s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 22 unt; 2 def)
% Number of atoms : 61 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f19,axiom,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
fof(f20,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_79,plain,
less_equal(a,b),
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_203,definition,
iPr_def_10 = divide(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_204,definition,
iPr_def_11 = divide(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_205,negated_conjecture,
~ less_equal(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_80,c_204,c_203]) ).
tcf(c_461,plain,
divide(a,b) = zero,
inference(superposition,[status(thm)],[c_79,c_65]) ).
tcf(c_587,plain,
( less_equal(iPr_def_10,iPr_def_11)
| ( divide(iPr_def_10,iPr_def_11) != zero ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_682,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_743,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[c_461,c_68]) ).
tcf(c_760,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),zero),
inference(light_normalisation,[status(thm)],[c_743,c_73]) ).
tcf(c_2620,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(divide(a,X1),divide(b,X1)),X0)
| ~ less_equal(zero,X0) ),
inference(superposition,[status(thm)],[c_760,c_76]) ).
tcf(c_2627,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_2620,c_69]) ).
tcf(c_3743,plain,
! [X0: $i] : less_equal(divide(divide(a,c),iPr_def_11),X0),
inference(superposition,[status(thm)],[c_204,c_2627]) ).
tcf(c_3752,plain,
! [X0: $i] : less_equal(divide(iPr_def_10,iPr_def_11),X0),
inference(light_normalisation,[status(thm)],[c_3743,c_203]) ).
tcf(c_3786,plain,
divide(iPr_def_10,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_3752,c_682]) ).
tcf(c_3793,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3786,c_587,c_205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 16:14:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.12/1.08 % SZS status Started for theBenchmark.p
% 2.12/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 2.12/1.08
% 2.12/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.12/1.08
% 2.12/1.08 % ------ iProver source info
% 2.12/1.08
% 2.12/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.12/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.12/1.08 % git: non_committed_changes: false
% 2.12/1.08
% 2.12/1.08 % ------ Parsing...% successful
% 2.12/1.08
% 2.12/1.08
% 2.12/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.12/1.08
% 2.12/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.12/1.08
% 2.12/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.12/1.08
% 2.12/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.12/1.08 % ------ Proving...
% 2.12/1.08 % ------ Problem Properties
% 2.12/1.08
% 2.12/1.08 %
% 2.12/1.08 % clauses 18
% 2.12/1.08 % conjectures 1
% 2.12/1.08 % EPR 6
% 2.12/1.08 % Horn 18
% 2.12/1.08 % unary 12
% 2.12/1.08 % binary 4
% 2.12/1.08 % lits 26
% 2.12/1.08 % lits eq 9
% 2.12/1.09 % fd_pure 0
% 2.12/1.09 % fd_pseudo 0
% 2.12/1.09 % fd_cond 0
% 2.12/1.09 % fd_pseudo_cond 1
% 2.12/1.09 % AC symbols 0
% 2.12/1.09
% 2.12/1.09 % ------ Schedule dynamic 5 is on
% 2.12/1.09
% 2.12/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.12/1.09
% 2.12/1.09
% 2.12/1.09 % ------
% 2.12/1.09 % Current options:
% 2.12/1.09 % ------
% 2.12/1.09
% 2.12/1.09
% 2.12/1.09 %
% 2.12/1.09
% 2.12/1.09 % ------ Proving...
% 2.12/1.09 %
% 2.12/1.09
% 2.12/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 2.12/1.09
% 2.12/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.12/1.09
% 2.12/1.09
%------------------------------------------------------------------------------