%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN007-2 : 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 : n015.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 01:37:22 PM UTC 2026
% Result : Unsatisfiable 0.70s 6.28s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 19 unt; 0 def)
% Number of atoms : 75 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4] :
( less_equal(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f16,axiom,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f17,axiom,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQy) ).
fof(f18,axiom,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQx) ).
fof(f19,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i] : quotient(X0,zero,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X1)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_83,plain,
less_equal(x,y),
inference(cnf_transformation,[],[f16]) ).
tcf(c_84,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[],[f17]) ).
tcf(c_85,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[],[f18]) ).
tcf(c_86,negated_conjecture,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X1)
| ~ less_equal(X2,X3)
| ( divide(X0,X3) != X4 )
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_100,plain,
divide(z,y) = zQy,
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_101,plain,
divide(z,x) = zQx,
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(X0,X1) != X2 )
| less_equal(X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_104]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(renaming,[status(thm)],[c_116]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(unflattening,[status(thm)],[c_117]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(unflattening,[status(thm)],[c_98]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(prop_impl_just,[status(thm)],[c_248]) ).
tcf(c_368,negated_conjecture,
~ less_equal(zQy,zQx),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_698,plain,
! [X0: $i] : less_equal(X0,X0),
inference(superposition,[status(thm)],[c_97,c_228]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(superposition,[status(thm)],[c_698,c_265]) ).
tcf(c_924,plain,
less_equal(divide(z,zQx),x),
inference(superposition,[status(thm)],[c_101,c_717]) ).
tcf(c_979,plain,
! [X0: $i] :
( less_equal(divide(z,zQx),X0)
| ~ less_equal(x,X0) ),
inference(superposition,[status(thm)],[c_924,c_81]) ).
tcf(c_2071,plain,
! [X0: $i] :
( less_equal(divide(z,X0),zQx)
| ~ less_equal(x,X0) ),
inference(superposition,[status(thm)],[c_979,c_265]) ).
tcf(c_3214,plain,
( less_equal(zQy,zQx)
| ~ less_equal(x,y) ),
inference(superposition,[status(thm)],[c_100,c_2071]) ).
tcf(c_3220,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3214,c_368,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/5.37 % Computer : n015.cluster.edu
% 0.07/5.37 % Model : x86_64 x86_64
% 0.07/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.37 % Memory : 8046.5625MB
% 0.07/5.37 % OS : Linux 6.8.0-71-generic
% 0.07/5.37 % CPULimit : 300
% 0.07/5.37 % WCLimit : 300
% 0.07/5.37 % DateTime : Wed Sep 23 16:16:30 UTC 2026
% 0.07/5.37 % CPUTime :
% 0.07/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 0.70/6.28 % SZS status Started for theBenchmark.p
% 0.70/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.70/6.28
% 0.70/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.70/6.28
% 0.70/6.28 % ------ iProver source info
% 0.70/6.28
% 0.70/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.70/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.70/6.28 % git: non_committed_changes: false
% 0.70/6.28
% 0.70/6.28 % ------ Parsing...% successful
% 0.70/6.28
% 0.70/6.28
% 0.70/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.70/6.28
% 0.70/6.28 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.70/6.28
% 0.70/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.70/6.28
% 0.70/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.70/6.28 % ------ Proving...
% 0.70/6.28 % ------ Problem Properties
% 0.70/6.28
% 0.70/6.28 %
% 0.70/6.28 % clauses 17
% 0.70/6.28 % conjectures 1
% 0.70/6.28 % EPR 6
% 0.70/6.28 % Horn 17
% 0.70/6.28 % unary 12
% 0.70/6.28 % binary 3
% 0.70/6.28 % lits 24
% 0.70/6.28 % lits eq 9
% 0.70/6.28 % fd_pure 0
% 0.70/6.28 % fd_pseudo 0
% 0.70/6.28 % fd_cond 0
% 0.70/6.28 % fd_pseudo_cond 1
% 0.70/6.28 % AC symbols 0
% 0.70/6.28
% 0.70/6.28 % ------ Schedule dynamic 5 is on
% 0.70/6.28
% 0.70/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.70/6.28
% 0.70/6.28
% 0.70/6.28 % ------
% 0.70/6.28 % Current options:
% 0.70/6.28 % ------
% 0.70/6.28
% 0.70/6.28
% 0.70/6.28 %
% 0.70/6.28
% 0.70/6.28 % ------ Proving...
% 0.70/6.28 %
% 0.70/6.28
% 0.70/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.70/6.28
% 0.70/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.70/6.28
% 0.70/6.28
%------------------------------------------------------------------------------