%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN002-2 : 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 : n017.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 01:37:18 PM UTC 2026
% Result : Unsatisfiable 1.61s 1.27s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 11 unt; 1 def)
% Number of atoms : 29 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
fof(f11,negated_conjecture,
~ quotient(zero,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_divide_anything_is_zero) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,negated_conjecture,
~ quotient(zero,x,zero),
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
divide(zero,x) != zero,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_80]) ).
tcf(c_252,definition,
iPr_def_10 = divide(zero,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_253,plain,
iPr_def_10 != zero,
inference(demodulation,[status(thm)],[c_79,c_252]) ).
tcf(c_428,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_64,c_193]) ).
tcf(c_432,plain,
zero = iPr_def_10,
inference(demodulation,[status(thm)],[c_252,c_428]) ).
tcf(c_438,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_253,c_432]) ).
tcf(c_439,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n017.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 : Wed Sep 23 16:03:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 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...
% 1.61/1.27 % SZS status Started for theBenchmark.p
% 1.61/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.27
% 1.61/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.27
% 1.61/1.27 % ------ iProver source info
% 1.61/1.27
% 1.61/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.27 % git: non_committed_changes: false
% 1.61/1.27
% 1.61/1.27 % ------ Parsing...% successful
% 1.61/1.27
% 1.61/1.27
% 1.61/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.27
% 1.61/1.27 % ------ Preprocessing... sup_sim: 4 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 %
% 1.61/1.27
% 1.61/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.27
% 1.61/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.27 % ------ Proving...
% 1.61/1.27 % ------ Problem Properties
% 1.61/1.27
% 1.61/1.27 %
% 1.61/1.27 % clauses 10
% 1.61/1.27 % conjectures 0
% 1.61/1.27 % EPR 4
% 1.61/1.27 % Horn 10
% 1.61/1.27 % unary 7
% 1.61/1.27 % binary 2
% 1.61/1.27 % lits 14
% 1.61/1.27 % lits eq 6
% 1.61/1.27 % fd_pure 0
% 1.61/1.27 % fd_pseudo 0
% 1.61/1.27 % fd_cond 0
% 1.61/1.27 % fd_pseudo_cond 1
% 1.61/1.27 % AC symbols 0
% 1.61/1.27
% 1.61/1.27 % ------ Schedule dynamic 5 is on
% 1.61/1.27
% 1.61/1.27 % ------ no conjectures: strip conj schedule
% 1.61/1.27
% 1.61/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.61/1.27
% 1.61/1.27
% 1.61/1.27 % ------
% 1.61/1.27 % Current options:
% 1.61/1.27 % ------
% 1.61/1.27
% 1.61/1.27
% 1.61/1.27 %
% 1.61/1.27
% 1.61/1.27 % ------ Proving...
% 1.61/1.27 %
% 1.61/1.27
% 1.61/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.27
% 1.61/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.27
% 1.61/1.27
%------------------------------------------------------------------------------