%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN003-2 : 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 : n012.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 01:37:19 PM UTC 2026
% Result : Unsatisfiable 0.07s 5.96s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 19 unt; 1 def)
% Number of atoms : 146 ( 37 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 92 ( 48 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
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(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f12,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( less_equal(X7,X6)
| ~ quotient(X4,X5,X7)
| ~ quotient(X2,X3,X6)
| ~ quotient(X1,X3,X5)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,negated_conjecture,
~ quotient(x,x,zero),
inference(cnf_transformation,[],[f12]) ).
tcf(c_82,plain,
divide(x,x) != zero,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( less_equal(X7,X6)
| ( divide(X4,X5) != X7 )
| ( divide(X2,X3) != X6 )
| ( divide(X1,X3) != X5 )
| ( divide(X0,X3) != X4 )
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_64]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(X0,X1) != X2 )
| less_equal(X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(renaming,[status(thm)],[c_97]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(unflattening,[status(thm)],[c_98]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(unflattening,[status(thm)],[c_87]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) != zero )
| less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(renaming,[status(thm)],[c_198]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
tcf(c_262,definition,
iPr_def_10 = divide(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_263,plain,
iPr_def_10 != zero,
inference(demodulation,[status(thm)],[c_82,c_262]) ).
tcf(c_264,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_436,plain,
less_equal(iPr_def_10,x),
inference(superposition,[status(thm)],[c_262,c_176]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_176,c_200]) ).
tcf(c_451,plain,
divide(iPr_def_10,x) = zero,
inference(superposition,[status(thm)],[c_436,c_200]) ).
tcf(c_459,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_65,c_66]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = X0 )
| ~ less_equal(X0,divide(X0,X1)) ),
inference(superposition,[status(thm)],[c_176,c_66]) ).
tcf(c_510,plain,
( ( divide(iPr_def_10,x) = iPr_def_10 )
| ~ less_equal(iPr_def_10,zero) ),
inference(superposition,[status(thm)],[c_451,c_461]) ).
tcf(c_511,plain,
( ( zero = iPr_def_10 )
| ~ less_equal(iPr_def_10,zero) ),
inference(light_normalisation,[status(thm)],[c_510,c_451]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[c_450,c_190]) ).
tcf(c_571,plain,
! [X0: $i] :
( ( iPr_def_10 = zero )
| ( iPr_def_10 != X0 )
| ( zero != X0 ) ),
inference(instantiation,[status(thm)],[c_266]) ).
tcf(c_572,plain,
( less_equal(iPr_def_10,zero)
| ( divide(iPr_def_10,zero) != zero ) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_575,plain,
( ( iPr_def_10 = zero )
| ( iPr_def_10 != iPr_def_10 )
| ( zero != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_571]) ).
tcf(c_576,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_264]) ).
tcf(c_586,plain,
less_equal(divide(divide(x,x),zero),zero),
inference(superposition,[status(thm)],[c_451,c_535]) ).
tcf(c_590,plain,
less_equal(divide(iPr_def_10,zero),zero),
inference(light_normalisation,[status(thm)],[c_586,c_262]) ).
tcf(c_606,plain,
divide(iPr_def_10,zero) = zero,
inference(superposition,[status(thm)],[c_590,c_459]) ).
tcf(c_608,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_606,c_576,c_575,c_572,c_511,c_263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.31 % Computer : n012.cluster.edu
% 0.03/5.31 % Model : x86_64 x86_64
% 0.03/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.31 % Memory : 8046.5625MB
% 0.03/5.31 % OS : Linux 6.8.0-71-generic
% 0.03/5.31 % CPULimit : 300
% 0.03/5.31 % WCLimit : 300
% 0.03/5.31 % DateTime : Wed Sep 23 16:08:57 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.33 Running first-order theorem proving
% 0.03/5.33 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
% 0.03/5.33
% 0.03/5.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/5.33
% 0.03/5.33 % Detected problem language: tptp
% 0.03/5.34 % Proving...
% 0.07/5.96 % SZS status Started for theBenchmark.p
% 0.07/5.96 % SZS status Unsatisfiable for theBenchmark.p
% 0.07/5.96
% 0.07/5.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.07/5.96
% 0.07/5.96 % ------ iProver source info
% 0.07/5.96
% 0.07/5.96 % git: date: 2026-07-19 20:42:38 +0200
% 0.07/5.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.07/5.96 % git: non_committed_changes: false
% 0.07/5.96
% 0.07/5.96 % ------ Parsing...% successful
% 0.07/5.96
% 0.07/5.96
% 0.07/5.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.07/5.96
% 0.07/5.96 % ------ 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 %
% 0.07/5.96
% 0.07/5.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.07/5.96
% 0.07/5.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.07/5.96 % ------ Proving...
% 0.07/5.96 % ------ Problem Properties
% 0.07/5.96
% 0.07/5.96 %
% 0.07/5.96 % clauses 11
% 0.07/5.96 % conjectures 0
% 0.07/5.96 % EPR 4
% 0.07/5.96 % Horn 11
% 0.07/5.96 % unary 8
% 0.07/5.96 % binary 2
% 0.07/5.96 % lits 15
% 0.07/5.96 % lits eq 7
% 0.07/5.96 % fd_pure 0
% 0.07/5.96 % fd_pseudo 0
% 0.07/5.96 % fd_cond 0
% 0.07/5.96 % fd_pseudo_cond 1
% 0.07/5.96 % AC symbols 0
% 0.07/5.96
% 0.07/5.96 % ------ Schedule dynamic 5 is on
% 0.07/5.96
% 0.07/5.96 % ------ no conjectures: strip conj schedule
% 0.07/5.96
% 0.07/5.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.07/5.96
% 0.07/5.96
% 0.07/5.96 % ------
% 0.07/5.96 % Current options:
% 0.07/5.96 % ------
% 0.07/5.96
% 0.07/5.96
% 0.07/5.96 %
% 0.07/5.96
% 0.07/5.96 % ------ Proving...
% 0.07/5.96 %
% 0.07/5.96
% 0.07/5.96 % SZS status Unsatisfiable for theBenchmark.p
% 0.07/5.96
% 0.07/5.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.07/5.96
% 0.07/5.96
%------------------------------------------------------------------------------