%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN005-2 : 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 : n003.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 01:37:20 PM UTC 2026
% Result : Unsatisfiable 3.37s 1.18s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 23 unt; 0 def)
% Number of atoms : 100 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 43 :)
% 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(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(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f14,axiom,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f15,axiom,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yLEz) ).
fof(f16,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,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_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_75,plain,
! [X0: $i] : quotient(zero,X0,zero),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i] : quotient(X0,zero,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,plain,
less_equal(x,y),
inference(cnf_transformation,[],[f14]) ).
tcf(c_79,plain,
less_equal(y,z),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,negated_conjecture,
~ less_equal(x,z),
inference(cnf_transformation,[],[f16]) ).
tcf(c_89,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_91,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(well_definedness,[status(thm)],[c_77]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_65]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(well_definedness,[status(thm)],[c_66]) ).
tcf(c_96,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_68]) ).
tcf(c_211,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_96]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) != zero )
| less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_93]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(renaming,[status(thm)],[c_219]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_92]) ).
tcf(c_505,plain,
divide(x,y) = zero,
inference(superposition,[status(thm)],[c_78,c_221]) ).
tcf(c_506,plain,
divide(y,z) = zero,
inference(superposition,[status(thm)],[c_79,c_221]) ).
tcf(c_521,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_551,plain,
( less_equal(x,z)
| ( divide(x,z) != zero ) ),
inference(instantiation,[status(thm)],[c_220]) ).
tcf(c_570,plain,
! [X0: $i] : less_equal(divide(divide(x,X0),divide(y,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[c_505,c_211]) ).
tcf(c_571,plain,
! [X0: $i] : less_equal(divide(divide(x,X0),divide(y,X0)),zero),
inference(light_normalisation,[status(thm)],[c_570,c_89]) ).
tcf(c_864,plain,
less_equal(divide(divide(x,z),zero),zero),
inference(superposition,[status(thm)],[c_506,c_571]) ).
tcf(c_878,plain,
less_equal(divide(x,z),zero),
inference(demodulation,[status(thm)],[c_864,c_91]) ).
tcf(c_881,plain,
divide(x,z) = zero,
inference(superposition,[status(thm)],[c_878,c_521]) ).
tcf(c_883,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_881,c_551,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 16:13:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 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...
% 3.37/1.18 % SZS status Started for theBenchmark.p
% 3.37/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.37/1.18
% 3.37/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.37/1.18
% 3.37/1.18 % ------ iProver source info
% 3.37/1.18
% 3.37/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.37/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.37/1.18 % git: non_committed_changes: false
% 3.37/1.18
% 3.37/1.18 % ------ Parsing...% successful
% 3.37/1.18
% 3.37/1.18
% 3.37/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.37/1.18
% 3.37/1.18 % ------ 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 %
% 3.37/1.18
% 3.37/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.37/1.18
% 3.37/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.37/1.18 % ------ Proving...
% 3.37/1.18 % ------ Problem Properties
% 3.37/1.18
% 3.37/1.18 %
% 3.37/1.18 % clauses 14
% 3.37/1.18 % conjectures 1
% 3.37/1.18 % EPR 6
% 3.37/1.18 % Horn 14
% 3.37/1.18 % unary 11
% 3.37/1.18 % binary 2
% 3.37/1.18 % lits 18
% 3.37/1.18 % lits eq 7
% 3.37/1.18 % fd_pure 0
% 3.37/1.18 % fd_pseudo 0
% 3.37/1.18 % fd_cond 0
% 3.37/1.18 % fd_pseudo_cond 1
% 3.37/1.18 % AC symbols 0
% 3.37/1.18
% 3.37/1.18 % ------ Schedule dynamic 5 is on
% 3.37/1.18
% 3.37/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.37/1.18
% 3.37/1.18
% 3.37/1.18 % ------
% 3.37/1.18 % Current options:
% 3.37/1.18 % ------
% 3.37/1.18
% 3.37/1.18
% 3.37/1.18 %
% 3.37/1.18
% 3.37/1.18 % ------ Proving...
% 3.37/1.18 %
% 3.37/1.18
% 3.37/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.37/1.18
% 3.37/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.37/1.18
% 3.37/1.18
%------------------------------------------------------------------------------