%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN008-2 : 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 01:37:23 PM UTC 2026
% Result : Unsatisfiable 3.30s 6.19s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 24 unt; 0 def)
% Number of atoms : 115 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 37 ~; 35 |; 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 50 :)
% 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(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(f17,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
fof(f18,axiom,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
fof(f19,axiom,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
fof(f20,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,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_73,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_79,plain,
! [X0: $i] : quotient(zero,X0,zero),
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,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_85,plain,
less_equal(a,b),
inference(cnf_transformation,[],[f17]) ).
tcf(c_86,plain,
quotient(a,c,aQc),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,plain,
quotient(b,c,bQc),
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
~ less_equal(aQc,bQc),
inference(cnf_transformation,[],[f20]) ).
tcf(c_97,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_104,plain,
divide(a,c) = aQc,
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_105,plain,
divide(b,c) = bQc,
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_110,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_72]) ).
tcf(c_272,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_110]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) != zero )
| less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_107]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(renaming,[status(thm)],[c_281]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_106]) ).
tcf(c_681,plain,
divide(a,b) = zero,
inference(superposition,[status(thm)],[c_85,c_283]) ).
tcf(c_750,plain,
( less_equal(aQc,bQc)
| ( divide(aQc,bQc) != zero ) ),
inference(instantiation,[status(thm)],[c_282]) ).
tcf(c_852,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[c_681,c_272]) ).
tcf(c_859,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),zero),
inference(light_normalisation,[status(thm)],[c_852,c_97]) ).
tcf(c_975,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_73,c_74]) ).
tcf(c_2546,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(divide(a,X1),divide(b,X1)),X0)
| ~ less_equal(zero,X0) ),
inference(superposition,[status(thm)],[c_859,c_82]) ).
tcf(c_2553,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_2546,c_73]) ).
tcf(c_4062,plain,
! [X0: $i] : less_equal(divide(divide(a,c),bQc),X0),
inference(superposition,[status(thm)],[c_105,c_2553]) ).
tcf(c_4070,plain,
! [X0: $i] : less_equal(divide(aQc,bQc),X0),
inference(light_normalisation,[status(thm)],[c_4062,c_104]) ).
tcf(c_4321,plain,
divide(aQc,bQc) = zero,
inference(superposition,[status(thm)],[c_4070,c_975]) ).
tcf(c_4328,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4321,c_750,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n003.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 16:16:10 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 3.30/6.19 % SZS status Started for theBenchmark.p
% 3.30/6.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.30/6.19
% 3.30/6.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.30/6.19
% 3.30/6.19 % ------ iProver source info
% 3.30/6.19
% 3.30/6.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.30/6.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.30/6.19 % git: non_committed_changes: false
% 3.30/6.19
% 3.30/6.19 % ------ Parsing...% successful
% 3.30/6.19
% 3.30/6.19
% 3.30/6.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.30/6.19
% 3.30/6.19 % ------ Preprocessing... sup_sim: 6 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 %
% 3.30/6.19
% 3.30/6.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.30/6.19
% 3.30/6.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.30/6.19 % ------ Proving...
% 3.30/6.19 % ------ Problem Properties
% 3.30/6.19
% 3.30/6.19 %
% 3.30/6.19 % clauses 18
% 3.30/6.19 % conjectures 1
% 3.30/6.19 % EPR 6
% 3.30/6.19 % Horn 18
% 3.30/6.19 % unary 12
% 3.30/6.19 % binary 4
% 3.30/6.19 % lits 26
% 3.30/6.19 % lits eq 9
% 3.30/6.19 % fd_pure 0
% 3.30/6.19 % fd_pseudo 0
% 3.30/6.19 % fd_cond 0
% 3.30/6.19 % fd_pseudo_cond 1
% 3.30/6.19 % AC symbols 0
% 3.30/6.19
% 3.30/6.19 % ------ Schedule dynamic 5 is on
% 3.30/6.19
% 3.30/6.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.30/6.19
% 3.30/6.19
% 3.30/6.19 % ------
% 3.30/6.19 % Current options:
% 3.30/6.19 % ------
% 3.30/6.19
% 3.30/6.19
% 3.30/6.19 %
% 3.30/6.19
% 3.30/6.19 % ------ Proving...
% 3.30/6.19 %
% 3.30/6.19
% 3.30/6.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.30/6.19
% 3.30/6.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.30/6.19
% 3.30/6.19
%------------------------------------------------------------------------------