%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-7 : 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 : n020.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 01:37:26 PM UTC 2026
% Result : Unsatisfiable 17.35s 3.29s
% Output : CNFRefutation 17.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 55 unt; 0 def)
% Number of atoms : 222 ( 47 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 39 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 100 ( 0 sgn 100 !; 0 ?; 79 :)
% 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(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : quotient(X0,identity,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
fof(f11,axiom,
! [X0] : quotient(zero,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,axiom,
! [X0] : quotient(X0,zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f18,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f19,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f20,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f21,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,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] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,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_75,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(X0,identity,zero),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i] : quotient(zero,X0,zero),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
! [X0: $i] : quotient(X0,X0,zero),
inference(cnf_transformation,[],[f12]) ).
tcf(c_82,plain,
! [X0: $i] : quotient(X0,zero,X0),
inference(cnf_transformation,[],[f13]) ).
tcf(c_87,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[],[f21]) ).
tcf(c_98,plain,
! [X0: $i] : divide(X0,identity) = zero,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_99,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_100,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_101,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_108,plain,
divide(identity,a) = idQa,
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_109,plain,
divide(identity,idQa) = idQ_idQa,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_110,plain,
divide(idQa,idQ_idQa) = idQa_Q__idQ_idQa,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_115,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_73]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(X0,X1) != X2 )
| less_equal(X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_113]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(renaming,[status(thm)],[c_125]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(unflattening,[status(thm)],[c_126]) ).
tcf(c_277,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_115]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) != zero )
| less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(renaming,[status(thm)],[c_286]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
tcf(c_2554,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(superposition,[status(thm)],[c_110,c_258]) ).
tcf(c_2569,plain,
! [X0: $i] : less_equal(divide(idQa,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[status(thm)],[c_108,c_277]) ).
tcf(c_2618,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_258,c_288]) ).
tcf(c_2619,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(superposition,[status(thm)],[c_277,c_288]) ).
tcf(c_2649,plain,
! [X0: $i] : divide(divide(idQ_idQa,divide(X0,idQa)),divide(divide(identity,X0),idQa)) = zero,
inference(superposition,[status(thm)],[c_109,c_2619]) ).
tcf(c_2650,plain,
! [X0: $i] : divide(divide(idQa_Q__idQ_idQa,divide(X0,idQ_idQa)),divide(divide(idQa,X0),idQ_idQa)) = zero,
inference(superposition,[status(thm)],[c_110,c_2619]) ).
tcf(c_2657,plain,
! [X0: $i] : divide(divide(divide(X0,a),idQa),divide(divide(X0,identity),a)) = zero,
inference(superposition,[status(thm)],[c_108,c_2619]) ).
tcf(c_2658,plain,
! [X0: $i] : divide(divide(divide(X0,idQa),idQ_idQa),divide(divide(X0,identity),idQa)) = zero,
inference(superposition,[status(thm)],[c_109,c_2619]) ).
tcf(c_2659,plain,
! [X0: $i] : divide(divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(X0,idQa),idQ_idQa)) = zero,
inference(superposition,[status(thm)],[c_110,c_2619]) ).
tcf(c_2660,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)) = zero,
inference(superposition,[status(thm)],[c_2618,c_2619]) ).
tcf(c_2688,plain,
! [X0: $i] : divide(divide(X0,idQa),idQ_idQa) = zero,
inference(demodulation,[status(thm)],[c_2658,c_98,c_99,c_101]) ).
tcf(c_2689,plain,
! [X0: $i] : divide(divide(X0,a),idQa) = zero,
inference(demodulation,[status(thm)],[c_2657,c_98,c_99,c_101]) ).
tcf(c_2693,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)) = zero,
inference(demodulation,[status(thm)],[c_2660,c_101]) ).
tcf(c_2751,plain,
divide(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)) = zero,
inference(superposition,[status(thm)],[c_108,c_2649]) ).
tcf(c_2765,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(demodulation,[status(thm)],[c_2751,c_100,c_101]) ).
tcf(c_2779,plain,
divide(divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),divide(zero,idQ_idQa)) = zero,
inference(superposition,[status(thm)],[c_98,c_2650]) ).
tcf(c_2795,plain,
divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero,
inference(demodulation,[status(thm)],[c_2779,c_99,c_101]) ).
tcf(c_2804,plain,
! [X0: $i] : divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference(demodulation,[status(thm)],[c_2659,c_101,c_2688]) ).
tcf(c_2811,plain,
! [X0: $i] : less_equal(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),
inference(superposition,[status(thm)],[c_2804,c_287]) ).
tcf(c_2828,plain,
( ( idQa = idQa_Q__idQ_idQa )
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(superposition,[status(thm)],[c_2554,c_75]) ).
tcf(c_2829,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[c_2828,c_90]) ).
tcf(c_3051,plain,
! [X0: $i] : less_equal(divide(X0,a),idQa),
inference(superposition,[status(thm)],[c_2689,c_287]) ).
tcf(c_4870,plain,
divide(divide(idQ_idQa,a),divide(zero,a)) = zero,
inference(superposition,[status(thm)],[c_2765,c_2693]) ).
tcf(c_4871,plain,
divide(idQ_idQa,a) = zero,
inference(demodulation,[status(thm)],[c_4870,c_99,c_101]) ).
tcf(c_5370,plain,
less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),
inference(superposition,[status(thm)],[c_2795,c_287]) ).
tcf(c_5450,plain,
( ( divide(identity,idQ_idQa) = idQa_Q__idQ_idQa )
| ~ less_equal(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) ),
inference(superposition,[status(thm)],[c_5370,c_75]) ).
tcf(c_5451,plain,
divide(identity,idQ_idQa) = idQa_Q__idQ_idQa,
inference(forward_subsumption_resolution,[status(thm)],[c_5450,c_2811]) ).
tcf(c_5481,plain,
less_equal(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)),
inference(superposition,[status(thm)],[c_4871,c_2569]) ).
tcf(c_5486,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference(demodulation,[status(thm)],[c_5481,c_101,c_5451]) ).
tcf(c_5525,plain,
( ( divide(idQa_Q__idQ_idQa,a) = idQa )
| ~ less_equal(divide(idQa_Q__idQ_idQa,a),idQa) ),
inference(superposition,[status(thm)],[c_5486,c_75]) ).
tcf(c_5526,plain,
divide(idQa_Q__idQ_idQa,a) = idQa,
inference(forward_subsumption_resolution,[status(thm)],[c_5525,c_3051]) ).
tcf(c_7320,plain,
less_equal(idQa,idQa_Q__idQ_idQa),
inference(superposition,[status(thm)],[c_5526,c_258]) ).
tcf(c_7347,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7320,c_2829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 16:17:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 17.35/3.29 % SZS status Started for theBenchmark.p
% 17.35/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 17.35/3.29
% 17.35/3.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.35/3.29
% 17.35/3.29 % ------ iProver source info
% 17.35/3.29
% 17.35/3.29 % git: date: 2026-07-19 20:42:38 +0200
% 17.35/3.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.35/3.29 % git: non_committed_changes: false
% 17.35/3.29
% 17.35/3.29 % ------ Parsing...% successful
% 17.35/3.29
% 17.35/3.29
% 17.35/3.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.35/3.29
% 17.35/3.29 % ------ Preprocessing... sup_sim: 7 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 %
% 17.35/3.29
% 17.35/3.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.35/3.29
% 17.35/3.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.35/3.29 % ------ Proving...
% 17.35/3.29 % ------ Problem Properties
% 17.35/3.29
% 17.35/3.29 %
% 17.35/3.29 % clauses 19
% 17.35/3.29 % conjectures 1
% 17.35/3.29 % EPR 5
% 17.35/3.29 % Horn 19
% 17.35/3.29 % unary 12
% 17.35/3.29 % binary 5
% 17.35/3.29 % lits 28
% 17.35/3.29 % lits eq 11
% 17.35/3.29 % fd_pure 0
% 17.35/3.29 % fd_pseudo 0
% 17.35/3.29 % fd_cond 0
% 17.35/3.29 % fd_pseudo_cond 1
% 17.35/3.29 % AC symbols 0
% 17.35/3.29
% 17.35/3.29 % ------ Input Options Time Limit: Unbounded
% 17.35/3.29
% 17.35/3.29
% 17.35/3.29 % ------
% 17.35/3.29 % Current options:
% 17.35/3.29 % ------
% 17.35/3.29
% 17.35/3.29
% 17.35/3.29 %
% 17.35/3.29
% 17.35/3.29 % ------ Proving...
% 17.35/3.29 %
% 17.35/3.29
% 17.35/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 17.35/3.29
% 17.35/3.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.35/3.29
% 17.35/3.29
%------------------------------------------------------------------------------