%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-2 : 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 : n011.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 01:37:25 PM UTC 2026
% Result : Unsatisfiable 1.72s 1.28s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 172 ( 37 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 96 ( 49 ~; 47 |; 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 : 81 ( 0 sgn 81 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( X1 = X3
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f19,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f20,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f21,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f22,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,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] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,plain,
! [X0: $i] : quotient(X0,X0,zero),
inference(cnf_transformation,[],[f12]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ quotient(identity,X2,X3)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[],[f22]) ).
tcf(c_103,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( divide(identity,X2) != X3 )
| ( divide(identity,X1) != X2 )
| ( divide(identity,X0) != X1 ) ),
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_113,plain,
divide(identity,a) = idQa,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_114,plain,
divide(identity,idQa) = idQ_idQa,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_115,plain,
divide(idQa,idQ_idQa) = idQa_Q__idQ_idQa,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_120,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_74]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(X0,X1) != X2 )
| less_equal(X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_118]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X2,X0)
| ( divide(X0,X1) != X2 ) ),
inference(renaming,[status(thm)],[c_130]) ).
tcf(c_282,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_120]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(unflattening,[status(thm)],[c_131]) ).
tcf(c_286,plain,
! [X0: $i] : divide(identity,X0) = divide(identity,divide(identity,divide(identity,X0))),
inference(unflattening,[status(thm)],[c_111]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) != zero )
| less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(renaming,[status(thm)],[c_398]) ).
tcf(c_797,plain,
( ( idQa = idQa_Q__idQ_idQa )
| ~ less_equal(idQa_Q__idQ_idQa,idQa)
| ~ less_equal(idQa,idQa_Q__idQ_idQa) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2) )
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(superposition,[status(thm)],[c_282,c_76]) ).
tcf(c_971,plain,
! [X0: $i] :
( ( divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)) = divide(divide(X0,idQa),idQ_idQa) )
| ~ less_equal(divide(divide(X0,idQa),idQ_idQa),divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa)) ),
inference(superposition,[status(thm)],[c_115,c_834]) ).
tcf(c_985,plain,
! [X0: $i] :
( ( divide(divide(X0,idQa),idQ_idQa) = divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa) )
| ~ less_equal(divide(divide(X0,idQa),idQ_idQa),divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa)) ),
inference(light_normalisation,[status(thm)],[c_971,c_115]) ).
tcf(c_1382,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(superposition,[status(thm)],[c_115,c_284]) ).
tcf(c_1591,plain,
( less_equal(idQa,idQa_Q__idQ_idQa)
| ( divide(idQa,idQa_Q__idQ_idQa) != zero ) ),
inference(instantiation,[status(thm)],[c_399]) ).
tcf(c_1742,plain,
divide(identity,divide(identity,idQa)) = idQa,
inference(superposition,[status(thm)],[c_113,c_286]) ).
tcf(c_1760,plain,
divide(identity,idQ_idQa) = idQa,
inference(light_normalisation,[status(thm)],[c_1742,c_114]) ).
tcf(c_1945,plain,
( ( divide(divide(identity,idQa),idQ_idQa) = divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) )
| ~ less_equal(divide(idQ_idQa,idQ_idQa),divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa)) ),
inference(superposition,[status(thm)],[c_114,c_985]) ).
tcf(c_1959,plain,
( ( divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) = divide(idQ_idQa,idQ_idQa) )
| ~ less_equal(divide(idQ_idQa,idQ_idQa),divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa)) ),
inference(light_normalisation,[status(thm)],[c_1945,c_114]) ).
tcf(c_1960,plain,
( ( divide(idQa,idQa_Q__idQ_idQa) = zero )
| ~ less_equal(zero,divide(idQa,idQa_Q__idQ_idQa)) ),
inference(demodulation,[status(thm)],[c_1959,c_103,c_1760]) ).
tcf(c_1984,plain,
divide(idQa,idQa_Q__idQ_idQa) = zero,
inference(superposition,[status(thm)],[c_75,c_1960]) ).
tcf(c_1987,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1984,c_1591,c_1382,c_797,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 16:16:27 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.72/1.28 % SZS status Started for theBenchmark.p
% 1.72/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.72/1.28
% 1.72/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.72/1.28
% 1.72/1.28 % ------ iProver source info
% 1.72/1.28
% 1.72/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.72/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.72/1.28 % git: non_committed_changes: false
% 1.72/1.28
% 1.72/1.28 % ------ Parsing...% successful
% 1.72/1.28
% 1.72/1.28
% 1.72/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.72/1.28
% 1.72/1.28 % ------ Preprocessing... sup_sim: 1 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 sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.72/1.28
% 1.72/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.72/1.28
% 1.72/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.72/1.28 % ------ Proving...
% 1.72/1.28 % ------ Problem Properties
% 1.72/1.28
% 1.72/1.28 %
% 1.72/1.28 % clauses 20
% 1.72/1.28 % conjectures 1
% 1.72/1.28 % EPR 5
% 1.72/1.28 % Horn 20
% 1.72/1.28 % unary 13
% 1.72/1.28 % binary 5
% 1.72/1.28 % lits 29
% 1.72/1.28 % lits eq 12
% 1.72/1.28 % fd_pure 0
% 1.72/1.28 % fd_pseudo 0
% 1.72/1.28 % fd_cond 0
% 1.72/1.28 % fd_pseudo_cond 1
% 1.72/1.28 % AC symbols 0
% 1.72/1.28
% 1.72/1.28 % ------ Input Options Time Limit: Unbounded
% 1.72/1.28
% 1.72/1.28
% 1.72/1.28 % ------
% 1.72/1.28 % Current options:
% 1.72/1.28 % ------
% 1.72/1.28
% 1.72/1.28
% 1.72/1.28 %
% 1.72/1.28
% 1.72/1.28 % ------ Proving...
% 1.72/1.28 %
% 1.72/1.28
% 1.72/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.72/1.28
% 1.72/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.72/1.28
% 1.72/1.28
%------------------------------------------------------------------------------