%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP018^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 : Wed Sep 30 08:06:23 AM UTC 2026
% Result : Theorem 5.04s 2.53s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 223 ( 12 ~; 2 |; 6 &; 201 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 50 ( 0 ^; 48 !; 2 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(c_2Emin_2E_3D_3D_3E_decl,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F_decl,type,
c_2Ebool_2E_3F:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F_decl,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebinary__ieee_2Efloat__negate_decl,type,
c_2Ebinary__ieee_2Efloat__negate:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat @ TB @ TA ) > ( tyop_2Ebinary__ieee_2Efloat @ TB @ TA ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) > ( tyop_2Ebinary__ieee_2Efloat @ TB @ TA ) ) ).
thf(c_2Ebinary__ieee_2Efloat__to__real_decl,type,
c_2Ebinary__ieee_2Efloat__to__real:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Ebinary__ieee_2Efloat @ TB @ TA ) > tyop_2Erealax_2Ereal ) ).
thf(c_2Erealax_2Ereal__neg_decl,type,
c_2Erealax_2Ereal__neg: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebool_2Ethe__value_decl,type,
c_2Ebool_2Ethe__value:
!>[TA: $tType] : ( tyop_2Ebool_2Eitself @ TA ) ).
thf(c_2Ebinary__ieee_2Eulp_decl,type,
c_2Ebinary__ieee_2Eulp:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) > tyop_2Erealax_2Ereal ) ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $o > $o ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ebinary__ieee_2Eulp @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__plus__min @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(61,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ebinary__ieee_2Eulp @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__plus__min @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(17,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $false )
= ( $true
& $false ) ),
inference(instance,[status(thm)],[17]) ).
thf(21,plain,
~ ( c_2Ebool_2E_2F_5C @ $true @ $false ),
inference(simp,[status(thm)],[20]) ).
thf(13,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(65,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(49,plain,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(35,plain,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,plain,
( ( c_2Ebool_2E_7E @ $false )
= ( ~ $false ) ),
inference(instance,[status(thm)],[35]) ).
thf(39,plain,
c_2Ebool_2E_7E @ $false,
inference(simp,[status(thm)],[38]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType] :
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__negate @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__plus__min @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType] :
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__negate @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__plus__min @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [TA: $tType,TB: $tType] :
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) )
= ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__negate @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__plus__min @ TB @ TA @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ TB @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ skt1 @ skt2 @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ skt1 @ skt2 ) ) ) )
!= ( c_2Ebinary__ieee_2Efloat__to__real @ skt1 @ skt2 @ ( c_2Ebinary__ieee_2Efloat__negate @ skt1 @ skt2 @ ( c_2Ebinary__ieee_2Efloat__plus__min @ skt1 @ skt2 @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ skt1 @ skt2 ) ) ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Eulp @ skt1 @ skt2 @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ skt1 @ skt2 ) ) ) )
!= ( c_2Ebinary__ieee_2Efloat__to__real @ skt1 @ skt2 @ ( c_2Ebinary__ieee_2Efloat__negate @ skt1 @ skt2 @ ( c_2Ebinary__ieee_2Efloat__plus__min @ skt1 @ skt2 @ ( c_2Ebool_2Ethe__value @ ( tyop_2Epair_2Eprod @ skt1 @ skt2 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Ebinary__ieee_2Efloat @ TB @ TA] :
( ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__negate @ TB @ TA @ A ) )
= ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(58,plain,
! [TA: $tType,TB: $tType,A: tyop_2Ebinary__ieee_2Efloat @ TB @ TA] :
( ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ ( c_2Ebinary__ieee_2Efloat__negate @ TB @ TA @ A ) )
= ( c_2Erealax_2Ereal__neg @ ( c_2Ebinary__ieee_2Efloat__to__real @ TB @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $true )
= ( $true
& $true ) ),
inference(instance,[status(thm)],[17]) ).
thf(19,plain,
c_2Ebool_2E_2F_5C @ $true @ $true,
inference(simp,[status(thm)],[18]) ).
thf(36,plain,
( ( c_2Ebool_2E_7E @ $true )
= ( ~ $true ) ),
inference(instance,[status(thm)],[35]) ).
thf(37,plain,
~ ( c_2Ebool_2E_7E @ $true ),
inference(simp,[status(thm)],[36]) ).
thf(24,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $false )
= ( $false
& $false ) ),
inference(instance,[status(thm)],[17]) ).
thf(25,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $false ),
inference(simp,[status(thm)],[24]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(52,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(64,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(40,plain,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(26,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(55,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $true )
= ( $false
& $true ) ),
inference(instance,[status(thm)],[17]) ).
thf(23,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $true ),
inference(simp,[status(thm)],[22]) ).
thf(102,plain,
$false,
inference(e,[status(thm)],[61,21,65,49,39,35,16,58,19,37,25,52,14,64,17,40,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n015.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 19:36:23 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.01 % [INFO] Parsing done (215ms).
% 1.23/1.02 % [INFO] Running in sequential loop mode.
% 2.17/1.43 % [INFO] eprover registered as external prover.
% 2.17/1.43 % [INFO] Scanning for conjecture ...
% 2.35/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.35/1.57 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.53/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.61 % [INFO] Type checking passed.
% 2.53/1.61 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.04/2.53 % External prover 'e' found a proof!
% 5.04/2.53 % [INFO] Killing All external provers ...
% 5.04/2.53 % Time passed: 2174ms (effective reasoning time: 1499ms)
% 5.04/2.53 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.04/2.53 % Axioms used in derivation (11): logicdef_2E_5C_2F, logicdef_2E_3D_3D_3E, logicdef_2E_2F_5C, logicdef_2E_7E, thm_2Ebinary__ieee_2Eulp, quantdef_2E_3F, logicdef_2E_3D, thm_2Ebool_2EREFL__CLAUSE, quantdef_2E_21, thm_2Ebinary__ieee_2Efloat__to__real__negate, thm_2Ebool_2ETRUTH
% 5.04/2.53 % No. of inferences in proof: 40
% 5.04/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2174 ms resp. 1499 ms w/o parsing
% 5.04/2.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.04/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------