%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX190+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 : Sun Sep 27 09:15:14 AM UTC 2026
% Result : Theorem 5.06s 2.94s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 143 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 700 ( 51 ~; 0 |; 0 &; 615 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 3 con; 0-2 aty)
% Number of variables : 191 ( 0 ^; 188 !; 3 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(opt_decl,type,
opt: $i > $i ).
thf(d_decl,type,
d: $i > $i ).
thf(fail22_decl,type,
fail22: $i > $i > $i ).
thf(n_decl,type,
n: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(fail32_decl,type,
fail32: $i > $i > $i ).
thf(mulNat_decl,type,
mulNat: $i > $i > $i ).
thf(proj22_decl,type,
proj22: $i > $i ).
thf(y_decl,type,
y: $i > $i > $i ).
thf(x_decl,type,
x: $i > $i > $i ).
thf(proj12_decl,type,
proj12: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(fail_decl,type,
fail: $i > $i > $i ).
thf(fail1_decl,type,
fail1: $i > $i > $i ).
thf(x2_decl,type,
x2: $i ).
thf(proj1N_decl,type,
proj1N: $i > $i ).
thf(fail4_decl,type,
fail4: $i > $i > $i ).
thf(addNat_decl,type,
addNat: $i > $i > $i ).
thf(fail3_decl,type,
fail3: $i > $i > $i ).
thf(fail12_decl,type,
fail12: $i > $i > $i ).
thf(proj2_decl,type,
proj2: $i > $i ).
thf(fail2_decl,type,
fail2: $i > $i > $i ).
thf(proj1_decl,type,
proj1: $i > $i ).
thf(proj1S_decl,type,
proj1S: $i > $i ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ fail4 ) )
= ( B @ opt @ ( A @ opt @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ fail4 ) )
= ( B @ opt @ ( A @ opt @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ n @ d )
= ( z @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(211,plain,
! [A: $i] :
( ( A @ n @ d )
= ( z @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail22 ) )
= ( B @ ( A @ fail32 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail22 ) )
= ( B @ ( A @ fail32 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ y ) @ fail32 ) )
= ( A @ ( C @ y ) @ ( B @ y ) @ opt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ y ) @ fail32 ) )
= ( A @ ( C @ y ) @ ( B @ y ) @ opt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ fail1 ) )
= ( B @ ( A @ fail2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ fail1 ) )
= ( B @ ( A @ fail2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ s @ s @ n @ ( A @ fail22 ) )
= ( B @ s @ s @ n @ ( A @ fail32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( B @ s @ s @ n @ ( A @ fail22 ) )
= ( B @ s @ s @ n @ ( A @ fail32 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ mulNat ) )
= ( A @ ( B @ mulNat ) @ ( A @ addNat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ mulNat ) )
= ( A @ ( B @ mulNat ) @ ( A @ addNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ x ) @ opt )
= ( B @ ( A @ fail ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ x ) @ opt )
= ( B @ ( A @ fail ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail3 ) )
= ( B @ ( A @ fail12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail3 ) )
= ( B @ ( A @ fail12 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(69,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] :
( ( z @ s @ n @ ( A @ fail22 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(101,plain,
! [A: $i] :
( ( z @ s @ n @ ( A @ fail22 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( z @ s @ n @ fail12 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(170,plain,
! [A: $i] :
( ( A @ ( z @ s @ n @ fail12 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( z @ n @ fail12 ) )
= ( A @ ( z @ n @ fail22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(120,plain,
! [A: $i] :
( ( A @ ( z @ n @ fail12 ) )
= ( A @ ( z @ n @ fail22 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ x ) )
!= A )
=> ( ( A @ ( C @ ( B @ x ) @ fail2 ) )
= ( A @ ( C @ x ) @ ( B @ x ) @ opt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ x ) )
!= A )
=> ( ( A @ ( C @ ( B @ x ) @ fail2 ) )
= ( A @ ( C @ x ) @ ( B @ x ) @ opt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1,conjecture,
? [A: $i] :
( ( A @ d @ opt )
!= ( A @ opt @ d @ opt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_054) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ d @ opt )
!= ( A @ opt @ d @ opt ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
~ ? [A: $i] :
( ( A @ d @ opt )
!= ( A @ opt @ d @ opt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ s @ n @ fail12 ) )
= ( A @ ( B @ s @ s @ n @ fail22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ s @ n @ fail12 ) )
= ( A @ ( B @ s @ s @ n @ fail22 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ d )
= ( B @ d @ ( A @ d @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ d )
= ( B @ d @ ( A @ d @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( z @ addNat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(133,plain,
! [A: $i] :
( ( A @ ( z @ addNat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,axiom,
! [A: $i] :
( ( z @ n @ ( A @ fail22 ) )
= ( z @ n @ ( A @ fail32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(60,plain,
! [A: $i] :
( ( z @ n @ ( A @ fail22 ) )
= ( z @ n @ ( A @ fail32 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [A: $i] :
( ( z @ n @ ( A @ fail3 ) )
= ( z @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(117,plain,
! [A: $i] :
( ( z @ n @ ( A @ fail3 ) )
= ( z @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ y ) @ opt )
= ( B @ ( A @ fail3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(229,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ y ) @ opt )
= ( B @ ( A @ fail3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(53,axiom,
( ( x2 @ d )
= ( z @ s @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(224,plain,
( ( x2 @ d )
= ( z @ s @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ n )
!= x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(173,plain,
! [A: $i] :
( ( A @ n )
!= x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A @ ( B @ n @ fail1 ) )
= ( A @ ( B @ n @ fail2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A @ ( B @ n @ fail1 ) )
= ( A @ ( B @ n @ fail2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ proj12 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ proj12 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ n @ y ) @ opt )
= ( A @ ( B @ s @ n @ fail3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ n @ y ) @ opt )
= ( A @ ( B @ s @ n @ fail3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) )
!= x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) )
!= x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( z @ mulNat ) )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(180,plain,
! [A: $i] :
( ( A @ ( z @ mulNat ) )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ s )
!= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(76,plain,
! [A: $i] :
( ( A @ s )
!= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail ) )
= ( B @ ( A @ fail1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( B
!= ( B @ proj1N @ n ) )
=> ( ( B @ ( A @ fail ) )
= ( B @ ( A @ fail1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A
!= ( A @ proj2 @ ( A @ proj1 @ x ) ) )
=> ( ( B @ ( A @ fail2 ) )
= ( B @ opt @ ( A @ opt @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A
!= ( A @ proj2 @ ( A @ proj1 @ x ) ) )
=> ( ( B @ ( A @ fail2 ) )
= ( B @ opt @ ( A @ opt @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A @ ( B @ n @ fail32 ) )
= ( A @ ( B @ n @ fail4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A @ ( B @ n @ fail32 ) )
= ( A @ ( B @ n @ fail4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ proj22 )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ proj22 )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ n @ fail1 ) )
= ( B @ ( A @ addNat ) @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ n @ fail1 ) )
= ( B @ ( A @ addNat ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ( z @ n @ x ) @ opt )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(226,plain,
! [A: $i] :
( ( A @ ( z @ n @ x ) @ opt )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ s @ n @ ( A @ fail ) )
= ( B @ s @ n @ ( A @ fail1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ s @ n @ ( A @ fail ) )
= ( B @ s @ n @ ( A @ fail1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ n @ fail32 ) )
= ( B @ ( A @ mulNat ) @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ n @ fail32 ) )
= ( B @ ( A @ mulNat ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(150,plain,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
! [A: $i] :
( ( z @ n @ ( A @ fail ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(95,plain,
! [A: $i] :
( ( z @ n @ ( A @ fail ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ d )
= ( B @ d @ ( A @ y ) @ ( B @ ( A @ d @ y ) @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ y ) @ d )
= ( B @ d @ ( A @ y ) @ ( B @ ( A @ d @ y ) @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ n @ proj1N )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(177,plain,
! [A: $i] :
( ( A @ n @ proj1N )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ( z @ n @ y ) @ opt )
= ( z @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(218,plain,
! [A: $i] :
( ( A @ ( z @ n @ y ) @ opt )
= ( z @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ x ) )
!= ( D @ ( C @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ x ) )
!= ( D @ ( C @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( B @ ( A @ fail2 ) )
= ( A @ opt @ ( z @ s @ s @ n @ y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( B @ ( A @ fail2 ) )
= ( A @ opt @ ( z @ s @ s @ n @ y ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ s @ n @ ( A @ fail3 ) )
= ( B @ s @ n @ ( A @ fail12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( B @ s @ n @ ( A @ fail3 ) )
= ( B @ s @ n @ ( A @ fail12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A
!= ( A @ proj22 @ ( A @ proj12 @ y ) ) )
=> ( ( B @ ( A @ fail32 ) )
= ( B @ ( A @ fail4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( A
!= ( A @ proj22 @ ( A @ proj12 @ y ) ) )
=> ( ( B @ ( A @ fail32 ) )
= ( B @ ( A @ fail4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ n @ x ) @ opt )
= ( A @ ( B @ s @ n @ fail ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(190,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ n @ x ) @ opt )
= ( A @ ( B @ s @ n @ fail ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(40,axiom,
! [A: $i] :
( ( A
!= ( A @ proj2 @ ( A @ proj1 @ x ) ) )
=> ( ( A
!= ( A @ proj22 @ ( A @ proj12 @ y ) ) )
=> ( ( A @ opt )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(183,plain,
! [A: $i] :
( ( A
!= ( A @ proj2 @ ( A @ proj1 @ x ) ) )
=> ( ( A
!= ( A @ proj22 @ ( A @ proj12 @ y ) ) )
=> ( ( A @ opt )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj2 )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj2 )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ fail12 ) )
= ( B @ ( A @ fail22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( A
!= ( A @ proj1N @ n ) )
=> ( ( B @ ( A @ fail12 ) )
= ( B @ ( A @ fail22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ addNat ) )
= ( A @ ( B @ addNat ) @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ addNat ) )
= ( A @ ( B @ addNat ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) )
!= x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) )
!= x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(233,plain,
$false,
inference(e,[status(thm)],[196,211,156,193,159,123,143,214,163,69,101,170,120,202,56,153,221,133,60,117,229,224,173,129,73,205,166,180,76,98,208,140,91,66,108,226,80,63,150,95,199,177,87,218,104,186,114,146,190,183,126,136,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX190+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n019.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:54:05 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.23 % [INFO] Parsing done (221ms).
% 1.35/1.25 % [INFO] Running in sequential loop mode.
% 2.02/1.65 % [INFO] eprover registered as external prover.
% 2.02/1.66 % [INFO] Scanning for conjecture ...
% 2.22/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.39/1.87 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.60/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/1.97 % [INFO] Type checking passed.
% 2.60/1.97 % [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 ...
% 5.06/2.93 % External prover 'e' found a proof!
% 5.06/2.93 % [INFO] Killing All external provers ...
% 5.06/2.93 % Time passed: 2375ms (effective reasoning time: 1682ms)
% 5.06/2.93 % 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)>
% 5.06/2.94 % Axioms used in derivation (53): axiom_010, axiom_002, axiom_028, axiom_023, axiom_012, axiom_001, axiom_044, axiom_011, axiom_041, axiom_029, axiom_036, axiom_025, axiom_014, axiom_039, axiom_024, axiom_009, axiom_040, axiom_046, axiom_017, axiom_035, axiom_050, axiom_051, axiom_021, axiom_032, axiom_013, axiom_043, axiom_006, axiom_049, axiom_034, axiom_016, axiom_027, axiom_005, axiom_045, axiom_038, axiom_031, axiom_015, axiom_004, axiom_033, axiom_022, axiom_026, axiom_052, axiom_037, axiom_020, axiom_048, axiom_030, axiom_019, axiom_008, axiom_003, axiom_042, axiom_047, axiom_007, axiom_018, axiom_053
% 5.06/2.94 % No. of inferences in proof: 110
% 5.06/2.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2375 ms resp. 1682 ms w/o parsing
% 5.64/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.64/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------