%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX197+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n013.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 09:15:15 AM UTC 2026
% Result : Theorem 52.14s 16.08s
% Output : Refutation 45.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 74
% Syntax : Number of formulae : 150 ( 140 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 161 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 824 ( 49 ~; 0 |; 0 &; 763 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 5 con; 0-3 aty)
% Number of variables : 363 ( 0 ^; 360 !; 3 ?; 363 :)
% Comments :
%------------------------------------------------------------------------------
thf(run_decl,type,
run: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(cons2_decl,type,
cons2: $i > $i > $i ).
thf(nil2_decl,type,
nil2: $i ).
thf(opti2_decl,type,
opti2: $i > $i ).
thf(proj1V_decl,type,
proj1V: $i > $i ).
thf(v_decl,type,
v: $i > $i ).
thf(mul_decl,type,
mul: $i > $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(proj2Mul_decl,type,
proj2Mul: $i > $i ).
thf(proj1Mul_decl,type,
proj1Mul: $i > $i ).
thf(proj1Eq_decl,type,
proj1Eq: $i > $i ).
thf(proj2Eq_decl,type,
proj2Eq: $i > $i ).
thf(fetch_decl,type,
fetch: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(proj2Add_decl,type,
proj2Add: $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(proj1While_decl,type,
proj1While: $i > $i ).
thf(while_decl,type,
while: $i > $i > $i ).
thf(proj3If_decl,type,
proj3If: $i > $i ).
thf(if_decl,type,
if: $i > $i > $i > $i ).
thf(n_decl,type,
n: $i > $i ).
thf(print_decl,type,
print: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(head_decl,type,
head: $i > $i ).
thf(store_decl,type,
store: $i > $i > $i > $i ).
thf(x_decl,type,
x: $i > $i > $i ).
thf(proj2_decl,type,
proj2: $i > $i ).
thf(eval_decl,type,
eval: $i > $i > $i ).
thf(addNat_decl,type,
addNat: $i > $i > $i ).
thf(proj2If_decl,type,
proj2If: $i > $i ).
thf(proj2While_decl,type,
proj2While: $i > $i ).
thf(mulNat_decl,type,
mulNat: $i > $i > $i ).
thf(proj1Add_decl,type,
proj1Add: $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(proj1_decl,type,
proj1: $i > $i ).
thf(proj1Print_decl,type,
proj1Print: $i > $i ).
thf(proj1Suc_decl,type,
proj1Suc: $i > $i ).
thf(proj1N_decl,type,
proj1N: $i > $i ).
thf(proj1If_decl,type,
proj1If: $i > $i ).
thf(map_decl,type,
map: $i > $i > $i ).
thf(apply1_decl,type,
apply1: $i > $i > $i ).
thf(append_decl,type,
append: $i > $i > $i ).
thf(tail2_decl,type,
tail2: $i > $i ).
thf(head2_decl,type,
head2: $i > $i ).
thf(lam_decl,type,
lam: $i ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A @ n )
!= ( B @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(185,plain,
! [A: $i,B: $i] :
( ( A @ n )
!= ( B @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ add ) @ proj2Add )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ add ) @ proj2Add )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ( nil @ fetch ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_048) ).
thf(256,plain,
! [A: $i] :
( ( A @ ( nil @ fetch ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(30,axiom,
! [A: $i] :
( ( zero @ ( A @ suc @ addNat ) )
= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_052) ).
thf(173,plain,
! [A: $i] :
( ( zero @ ( A @ suc @ addNat ) )
= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ print )
!= ( C @ ( B @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(144,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ print )
!= ( C @ ( B @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ mul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ mul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( A @ eval ) )
= ( F @ suc ) )
=> ( ( B @ ( E @ ( D @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( D @ append ) @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_068) ).
thf(295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( A @ eval ) )
= ( F @ suc ) )
=> ( ( B @ ( E @ ( D @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( D @ append ) @ ( A @ run ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(74,axiom,
! [A: $i] :
( ( nil2 @ ( A @ run ) )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_063) ).
thf(314,plain,
! [A: $i] :
( ( nil2 @ ( A @ run ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ suc @ ( nil @ store ) ) )
= ( A @ ( B @ ( nil @ store ) ) @ ( zero @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
thf(262,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ suc @ ( nil @ store ) ) )
= ( A @ ( B @ ( nil @ store ) ) @ ( zero @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ eq ) @ proj1Eq )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ eq ) @ proj1Eq )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ x ) )
!= ( D @ ( C @ while ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
thf(249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ x ) )
!= ( D @ ( C @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ eval ) )
= ( C @ ( A @ eval ) ) )
=> ( ( C @ ( B @ eq ) @ ( A @ eval ) )
= ( zero @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_060) ).
thf(234,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ eval ) )
= ( C @ ( A @ eval ) ) )
=> ( ( C @ ( B @ eq ) @ ( A @ eval ) )
= ( zero @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ( zero @ ( nil @ store ) ) )
= ( nil @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
thf(308,plain,
! [A: $i] :
( ( A @ ( zero @ ( nil @ store ) ) )
= ( nil @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj3If )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(120,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj3If )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons2 ) @ tail2 )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons2 ) @ tail2 )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ suc @ ( C @ ( B @ cons ) @ store ) ) )
= ( A @ ( D @ ( C @ store ) ) @ ( B @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
thf(189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ suc @ ( C @ ( B @ cons ) @ store ) ) )
= ( A @ ( D @ ( C @ store ) ) @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ print )
!= ( D @ ( C @ ( B @ if ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ print )
!= ( D @ ( C @ ( B @ if ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ opti2 )
= ( B @ ( C @ ( A @ ( zero @ suc @ n @ add ) @ if ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
thf(289,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ opti2 )
= ( B @ ( C @ ( A @ ( zero @ suc @ n @ add ) @ if ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( zero @ addNat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_051) ).
thf(179,plain,
! [A: $i] :
( ( A @ ( zero @ addNat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ print @ proj1Print )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(211,plain,
! [A: $i] :
( ( A @ print @ proj1Print )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons2 ) @ ( A @ map ) )
= ( C @ ( A @ map ) @ ( B @ ( A @ apply1 ) @ cons2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_070) ).
thf(253,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons2 ) @ ( A @ map ) )
= ( C @ ( A @ map ) @ ( B @ ( A @ apply1 ) @ cons2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ suc @ ( A @ suc @ addNat ) )
= ( B @ suc @ ( A @ addNat ) @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_053) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( B @ suc @ ( A @ suc @ addNat ) )
= ( B @ suc @ ( A @ addNat ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ ( zero @ mulNat ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_054) ).
thf(243,plain,
! [A: $i] :
( ( A @ ( zero @ mulNat ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
thf(265,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(67,axiom,
! [A: $i] :
( ( A
!= ( A @ proj2While @ ( A @ proj1While @ while ) ) )
=> ( ( A
!= ( A @ proj3If @ ( A @ proj2If @ ( A @ proj1If @ if ) ) ) )
=> ( ( A @ opti2 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
thf(292,plain,
! [A: $i] :
( ( A
!= ( A @ proj2While @ ( A @ proj1While @ while ) ) )
=> ( ( A
!= ( A @ proj3If @ ( A @ proj2If @ ( A @ proj1If @ if ) ) ) )
=> ( ( A @ opti2 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj1While )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj1While )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ( lam @ apply1 ) )
= ( A @ opti2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_073) ).
thf(302,plain,
! [A: $i] :
( ( A @ ( lam @ apply1 ) )
= ( A @ opti2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj2 )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj2 )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ eval ) )
!= ( C @ ( A @ eval ) ) )
=> ( ( C @ ( B @ eq ) @ ( A @ eval ) )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_061) ).
thf(192,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ eval ) )
!= ( C @ ( A @ eval ) ) )
=> ( ( C @ ( B @ eq ) @ ( A @ eval ) )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons2 ) @ head2 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
thf(275,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons2 ) @ head2 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ while ) )
!= ( E @ ( D @ ( C @ if ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ while ) )
!= ( E @ ( D @ ( C @ if ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ mul ) )
!= ( C @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ mul ) )
!= ( C @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ eval ) )
= zero )
=> ( ( B @ ( E @ ( D @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( E @ append ) @ ( A @ run ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_067) ).
thf(285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ eval ) )
= zero )
=> ( ( B @ ( E @ ( D @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( E @ append ) @ ( A @ run ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ v @ ( A @ eval ) )
= ( B @ ( A @ fetch ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_062) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( B @ v @ ( A @ eval ) )
= ( B @ ( A @ fetch ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons2 ) @ append ) )
= ( A @ ( C @ append ) @ ( B @ cons2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_072) ).
thf(317,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons2 ) @ append ) )
= ( A @ ( C @ append ) @ ( B @ cons2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(25,axiom,
! [A: $i] :
( zero
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(156,plain,
! [A: $i] :
( zero
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ x ) )
!= ( E @ ( D @ ( C @ if ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
thf(169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ x ) )
!= ( E @ ( D @ ( C @ if ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( zero @ ( C @ ( B @ cons ) @ store ) ) )
= ( C @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_043) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( zero @ ( C @ ( B @ cons ) @ store ) ) )
= ( C @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ n @ proj1N )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(237,plain,
! [A: $i] :
( ( A @ n @ proj1N )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ suc @ ( A @ suc @ mulNat ) )
= ( B @ suc @ ( B @ suc @ ( A @ mulNat ) @ addNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_056) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( B @ suc @ ( A @ suc @ mulNat ) )
= ( B @ suc @ ( B @ suc @ ( A @ mulNat ) @ addNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(73,axiom,
! [A: $i] :
( ( nil2 @ ( A @ map ) )
= nil2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_069) ).
thf(311,plain,
! [A: $i] :
( ( nil2 @ ( A @ map ) )
= nil2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj2If )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(166,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj2If )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(148,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ n )
!= ( C @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj2While )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ proj2While )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( nil2
!= ( B @ ( A @ cons2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
thf(281,plain,
! [A: $i,B: $i] :
( nil2
!= ( B @ ( A @ cons2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ( nil2 @ append ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_071) ).
thf(259,plain,
! [A: $i] :
( ( A @ ( nil2 @ append ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ add ) )
!= ( D @ ( C @ mul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ add ) )
!= ( D @ ( C @ mul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ add ) )
!= ( C @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ add ) )
!= ( C @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
? [A: $i] :
( ( nil2 @ ( A @ cons2 ) @ ( nil @ run ) )
!= ( nil2 @ ( A @ opti2 @ cons2 ) @ ( nil @ run ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_074) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( nil2 @ ( A @ cons2 ) @ ( nil @ run ) )
!= ( nil2 @ ( A @ opti2 @ cons2 ) @ ( nil @ run ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(76,plain,
~ ? [A: $i] :
( ( nil2 @ ( A @ cons2 ) @ ( nil @ run ) )
!= ( nil2 @ ( A @ opti2 @ cons2 ) @ ( nil @ run ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ x ) @ proj1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ mul ) @ proj2Mul )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ mul ) @ proj2Mul )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ eval ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_057) ).
thf(240,plain,
! [A: $i,B: $i] :
( ( B @ n @ ( A @ eval ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ opti2 )
= ( B @ ( lam @ map ) @ ( A @ while ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
thf(278,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ while ) @ opti2 )
= ( B @ ( lam @ map ) @ ( A @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ while ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( nil2 @ ( nil2 @ ( D @ ( C @ while ) @ cons2 ) @ ( D @ append ) @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_066) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ while ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( nil2 @ ( nil2 @ ( D @ ( C @ while ) @ cons2 ) @ ( D @ append ) @ ( C @ if ) ) @ cons2 ) @ ( A @ run ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v @ proj1V )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(80,plain,
! [A: $i] :
( ( A @ v @ proj1V )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: $i] :
( ( zero @ ( A @ suc @ mulNat ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_055) ).
thf(182,plain,
! [A: $i] :
( ( zero @ ( A @ suc @ mulNat ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ print )
!= ( C @ ( B @ while ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ print )
!= ( C @ ( B @ while ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ eq ) )
!= ( C @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ eq ) )
!= ( C @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(218,plain,
! [A: $i] :
( ( A @ suc @ proj1Suc )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ eq ) @ proj2Eq )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ eq ) @ proj2Eq )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj1If )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(246,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ if ) ) @ proj1If )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ x ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( D @ ( A @ eval ) @ ( C @ ( A @ store ) ) @ run ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_065) ).
thf(272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ ( C @ x ) @ cons2 ) @ ( A @ run ) )
= ( B @ ( D @ ( A @ eval ) @ ( C @ ( A @ store ) ) @ run ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ add ) )
!= ( D @ ( C @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ add ) )
!= ( D @ ( C @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ print @ cons2 ) @ ( A @ run ) )
= ( B @ ( A @ run ) @ ( C @ ( A @ eval ) @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_064) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ print @ cons2 ) @ ( A @ run ) )
= ( B @ ( A @ run ) @ ( C @ ( A @ eval ) @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( zero @ ( B @ ( A @ cons ) @ fetch ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_049) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( zero @ ( B @ ( A @ cons ) @ fetch ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ add ) @ proj1Add )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ add ) @ proj1Add )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ mul ) @ proj1Mul )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ mul ) @ proj1Mul )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ suc @ ( B @ ( A @ cons ) @ fetch ) )
= ( C @ ( B @ fetch ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_050) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ suc @ ( B @ ( A @ cons ) @ fetch ) )
= ( C @ ( B @ fetch ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ add ) @ ( A @ eval ) )
= ( C @ ( A @ eval ) @ ( B @ ( A @ eval ) @ addNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_058) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ add ) @ ( A @ eval ) )
= ( C @ ( A @ eval ) @ ( B @ ( A @ eval ) @ addNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mul ) @ ( A @ eval ) )
= ( C @ ( A @ eval ) @ ( B @ ( A @ eval ) @ mulNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_059) ).
thf(227,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ mul ) @ ( A @ eval ) )
= ( C @ ( A @ eval ) @ ( B @ ( A @ eval ) @ mulNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ mul ) )
!= ( D @ ( C @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(83,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ mul ) )
!= ( D @ ( C @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13192,plain,
$false,
inference(e,[status(thm)],[185,110,256,173,144,123,295,314,262,101,249,234,308,120,269,189,152,289,179,211,253,221,243,265,292,117,201,302,160,192,275,137,97,285,224,317,156,169,141,134,237,205,311,166,148,176,281,259,113,230,76,208,91,240,198,278,299,80,182,127,87,218,104,246,272,214,305,107,195,94,131,163,227,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX197+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % 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
% 0.13/5.63 % Computer : n013.cluster.edu
% 0.13/5.63 % Model : x86_64 x86_64
% 0.13/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.63 % Memory : 8046.5625MB
% 0.13/5.63 % OS : Linux 6.8.0-71-generic
% 0.13/5.63 % CPULimit : 300
% 0.13/5.63 % WCLimit : 300
% 0.13/5.63 % DateTime : Sat Sep 26 16:51:28 UTC 2026
% 0.13/5.63 % CPUTime :
% 0.13/5.63 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
% 0.98/6.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/6.45 % [INFO] Parsing done (231ms).
% 1.43/6.47 % [INFO] Running in sequential loop mode.
% 2.16/6.86 % [INFO] eprover registered as external prover.
% 2.16/6.87 % [INFO] Scanning for conjecture ...
% 2.36/6.99 % [INFO] Found a conjecture (or negated_conjecture) and 73 axioms. Running axiom selection ...
% 2.58/7.09 % [INFO] Axiom selection finished. Selected 73 axioms (removed 0 axioms).
% 2.82/7.19 % [INFO] Problem is first-order (TPTP FOF).
% 2.97/7.21 % [INFO] Type checking passed.
% 2.97/7.21 % [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 ...
% 52.14/16.07 % External prover 'e' found a proof!
% 52.14/16.07 % [INFO] Killing All external provers ...
% 52.14/16.07 % Time passed: 10291ms (effective reasoning time: 9597ms)
% 52.14/16.07 % 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)>
% 52.14/16.07 % Axioms used in derivation (73): axiom_028, axiom_023, axiom_068, axiom_069, axiom_041, axiom_029, axiom_036, axiom_025, axiom_039, axiom_024, axiom_009, axiom_040, axiom_046, axiom_017, axiom_057, axiom_035, axiom_050, axiom_067, axiom_051, axiom_073, axiom_061, axiom_010, axiom_021, axiom_032, axiom_054, axiom_002, axiom_013, axiom_043, axiom_006, axiom_049, axiom_034, axiom_016, axiom_056, axiom_027, axiom_005, axiom_045, axiom_065, axiom_038, axiom_012, axiom_062, axiom_072, axiom_001, axiom_059, axiom_044, axiom_031, axiom_015, axiom_004, axiom_055, axiom_033, axiom_022, axiom_063, axiom_011, axiom_026, axiom_052, axiom_037, axiom_071, axiom_020, axiom_060, axiom_048, axiom_030, axiom_019, axiom_008, axiom_003, axiom_042, axiom_014, axiom_066, axiom_070, axiom_047, axiom_007, axiom_018, axiom_058, axiom_053, axiom_064
% 52.14/16.07 % No. of inferences in proof: 150
% 52.14/16.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10291 ms resp. 9597 ms w/o parsing
% 45.22/16.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.22/16.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------