TSTP Solution File: SYN726+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:29:24 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 45 unt; 6 typ; 0 def)
% Number of atoms : 429 ( 72 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1047 ( 253 ~; 182 |; 30 &; 566 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 274 ( 0 ^ 274 !; 0 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $i > $i > $o ).
thf(tp_q,type,
q: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_SY15,type,
sK4_SY15: $i ).
thf(1,conjecture,
( ( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( p @ X @ Y )
& ( p @ Y @ Z ) )
=> ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( q @ X @ Y )
& ( q @ Y @ Z ) )
=> ( q @ X @ Z ) )
& ! [X: $i,Y: $i] :
( ( q @ X @ Y )
=> ( q @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) ) )
=> ! [X: $i,Y: $i] : ( p @ X @ Y ) )
| ! [X: $i,Y: $i] : ( q @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm400) ).
thf(2,negated_conjecture,
( ( ( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( p @ X @ Y )
& ( p @ Y @ Z ) )
=> ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( q @ X @ Y )
& ( q @ Y @ Z ) )
=> ( q @ X @ Z ) )
& ! [X: $i,Y: $i] :
( ( q @ X @ Y )
=> ( q @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) ) )
=> ! [X: $i,Y: $i] : ( p @ X @ Y ) )
| ! [X: $i,Y: $i] : ( q @ X @ Y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( p @ X @ Y )
& ( p @ Y @ Z ) )
=> ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( q @ X @ Y )
& ( q @ Y @ Z ) )
=> ( q @ X @ Z ) )
& ! [X: $i,Y: $i] :
( ( q @ X @ Y )
=> ( q @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) ) )
=> ! [X: $i,Y: $i] : ( p @ X @ Y ) )
| ! [X: $i,Y: $i] : ( q @ X @ Y ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ( ( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( p @ X @ Y )
& ( p @ Y @ Z ) )
=> ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( q @ X @ Y )
& ( q @ Y @ Z ) )
=> ( q @ X @ Z ) )
& ! [X: $i,Y: $i] :
( ( q @ X @ Y )
=> ( q @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) ) )
=> ! [X: $i,Y: $i] : ( p @ X @ Y ) )
| ! [X: $i,Y: $i] : ( q @ X @ Y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ( q @ sK3_X @ sK4_SY15 )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( q @ X @ Y )
| ( q @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ~ ( p @ X @ Y )
| ~ ( p @ Y @ Z )
| ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ~ ( q @ X @ Y )
| ~ ( q @ Y @ Z )
| ( q @ X @ Z ) )
& ~ ( p @ sK1_X @ sK2_SY14 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ~ ( q @ sK3_X @ sK4_SY15 )
& ! [X: $i,Y: $i] :
( ( p @ X @ Y )
| ( q @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( q @ X @ Y )
| ( q @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ~ ( p @ X @ Y )
| ~ ( p @ Y @ Z )
| ( p @ X @ Z ) )
& ! [X: $i,Y: $i,Z: $i] :
( ~ ( q @ X @ Y )
| ~ ( q @ Y @ Z )
| ( q @ X @ Z ) )
& ~ ( p @ sK1_X @ sK2_SY14 ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ~ ( q @ sK3_X @ sK4_SY15 )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
| ~ ~ ( p @ sK1_X @ sK2_SY14 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( q @ sK3_X @ sK4_SY15 )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
| ~ ~ ( p @ sK1_X @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ~ ( q @ sK3_X @ sK4_SY15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
| ~ ~ ( p @ sK1_X @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( q @ sK3_X @ sK4_SY15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
| ~ ~ ( p @ sK1_X @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( q @ sK3_X @ sK4_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
| ~ ~ ( p @ sK1_X @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ~ ( p @ sK1_X @ sK2_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( p @ sK1_X @ sK2_SY14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( p @ sK1_X @ sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( p @ SX0 @ SX1 )
| ( q @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ( p @ SV1 @ SY16 )
| ( q @ SV1 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 )
| ( q @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 )
= $true )
| ( ( q @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( q @ SX0 @ SX1 )
| ( q @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
( ~ ( q @ SV3 @ SY17 )
| ( q @ SY17 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( q @ SV3 @ SV4 )
| ( q @ SV4 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i,SV3: $i] :
( ( ( ~ ( q @ SV3 @ SV4 ) )
= $true )
| ( ( q @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( p @ SX0 @ SX1 )
| ~ ( p @ SX1 @ SX2 )
| ( p @ SX0 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( q @ SX0 @ SX1 )
| ~ ( q @ SX1 @ SX2 )
| ( q @ SX0 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i,SV3: $i] :
( ( ( q @ SV3 @ SV4 )
= $false )
| ( ( q @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( p @ SV5 @ SY18 )
| ~ ( p @ SY18 @ SY19 )
| ( p @ SV5 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( q @ SV6 @ SY20 )
| ~ ( q @ SY20 @ SY21 )
| ( q @ SV6 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV7: $i,SV5: $i] :
( ( ! [SY22: $i] :
( ~ ( p @ SV5 @ SV7 )
| ~ ( p @ SV7 @ SY22 )
| ( p @ SV5 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV8: $i,SV6: $i] :
( ( ! [SY23: $i] :
( ~ ( q @ SV6 @ SV8 )
| ~ ( q @ SV8 @ SY23 )
| ( q @ SV6 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ~ ( p @ SV5 @ SV7 )
| ~ ( p @ SV7 @ SV9 )
| ( p @ SV5 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ~ ( q @ SV6 @ SV8 )
| ~ ( q @ SV8 @ SV10 )
| ( q @ SV6 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( p @ SV5 @ SV7 )
| ~ ( p @ SV7 @ SV9 ) )
= $true )
| ( ( p @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( q @ SV6 @ SV8 )
| ~ ( q @ SV8 @ SV10 ) )
= $true )
| ( ( q @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( p @ SV5 @ SV7 ) )
= $true )
| ( ( ~ ( p @ SV7 @ SV9 ) )
= $true )
| ( ( p @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( q @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( q @ SV8 @ SV10 ) )
= $true )
| ( ( q @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( p @ SV5 @ SV7 )
= $false )
| ( ( ~ ( p @ SV7 @ SV9 ) )
= $true )
| ( ( p @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( q @ SV6 @ SV8 )
= $false )
| ( ( ~ ( q @ SV8 @ SV10 ) )
= $true )
| ( ( q @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV5: $i,SV9: $i,SV7: $i] :
( ( ( p @ SV7 @ SV9 )
= $false )
| ( ( p @ SV5 @ SV7 )
= $false )
| ( ( p @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: $i,SV10: $i,SV8: $i] :
( ( ( q @ SV8 @ SV10 )
= $false )
| ( ( q @ SV6 @ SV8 )
= $false )
| ( ( q @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,55,54,41,30,20]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 12 03:19:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.12/0.39
% 0.12/0.39 ********************************
% 0.12/0.39 * All subproblems solved! *
% 0.12/0.39 ********************************
% 0.12/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.39
% 0.12/0.39 %**** Beginning of derivation protocol ****
% 0.12/0.39 % SZS output start CNFRefutation
% See solution above
% 0.12/0.39
% 0.12/0.39 %**** End of derivation protocol ****
% 0.12/0.39 %**** no. of clauses in derivation: 57 ****
% 0.12/0.39 %**** clause counter: 56 ****
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------