%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO274^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 Oct 7 11:07:58 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 62 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 96 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 707 ( 123 ~; 98 |; 11 &; 433 @)
% ( 0 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 169 ( 0 ^; 169 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_cF,type,
cF: b > a ).
thf(tp_cG,type,
cG: c > b ).
thf(tp_sK1_Xx,type,
sK1_Xx: c ).
thf(tp_sK2_SY12,type,
sK2_SY12: c ).
thf(tp_sK3_SY16,type,
sK3_SY16: c > $o ).
thf(tp_sK4_Xq,type,
sK4_Xq: b > b > a > $o ).
thf(tp_sK5_Xq,type,
sK5_Xq: c > c > b > $o ).
thf(1,conjecture,
( ( ! [Xx: b,Xy: b] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ Xx ) )
=> ( Xq @ ( cF @ Xy ) ) )
=> ! [Xq: b > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) )
& ! [Xx: c,Xy: c] :
( ! [Xq: b > $o] :
( ( Xq @ ( cG @ Xx ) )
=> ( Xq @ ( cG @ Xy ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
=> ! [Xx: c,Xy: c] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ ( cG @ Xx ) ) )
=> ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM48_EXPD) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: b,Xy: b] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ Xx ) )
=> ( Xq @ ( cF @ Xy ) ) )
=> ! [Xq: b > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) )
& ! [Xx: c,Xy: c] :
( ! [Xq: b > $o] :
( ( Xq @ ( cG @ Xx ) )
=> ( Xq @ ( cG @ Xy ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
=> ! [Xx: c,Xy: c] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ ( cG @ Xx ) ) )
=> ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: b,Xy: b] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ Xx ) )
=> ( Xq @ ( cF @ Xy ) ) )
=> ! [Xq: b > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) )
& ! [Xx: c,Xy: c] :
( ! [Xq: b > $o] :
( ( Xq @ ( cG @ Xx ) )
=> ( Xq @ ( cG @ Xy ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
=> ! [Xx: c,Xy: c] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ ( cG @ Xx ) ) )
=> ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: b,Xy: b] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ Xx ) )
=> ( Xq @ ( cF @ Xy ) ) )
=> ! [Xq: b > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: c,Xy: c] :
( ! [Xq: b > $o] :
( ( Xq @ ( cG @ Xx ) )
=> ( Xq @ ( cG @ Xy ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: c,Xy: c] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ ( cG @ Xx ) ) )
=> ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Xx: c,Xy: c] :
( ! [Xq: a > $o] :
( ( Xq @ ( cF @ ( cG @ Xx ) ) )
=> ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
=> ! [Xq: c > $o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY15: a > $o] :
( ~ ( SY15 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SY15 @ ( cF @ ( cG @ sK2_SY12 ) ) ) )
& ( sK3_SY16 @ sK1_Xx )
& ~ ( sK3_SY16 @ sK2_SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [Xx: b,Xy: b] :
( ( ( sK4_Xq @ Xy @ Xx @ ( cF @ Xx ) )
& ~ ( sK4_Xq @ Xy @ Xx @ ( cF @ Xy ) ) )
| ! [Xq: b > $o] :
( ~ ( Xq @ Xx )
| ( Xq @ Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Xx: c,Xy: c] :
( ( ( sK5_Xq @ Xy @ Xx @ ( cG @ Xx ) )
& ~ ( sK5_Xq @ Xy @ Xx @ ( cG @ Xy ) ) )
| ! [Xq: c > $o] :
( ~ ( Xq @ Xx )
| ( Xq @ Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [Xx: c,Xy: c] :
( ( ( sK5_Xq @ Xy @ Xx @ ( cG @ Xx ) )
& ~ ( sK5_Xq @ Xy @ Xx @ ( cG @ Xy ) ) )
| ! [Xq: c > $o] :
( ~ ( Xq @ Xx )
| ( Xq @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [Xx: b,Xy: b] :
( ( ( sK4_Xq @ Xy @ Xx @ ( cF @ Xx ) )
& ~ ( sK4_Xq @ Xy @ Xx @ ( cF @ Xy ) ) )
| ! [Xq: b > $o] :
( ~ ( Xq @ Xx )
| ( Xq @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY15: a > $o] :
( ~ ( SY15 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SY15 @ ( cF @ ( cG @ sK2_SY12 ) ) ) )
& ( sK3_SY16 @ sK1_Xx )
& ~ ( sK3_SY16 @ sK2_SY12 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ! [SX0: a > $o] :
( ~ ( SX0 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SX0 @ ( cF @ ( cG @ sK2_SY12 ) ) ) )
| ~ ~ ( ~ ( sK3_SY16 @ sK1_Xx )
| ~ ~ ( sK3_SY16 @ sK2_SY12 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: b,SX1: b] :
( ~ ( ~ ( sK4_Xq @ SX1 @ SX0 @ ( cF @ SX0 ) )
| ~ ~ ( sK4_Xq @ SX1 @ SX0 @ ( cF @ SX1 ) ) )
| ! [SX2: b > $o] :
( ~ ( SX2 @ SX0 )
| ( SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: c,SX1: c] :
( ~ ( ~ ( sK5_Xq @ SX1 @ SX0 @ ( cG @ SX0 ) )
| ~ ~ ( sK5_Xq @ SX1 @ SX0 @ ( cG @ SX1 ) ) )
| ! [SX2: c > $o] :
( ~ ( SX2 @ SX0 )
| ( SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(17,plain,
( ( ~ ! [SX0: a > $o] :
( ~ ( SX0 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SX0 @ ( cF @ ( cG @ sK2_SY12 ) ) ) )
| ~ ~ ( ~ ( sK3_SY16 @ sK1_Xx )
| ~ ~ ( sK3_SY16 @ sK2_SY12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: b] :
( ( ! [SY17: b] :
( ~ ( ~ ( sK4_Xq @ SY17 @ SV1 @ ( cF @ SV1 ) )
| ~ ~ ( sK4_Xq @ SY17 @ SV1 @ ( cF @ SY17 ) ) )
| ! [SY18: b > $o] :
( ~ ( SY18 @ SV1 )
| ( SY18 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: c] :
( ( ! [SY19: c] :
( ~ ( ~ ( sK5_Xq @ SY19 @ SV2 @ ( cG @ SV2 ) )
| ~ ~ ( sK5_Xq @ SY19 @ SV2 @ ( cG @ SY19 ) ) )
| ! [SY20: c > $o] :
( ~ ( SY20 @ SV2 )
| ( SY20 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ! [SX0: a > $o] :
( ~ ( SX0 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SX0 @ ( cF @ ( cG @ sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( sK3_SY16 @ sK1_Xx )
| ~ ~ ( sK3_SY16 @ sK2_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: b,SV3: b] :
( ( ~ ( ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
| ~ ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) ) )
| ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: c,SV4: c] :
( ( ~ ( ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
| ~ ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) ) )
| ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: a > $o] :
( ~ ( SX0 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SX0 @ ( cF @ ( cG @ sK2_SY12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( sK3_SY16 @ sK1_Xx )
| ~ ~ ( sK3_SY16 @ sK2_SY12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: b,SV3: b] :
( ( ( ~ ( ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
| ~ ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) ) ) )
= $true )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: c,SV4: c] :
( ( ( ~ ( ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
| ~ ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) ) ) )
= $true )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV5: a > $o] :
( ( ~ ( SV5 @ ( cF @ ( cG @ sK1_Xx ) ) )
| ( SV5 @ ( cF @ ( cG @ sK2_SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( sK3_SY16 @ sK1_Xx )
| ~ ~ ( sK3_SY16 @ sK2_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: b,SV3: b] :
( ( ( ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
| ~ ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) ) )
= $false )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: c,SV4: c] :
( ( ( ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
| ~ ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) ) )
= $false )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: a > $o] :
( ( ( ~ ( SV5 @ ( cF @ ( cG @ sK1_Xx ) ) ) )
= $true )
| ( ( SV5 @ ( cF @ ( cG @ sK2_SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( sK3_SY16 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ~ ( sK3_SY16 @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: b,SV3: b] :
( ( ( ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) ) )
= $false )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: b,SV3: b] :
( ( ( ~ ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) ) )
= $false )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(37,plain,
! [SV2: c,SV4: c] :
( ( ( ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) ) )
= $false )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(38,plain,
! [SV2: c,SV4: c] :
( ( ( ~ ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) ) )
= $false )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(39,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( cF @ ( cG @ sK1_Xx ) ) )
= $false )
| ( ( SV5 @ ( cF @ ( cG @ sK2_SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(40,plain,
( ( sK3_SY16 @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ( sK3_SY16 @ sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV1: b,SV3: b] :
( ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
= $true )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(43,plain,
! [SV1: b,SV3: b] :
( ( ( ~ ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) ) )
= $true )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(44,plain,
! [SV2: c,SV4: c] :
( ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
= $true )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(45,plain,
! [SV2: c,SV4: c] :
( ( ( ~ ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) ) )
= $true )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(46,plain,
( ( sK3_SY16 @ sK2_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV3: b,SV1: b,SV6: b > $o] :
( ( ( ~ ( SV6 @ SV1 )
| ( SV6 @ SV3 ) )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV1: b,SV3: b] :
( ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) )
= $false )
| ( ( ! [SY21: b > $o] :
( ~ ( SY21 @ SV1 )
| ( SY21 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: c,SV2: c,SV7: c > $o] :
( ( ( ~ ( SV7 @ SV2 )
| ( SV7 @ SV4 ) )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: c,SV4: c] :
( ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) )
= $false )
| ( ( ! [SY22: c > $o] :
( ~ ( SY22 @ SV2 )
| ( SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: b,SV1: b,SV6: b > $o] :
( ( ( ~ ( SV6 @ SV1 ) )
= $true )
| ( ( SV6 @ SV3 )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV3: b,SV1: b,SV8: b > $o] :
( ( ( ~ ( SV8 @ SV1 )
| ( SV8 @ SV3 ) )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV4: c,SV2: c,SV7: c > $o] :
( ( ( ~ ( SV7 @ SV2 ) )
= $true )
| ( ( SV7 @ SV4 )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV4: c,SV2: c,SV9: c > $o] :
( ( ( ~ ( SV9 @ SV2 )
| ( SV9 @ SV4 ) )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: b,SV1: b,SV6: b > $o] :
( ( ( SV6 @ SV1 )
= $false )
| ( ( SV6 @ SV3 )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV3: b,SV1: b,SV8: b > $o] :
( ( ( ~ ( SV8 @ SV1 ) )
= $true )
| ( ( SV8 @ SV3 )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: c,SV2: c,SV7: c > $o] :
( ( ( SV7 @ SV2 )
= $false )
| ( ( SV7 @ SV4 )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: c,SV2: c,SV9: c > $o] :
( ( ( ~ ( SV9 @ SV2 ) )
= $true )
| ( ( SV9 @ SV4 )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV3: b,SV1: b,SV8: b > $o] :
( ( ( SV8 @ SV1 )
= $false )
| ( ( SV8 @ SV3 )
= $true )
| ( ( sK4_Xq @ SV3 @ SV1 @ ( cF @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV4: c,SV2: c,SV9: c > $o] :
( ( ( SV9 @ SV2 )
= $false )
| ( ( SV9 @ SV4 )
= $true )
| ( ( sK5_Xq @ SV4 @ SV2 @ ( cG @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,60,59,57,55,46,40]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO274^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n009.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 17:34:22 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 0
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20 .
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 62 ****
% 0.08/0.20 %**** clause counter: 61 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------