%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV398^5 : 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 : n014.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 10:50:02 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 89 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 515 ( 127 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 826 ( 112 ~; 118 |; 9 &; 544 @)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 230 ( 0 ^; 230 !; 0 ?; 230 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cF,type,
cF: ( a > $o ) > a > $o ).
thf(tp_cG,type,
cG: ( a > $o ) > a > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: a > $o ).
thf(tp_sK2_SY14,type,
sK2_SY14: a ).
thf(tp_sK3_SY15,type,
sK3_SY15: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK4_SX0,type,
sK4_SX0: a > $o ).
thf(tp_sK5_SY24,type,
sK5_SY24: a ).
thf(tp_sK6_SY22,type,
sK6_SY22: ( a > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM67A_pme) ).
thf(2,negated_conjecture,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(8,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(9,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 )
| ( cF @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: a > $o] :
~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 )
| ( cF @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: a > $o] :
( ( ! [SY9: a > $o] :
( ~ ! [SY10: a] :
( ~ ( SV1 @ SY10 )
| ( SY9 @ SY10 ) )
| ! [SY11: a] :
( ~ ( cF @ SY9 @ SY11 )
| ( cF @ SV1 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: a > $o] :
( ( ~ ( ~ ! [SY12: a] :
( ~ ( SV2 @ SY12 )
| ( cF @ ( cG @ SV2 ) @ SY12 ) )
| ~ ! [SY13: a] :
( ~ ( SV2 @ SY13 )
| ( cG @ ( cF @ SV2 ) @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SY14: a] :
( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ SY14 )
| ( cF @ sK1_SX0 @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ~ ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV3 @ SY15 ) )
| ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: a > $o] :
( ( ~ ! [SY12: a] :
( ~ ( SV2 @ SY12 )
| ( cF @ ( cG @ SV2 ) @ SY12 ) )
| ~ ! [SY13: a] :
( ~ ( SV2 @ SY13 )
| ( cG @ ( cF @ SV2 ) @ SY13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY14 )
| ( cF @ sK1_SX0 @ sK2_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(24,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ( ~ ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV3 @ SY15 ) ) )
= $true )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: a > $o] :
( ( ~ ! [SY12: a] :
( ~ ( SV2 @ SY12 )
| ( cF @ ( cG @ SV2 ) @ SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: a > $o] :
( ( ~ ! [SY13: a] :
( ~ ( SV2 @ SY13 )
| ( cG @ ( cF @ SV2 ) @ SY13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( cF @ sK1_SX0 @ sK2_SY14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ( ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV3 @ SY15 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV2: a > $o] :
( ( ! [SY12: a] :
( ~ ( SV2 @ SY12 )
| ( cF @ ( cG @ SV2 ) @ SY12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV2: a > $o] :
( ( ! [SY13: a] :
( ~ ( SV2 @ SY13 )
| ( cG @ ( cF @ SV2 ) @ SY13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) )
| ( SV3 @ ( sK3_SY15 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(34,plain,
! [SV4: a,SV2: a > $o] :
( ( ~ ( SV2 @ SV4 )
| ( cF @ ( cG @ SV2 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV5: a,SV2: a > $o] :
( ( ~ ( SV2 @ SV5 )
| ( cG @ ( cF @ SV2 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: a > $o,SV3: a > $o] :
( ( ( SV3 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV4 ) )
= $true )
| ( ( cF @ ( cG @ SV2 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV5 ) )
= $true )
| ( ( cG @ ( cF @ SV2 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: a > $o,SV1: a > $o] :
( ( ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV3 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: a > $o,SV6: a,SV3: a > $o] :
( ( ( ~ ( cF @ SV3 @ SV6 )
| ( cF @ SV1 @ SV6 ) )
= $true )
| ( ( SV3 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV4: a,SV2: a > $o] :
( ( ( SV2 @ SV4 )
= $false )
| ( ( cF @ ( cG @ SV2 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: a,SV2: a > $o] :
( ( ( SV2 @ SV5 )
= $false )
| ( ( cG @ ( cF @ SV2 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV1: a > $o,SV7: a,SV3: a > $o] :
( ( ( ~ ( cF @ SV3 @ SV7 )
| ( cF @ SV1 @ SV7 ) )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: a > $o,SV6: a,SV3: a > $o] :
( ( ( ~ ( cF @ SV3 @ SV6 ) )
= $true )
| ( ( cF @ SV1 @ SV6 )
= $true )
| ( ( SV3 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: a > $o,SV7: a,SV3: a > $o] :
( ( ( ~ ( cF @ SV3 @ SV7 ) )
= $true )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV1: a > $o,SV6: a,SV3: a > $o] :
( ( ( cF @ SV3 @ SV6 )
= $false )
| ( ( cF @ SV1 @ SV6 )
= $true )
| ( ( SV3 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV1: a > $o,SV7: a,SV3: a > $o] :
( ( ( cF @ SV3 @ SV7 )
= $false )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV3 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,48,47,43,42,32]) ).
thf(50,plain,
( ( ! [S: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(51,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(52,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(53,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ SX0 @ SX1 )
| ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(55,plain,
( ( ! [SX0: a > $o] :
~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) )
| ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(56,plain,
! [SV8: a > $o] :
( ( ! [SY17: a > $o] :
( ~ ! [SY18: a] :
( ~ ( SV8 @ SY18 )
| ( SY17 @ SY18 ) )
| ! [SY19: a] :
( ~ ( cF @ SY17 @ SY19 )
| ( cF @ SV8 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ SX0 @ SX1 )
| ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV9: a > $o] :
( ( ~ ( ~ ! [SY20: a] :
( ~ ( SV9 @ SY20 )
| ( cF @ ( cG @ SV9 ) @ SY20 ) )
| ~ ! [SY21: a] :
( ~ ( SV9 @ SY21 )
| ( cG @ ( cF @ SV9 ) @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ~ ! [SY22: a] :
( ~ ( SV8 @ SY22 )
| ( SV10 @ SY22 ) )
| ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(60,plain,
( ( ! [SY24: a] :
( ~ ( cF @ sK4_SX0 @ SY24 )
| ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ SY24 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(61,plain,
! [SV9: a > $o] :
( ( ~ ! [SY20: a] :
( ~ ( SV9 @ SY20 )
| ( cF @ ( cG @ SV9 ) @ SY20 ) )
| ~ ! [SY21: a] :
( ~ ( SV9 @ SY21 )
| ( cG @ ( cF @ SV9 ) @ SY21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ( ~ ! [SY22: a] :
( ~ ( SV8 @ SY22 )
| ( SV10 @ SY22 ) ) )
= $true )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( cF @ sK4_SX0 @ sK5_SY24 )
| ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ sK5_SY24 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(64,plain,
! [SV9: a > $o] :
( ( ~ ! [SY20: a] :
( ~ ( SV9 @ SY20 )
| ( cF @ ( cG @ SV9 ) @ SY20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV9: a > $o] :
( ( ~ ! [SY21: a] :
( ~ ( SV9 @ SY21 )
| ( cG @ ( cF @ SV9 ) @ SY21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ( ! [SY22: a] :
( ~ ( SV8 @ SY22 )
| ( SV10 @ SY22 ) ) )
= $false )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ ( cF @ sK4_SX0 @ sK5_SY24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ sK5_SY24 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV9: a > $o] :
( ( ! [SY20: a] :
( ~ ( SV9 @ SY20 )
| ( cF @ ( cG @ SV9 ) @ SY20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV9: a > $o] :
( ( ! [SY21: a] :
( ~ ( SV9 @ SY21 )
| ( cG @ ( cF @ SV9 ) @ SY21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) )
| ( SV10 @ ( sK6_SY22 @ SV10 @ SV8 ) ) )
= $false )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(72,plain,
( ( cF @ sK4_SX0 @ sK5_SY24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV11: a,SV9: a > $o] :
( ( ~ ( SV9 @ SV11 )
| ( cF @ ( cG @ SV9 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV12: a,SV9: a > $o] :
( ( ~ ( SV9 @ SV12 )
| ( cG @ ( cF @ SV9 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) ) )
= $false )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV8: a > $o,SV10: a > $o] :
( ( ( SV10 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $false )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(77,plain,
! [SV11: a,SV9: a > $o] :
( ( ( ~ ( SV9 @ SV11 ) )
= $true )
| ( ( cF @ ( cG @ SV9 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV12: a,SV9: a > $o] :
( ( ( ~ ( SV9 @ SV12 ) )
= $true )
| ( ( cG @ ( cF @ SV9 ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV10: a > $o,SV8: a > $o] :
( ( ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $true )
| ( ( ! [SY23: a] :
( ~ ( cF @ SV10 @ SY23 )
| ( cF @ SV8 @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV8: a > $o,SV13: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV13 )
| ( cF @ SV8 @ SV13 ) )
= $true )
| ( ( SV10 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV11: a,SV9: a > $o] :
( ( ( SV9 @ SV11 )
= $false )
| ( ( cF @ ( cG @ SV9 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV12: a,SV9: a > $o] :
( ( ( SV9 @ SV12 )
= $false )
| ( ( cG @ ( cF @ SV9 ) @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV8: a > $o,SV14: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV14 )
| ( cF @ SV8 @ SV14 ) )
= $true )
| ( ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV8: a > $o,SV13: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV13 ) )
= $true )
| ( ( cF @ SV8 @ SV13 )
= $true )
| ( ( SV10 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV8: a > $o,SV14: a,SV10: a > $o] :
( ( ( ~ ( cF @ SV10 @ SV14 ) )
= $true )
| ( ( cF @ SV8 @ SV14 )
= $true )
| ( ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(86,plain,
! [SV8: a > $o,SV13: a,SV10: a > $o] :
( ( ( cF @ SV10 @ SV13 )
= $false )
| ( ( cF @ SV8 @ SV13 )
= $true )
| ( ( SV10 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(87,plain,
! [SV8: a > $o,SV14: a,SV10: a > $o] :
( ( ( cF @ SV10 @ SV14 )
= $false )
| ( ( cF @ SV8 @ SV14 )
= $true )
| ( ( SV8 @ ( sK6_SY22 @ SV10 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,87,86,82,81,72]) ).
thf(89,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[88,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV398^5 : 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
% 0.11/0.18 % Computer : n014.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 15:45:56 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.29
% 0.11/0.29 No.of.Axioms: 0
% 0.11/0.29
% 0.11/0.29 Length.of.Defs: 0
% 0.11/0.29
% 0.11/0.29 Contains.Choice.Funs: false
% 0.11/0.29 ..
% 0.11/0.29
% 0.11/0.29 ********************************
% 0.11/0.29 * All subproblems solved! *
% 0.11/0.29 ********************************
% 0.11/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:88,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.29
% 0.11/0.29 %**** Beginning of derivation protocol ****
% 0.11/0.29 % SZS output start CNFRefutation
% See solution above
% 0.11/0.29
% 0.11/0.29 %**** End of derivation protocol ****
% 0.11/0.29 %**** no. of clauses in derivation: 89 ****
% 0.11/0.29 %**** clause counter: 88 ****
% 0.11/0.29
% 0.11/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:88,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------