%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV137^5 : 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 : n012.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 10:49:37 AM UTC 2026
% Result : Theorem 0.10s 0.14s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 73 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 345 ( 128 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 898 ( 162 ~; 143 |; 35 &; 467 @)
% ( 0 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 188 ( 0 ^; 188 !; 0 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > $o ).
thf(tp_sK2_SY13,type,
sK2_SY13: a ).
thf(tp_sK3_SY25,type,
sK3_SY25: a ).
thf(tp_sK4_SY36,type,
sK4_SY36: a ).
thf(tp_sK5_SX0,type,
sK5_SX0: a > $o ).
thf(tp_sK6_SY55,type,
sK6_SY55: ( a > $o ) > a ).
thf(tp_sK7_SY57,type,
sK7_SY57: ( a > $o ) > a ).
thf(tp_sK8_SY61,type,
sK8_SY61: ( a > $o ) > a ).
thf(tp_sK9_SY62,type,
sK9_SY62: ( a > $o ) > a ).
thf(1,conjecture,
! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) )
& ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xy )
=> ( Xx0 @ Xz ) ) ) )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM204_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) )
& ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xy )
=> ( Xx0 @ Xz ) ) ) )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) )
& ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xy )
=> ( Xx0 @ Xz ) ) ) )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz0: a] :
( ( ( Xr @ Xy0 @ Xz0 )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz0 ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY13: a,SY14: a,SY15: a] :
( ( ! [SY16: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY16 @ SY17 ) )
=> ( SY16 @ SY18 ) )
=> ( ( SY16 @ SY13 )
=> ( SY16 @ SY14 ) ) )
& ! [SY19: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY19 @ SY20 ) )
=> ( SY19 @ SY21 ) )
=> ( ( SY19 @ SY14 )
=> ( SY19 @ SY15 ) ) ) )
=> ! [SY22: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY22 @ SY23 ) )
=> ( SY22 @ SY24 ) )
=> ( ( SY22 @ SY13 )
=> ( SY22 @ SY15 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY25: a,SY26: a] :
( ( ! [SY27: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY27 @ SY17 ) )
=> ( SY27 @ SY18 ) )
=> ( ( SY27 @ sK2_SY13 )
=> ( SY27 @ SY25 ) ) )
& ! [SY19: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY19 @ SY20 ) )
=> ( SY19 @ SY21 ) )
=> ( ( SY19 @ SY25 )
=> ( SY19 @ SY26 ) ) ) )
=> ! [SY33: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY33 @ SY23 ) )
=> ( SY33 @ SY24 ) )
=> ( ( SY33 @ sK2_SY13 )
=> ( SY33 @ SY26 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY36: a] :
( ( ! [SY37: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY37 @ SY17 ) )
=> ( SY37 @ SY18 ) )
=> ( ( SY37 @ sK2_SY13 )
=> ( SY37 @ sK3_SY25 ) ) )
& ! [SY40: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY40 @ SY20 ) )
=> ( SY40 @ SY21 ) )
=> ( ( SY40 @ sK3_SY25 )
=> ( SY40 @ SY36 ) ) ) )
=> ! [SY33: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY33 @ SY23 ) )
=> ( SY33 @ SY24 ) )
=> ( ( SY33 @ sK2_SY13 )
=> ( SY33 @ SY36 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ! [SY37: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY37 @ SY17 ) )
=> ( SY37 @ SY18 ) )
=> ( ( SY37 @ sK2_SY13 )
=> ( SY37 @ sK3_SY25 ) ) )
& ! [SY49: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY49 @ SY20 ) )
=> ( SY49 @ SY21 ) )
=> ( ( SY49 @ sK3_SY25 )
=> ( SY49 @ sK4_SY36 ) ) ) )
=> ! [SY52: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY52 @ SY23 ) )
=> ( SY52 @ SY24 ) )
=> ( ( SY52 @ sK2_SY13 )
=> ( SY52 @ sK4_SY36 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY37: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY37 @ SY17 ) )
=> ( SY37 @ SY18 ) )
=> ( ( SY37 @ sK2_SY13 )
=> ( SY37 @ sK3_SY25 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY49: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY49 @ SY20 ) )
=> ( SY49 @ SY21 ) )
=> ( ( SY49 @ sK3_SY25 )
=> ( SY49 @ sK4_SY36 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SY52: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY52 @ SY23 ) )
=> ( SY52 @ SY24 ) )
=> ( ( SY52 @ sK2_SY13 )
=> ( SY52 @ sK4_SY36 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SY52: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY52 @ SY23 ) )
=> ( SY52 @ SY24 ) )
=> ( ( SY52 @ sK2_SY13 )
=> ( SY52 @ sK4_SY36 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY49: a > $o] :
( ! [SY20: a,SY21: a] :
( ( ( sK1_Xr @ SY20 @ SY21 )
& ( SY49 @ SY20 ) )
=> ( SY49 @ SY21 ) )
=> ( ( SY49 @ sK3_SY25 )
=> ( SY49 @ sK4_SY36 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY37: a > $o] :
( ! [SY17: a,SY18: a] :
( ( ( sK1_Xr @ SY17 @ SY18 )
& ( SY37 @ SY17 ) )
=> ( SY37 @ SY18 ) )
=> ( ( SY37 @ sK2_SY13 )
=> ( SY37 @ sK3_SY25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ! [SY52: a > $o] :
( ! [SY23: a,SY24: a] :
( ( ( sK1_Xr @ SY23 @ SY24 )
& ( SY52 @ SY23 ) )
=> ( SY52 @ SY24 ) )
=> ( ( SY52 @ sK2_SY13 )
=> ( SY52 @ sK4_SY36 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK2_SY13 )
| ( SX0 @ sK4_SY36 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK2_SY13 )
| ( SX0 @ sK3_SY25 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK3_SY25 )
| ( SX0 @ sK4_SY36 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK2_SY13 )
| ( SX0 @ sK4_SY36 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: a > $o] :
( ( ~ ! [SY55: a,SY56: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY55 @ SY56 )
| ~ ( SV1 @ SY55 ) )
| ( SV1 @ SY56 ) )
| ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a > $o] :
( ( ~ ! [SY57: a,SY58: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY57 @ SY58 )
| ~ ( SV2 @ SY57 ) )
| ( SV2 @ SY58 ) )
| ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SY59: a,SY60: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY59 @ SY60 )
| ~ ( sK5_SX0 @ SY59 ) )
| ( sK5_SX0 @ SY60 ) )
| ~ ( sK5_SX0 @ sK2_SY13 )
| ( sK5_SX0 @ sK4_SY36 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV1: a > $o] :
( ( ( ~ ! [SY55: a,SY56: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY55 @ SY56 )
| ~ ( SV1 @ SY55 ) )
| ( SV1 @ SY56 ) ) )
= $true )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a > $o] :
( ( ( ~ ! [SY57: a,SY58: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY57 @ SY58 )
| ~ ( SV2 @ SY57 ) )
| ( SV2 @ SY58 ) ) )
= $true )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SY59: a,SY60: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY59 @ SY60 )
| ~ ( sK5_SX0 @ SY59 ) )
| ( sK5_SX0 @ SY60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( sK5_SX0 @ sK2_SY13 )
| ( sK5_SX0 @ sK4_SY36 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: a > $o] :
( ( ( ! [SY55: a,SY56: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY55 @ SY56 )
| ~ ( SV1 @ SY55 ) )
| ( SV1 @ SY56 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: a > $o] :
( ( ( ! [SY57: a,SY58: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY57 @ SY58 )
| ~ ( SV2 @ SY57 ) )
| ( SV2 @ SY58 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SY59: a,SY60: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY59 @ SY60 )
| ~ ( sK5_SX0 @ SY59 ) )
| ( sK5_SX0 @ SY60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( sK5_SX0 @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( sK5_SX0 @ sK4_SY36 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: a > $o] :
( ( ( ! [SY61: a] :
( ~ ~ ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ SY61 )
| ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) )
| ( SV1 @ SY61 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(32,plain,
! [SV2: a > $o] :
( ( ( ! [SY62: a] :
( ~ ~ ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ SY62 )
| ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) )
| ( SV2 @ SY62 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(33,plain,
! [SV3: a] :
( ( ! [SY63: a] :
( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SY63 )
| ~ ( sK5_SX0 @ SV3 ) )
| ( sK5_SX0 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( sK5_SX0 @ sK2_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: a > $o] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
| ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) )
| ( SV1 @ ( sK8_SY61 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
! [SV2: a > $o] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
| ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) )
| ( SV2 @ ( sK9_SY62 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(37,plain,
! [SV4: a,SV3: a] :
( ( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV3 ) )
| ( sK5_SX0 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV1: a > $o] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
| ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( sK8_SY61 @ SV1 ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: a > $o] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
| ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: a > $o] :
( ( ( SV2 @ ( sK9_SY62 @ SV2 ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV4: a,SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV3 ) ) )
= $true )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV1: a > $o] :
( ( ( ~ ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
| ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(44,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ sK2_SY13 ) )
= $true )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( SV1 @ ( sK8_SY61 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV2: a > $o] :
( ( ( ~ ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
| ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV2: a > $o] :
( ( ( ~ ( SV2 @ sK3_SY25 ) )
= $true )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( SV2 @ ( sK9_SY62 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: a,SV3: a] :
( ( ( ~ ( ~ ( sK1_Xr @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV3 ) ) )
= $false )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV1: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
| ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV1: a > $o] :
( ( ( SV1 @ sK2_SY13 )
= $false )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( SV1 @ ( sK8_SY61 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
| ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: a > $o] :
( ( ( SV2 @ sK3_SY25 )
= $false )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( SV2 @ ( sK9_SY62 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV4: a,SV3: a] :
( ( ( ~ ( sK1_Xr @ SV3 @ SV4 )
| ~ ( sK5_SX0 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV1: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY55 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV2: a > $o] :
( ( ( ~ ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY57 @ SV2 ) ) )
= $false )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV4: a,SV3: a] :
( ( ( ~ ( sK1_Xr @ SV3 @ SV4 ) )
= $true )
| ( ( ~ ( sK5_SX0 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV1: a > $o] :
( ( ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( sK6_SY55 @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ sK2_SY13 )
| ( SV1 @ sK3_SY25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV2: a > $o] :
( ( ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
= $true )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV2: a > $o] :
( ( ( SV2 @ ( sK7_SY57 @ SV2 ) )
= $true )
| ( ( ~ ( SV2 @ sK3_SY25 )
| ( SV2 @ sK4_SY36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV4: a,SV3: a] :
( ( ( sK1_Xr @ SV3 @ SV4 )
= $false )
| ( ( ~ ( sK5_SX0 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ sK2_SY13 ) )
= $true )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ sK2_SY13 ) )
= $true )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( SV1 @ ( sK6_SY55 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV2: a > $o] :
( ( ( ~ ( SV2 @ sK3_SY25 ) )
= $true )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV2: a > $o] :
( ( ( ~ ( SV2 @ sK3_SY25 ) )
= $true )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( SV2 @ ( sK7_SY57 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV4: a,SV3: a] :
( ( ( sK5_SX0 @ SV3 )
= $false )
| ( ( sK1_Xr @ SV3 @ SV4 )
= $false )
| ( ( sK5_SX0 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV1: a > $o] :
( ( ( SV1 @ sK2_SY13 )
= $false )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( sK1_Xr @ ( sK6_SY55 @ SV1 ) @ ( sK8_SY61 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV1: a > $o] :
( ( ( SV1 @ sK2_SY13 )
= $false )
| ( ( SV1 @ sK3_SY25 )
= $true )
| ( ( SV1 @ ( sK6_SY55 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV2: a > $o] :
( ( ( SV2 @ sK3_SY25 )
= $false )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( sK1_Xr @ ( sK7_SY57 @ SV2 ) @ ( sK9_SY62 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV2: a > $o] :
( ( ( SV2 @ sK3_SY25 )
= $false )
| ( ( SV2 @ sK4_SY36 )
= $true )
| ( ( SV2 @ ( sK7_SY57 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,71,70,69,68,67,51,49,34]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV137^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 15:40:45 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.14
% 0.10/0.14 No.of.Axioms: 0
% 0.10/0.14
% 0.10/0.14 Length.of.Defs: 0
% 0.10/0.14
% 0.10/0.14 Contains.Choice.Funs: false
% 0.10/0.14 ..
% 0.10/0.14
% 0.10/0.14 ********************************
% 0.10/0.14 * All subproblems solved! *
% 0.10/0.14 ********************************
% 0.10/0.14 % 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:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.14
% 0.10/0.14 %**** Beginning of derivation protocol ****
% 0.10/0.14 % SZS output start CNFRefutation
% See solution above
% 0.10/0.14
% 0.10/0.14 %**** End of derivation protocol ****
% 0.10/0.14 %**** no. of clauses in derivation: 73 ****
% 0.10/0.14 %**** clause counter: 72 ****
% 0.10/0.14
% 0.10/0.14 % 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:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------