%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV104^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Wed Oct 7 10:49:33 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 83 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 122 equ; 0 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 1058 ( 246 ~; 147 |; 42 &; 596 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 230 ( 0 ^; 225 !; 5 ?; 230 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_cR,type,
cR: a > a > $o ).
thf(tp_cS,type,
cS: b > b > $o ).
thf(tp_f,type,
f: a > b > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: b ).
thf(tp_sK2_SY24,type,
sK2_SY24: a ).
thf(tp_sK3_SY17,type,
sK3_SY17: a > b ).
thf(tp_sK4_SY31,type,
sK4_SY31: a ).
thf(tp_z,type,
z: a ).
thf(1,conjecture,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM552D_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] : ( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: a] :
? [Xy: b] : ( f @ Xx @ Xy ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( ~ ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ~ ! [SX0: b,SX1: a,SX2: a] :
( ~ ~ ( ~ ! [SX3: a] :
( ( f @ SX1 @ SX0 )
| ~ ( ~ ~ ( f @ SX3 @ SX0 )
| ~ ( cR @ SX1 @ z ) ) )
| ~ ! [SX3: a] :
( ( f @ SX2 @ SX0 )
| ~ ( ~ ~ ( f @ SX3 @ SX0 )
| ~ ( cR @ SX2 @ z ) ) ) )
| ( cR @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [SX0: a] :
~ ! [SX1: b] :
~ ( f @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SX0: a,SX1: b,SX2: b] :
( ~ ~ ( ~ ( f @ SX0 @ SX1 )
| ~ ( f @ SX0 @ SX2 ) )
| ( cS @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(20,plain,
( ( ! [SX0: a,SX1: a,SX2: b] :
( ~ ~ ( ~ ( f @ SX0 @ SX2 )
| ~ ( f @ SX1 @ SX2 ) )
| ( cR @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( cR @ SX0 @ SX1 )
| ~ ( cR @ SX2 @ SX1 ) )
| ( cR @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: a] :
( ( cR @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(23,plain,
( ( ! [SX0: b,SX1: a,SX2: a] :
( ~ ~ ( ~ ! [SX3: a] :
( ( f @ SX1 @ SX0 )
| ~ ( ~ ~ ( f @ SX3 @ SX0 )
| ~ ( cR @ SX1 @ z ) ) )
| ~ ! [SX3: a] :
( ( f @ SX2 @ SX0 )
| ~ ( ~ ~ ( f @ SX3 @ SX0 )
| ~ ( cR @ SX2 @ z ) ) ) )
| ( cR @ SX1 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: a] :
( ( ~ ! [SY17: b] :
~ ( f @ SV2 @ SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: a] :
( ( ! [SY18: b,SY19: b] :
( ~ ~ ( ~ ( f @ SV3 @ SY18 )
| ~ ( f @ SV3 @ SY19 ) )
| ( cS @ SY18 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: a] :
( ( ! [SY20: a,SY21: b] :
( ~ ~ ( ~ ( f @ SV4 @ SY21 )
| ~ ( f @ SY20 @ SY21 ) )
| ( cR @ SV4 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: a] :
( ( ! [SY22: a,SY23: a] :
( ~ ~ ( ~ ( cR @ SV5 @ SY22 )
| ~ ( cR @ SY23 @ SY22 ) )
| ( cR @ SV5 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [SY24: a,SY25: a] :
( ~ ~ ( ~ ! [SY26: a] :
( ( f @ SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY26 @ sK1_SX0 )
| ~ ( cR @ SY24 @ z ) ) )
| ~ ! [SY27: a] :
( ( f @ SY25 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY27 @ sK1_SX0 )
| ~ ( cR @ SY25 @ z ) ) ) )
| ( cR @ SY24 @ SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(29,plain,
! [SV2: a] :
( ( ! [SY17: b] :
~ ( f @ SV2 @ SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV6: b,SV3: a] :
( ( ! [SY28: b] :
( ~ ~ ( ~ ( f @ SV3 @ SV6 )
| ~ ( f @ SV3 @ SY28 ) )
| ( cS @ SV6 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV7: a,SV4: a] :
( ( ! [SY29: b] :
( ~ ~ ( ~ ( f @ SV4 @ SY29 )
| ~ ( f @ SV7 @ SY29 ) )
| ( cR @ SV4 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV8: a,SV5: a] :
( ( ! [SY30: a] :
( ~ ~ ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SY30 @ SV8 ) )
| ( cR @ SV5 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [SY31: a] :
( ~ ~ ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
| ~ ! [SY27: a] :
( ( f @ SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY27 @ sK1_SX0 )
| ~ ( cR @ SY31 @ z ) ) ) )
| ( cR @ sK2_SY24 @ SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(34,plain,
! [SV2: a] :
( ( ~ ( f @ SV2 @ ( sK3_SY17 @ SV2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(35,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ~ ~ ( ~ ( f @ SV3 @ SV6 )
| ~ ( f @ SV3 @ SV9 ) )
| ( cS @ SV6 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ~ ~ ( ~ ( f @ SV4 @ SV10 )
| ~ ( f @ SV7 @ SV10 ) )
| ( cR @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ~ ~ ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV11 @ SV8 ) )
| ( cR @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ~ ~ ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
| ~ ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) )
| ( cR @ sK2_SY24 @ sK4_SY31 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(39,plain,
! [SV2: a] :
( ( f @ SV2 @ ( sK3_SY17 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ( ~ ~ ( ~ ( f @ SV3 @ SV6 )
| ~ ( f @ SV3 @ SV9 ) ) )
= $true )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ( ~ ~ ( ~ ( f @ SV4 @ SV10 )
| ~ ( f @ SV7 @ SV10 ) ) )
= $true )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ( ~ ~ ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV11 @ SV8 ) ) )
= $true )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ~ ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
| ~ ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(44,plain,
( ( cR @ sK2_SY24 @ sK4_SY31 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ( ~ ( ~ ( f @ SV3 @ SV6 )
| ~ ( f @ SV3 @ SV9 ) ) )
= $false )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ( ~ ( ~ ( f @ SV4 @ SV10 )
| ~ ( f @ SV7 @ SV10 ) ) )
= $false )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ( ~ ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV11 @ SV8 ) ) )
= $false )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( ~ ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
| ~ ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ( ~ ( f @ SV3 @ SV6 )
| ~ ( f @ SV3 @ SV9 ) )
= $true )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ( ~ ( f @ SV4 @ SV10 )
| ~ ( f @ SV7 @ SV10 ) )
= $true )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 )
| ~ ( cR @ SV11 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(52,plain,
( ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
| ~ ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ( ~ ( f @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( f @ SV3 @ SV9 ) )
= $true )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ( ~ ( f @ SV4 @ SV10 ) )
= $true )
| ( ( ~ ( f @ SV7 @ SV10 ) )
= $true )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ( ~ ( cR @ SV5 @ SV8 ) )
= $true )
| ( ( ~ ( cR @ SV11 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( ~ ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV9: b,SV6: b,SV3: a] :
( ( ( f @ SV3 @ SV6 )
= $false )
| ( ( ~ ( f @ SV3 @ SV9 ) )
= $true )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV7: a,SV10: b,SV4: a] :
( ( ( f @ SV4 @ SV10 )
= $false )
| ( ( ~ ( f @ SV7 @ SV10 ) )
= $true )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV11: a,SV8: a,SV5: a] :
( ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( ~ ( cR @ SV11 @ SV8 ) )
= $true )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
( ( ! [SY32: a] :
( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY32 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ! [SY35: a] :
( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SY35 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV6: b,SV9: b,SV3: a] :
( ( ( f @ SV3 @ SV9 )
= $false )
| ( ( f @ SV3 @ SV6 )
= $false )
| ( ( cS @ SV6 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV4: a,SV10: b,SV7: a] :
( ( ( f @ SV7 @ SV10 )
= $false )
| ( ( f @ SV4 @ SV10 )
= $false )
| ( ( cR @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV5: a,SV8: a,SV11: a] :
( ( ( cR @ SV11 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV8 )
= $false )
| ( ( cR @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV12: a] :
( ( ( f @ sK2_SY24 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SV12 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV13: a] :
( ( ( f @ sK4_SY31 @ sK1_SX0 )
| ~ ( ~ ~ ( f @ SV13 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV12: a] :
( ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true )
| ( ( ~ ( ~ ~ ( f @ SV12 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(69,plain,
! [SV13: a] :
( ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true )
| ( ( ~ ( ~ ~ ( f @ SV13 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV12: a] :
( ( ( ~ ~ ( f @ SV12 @ sK1_SX0 )
| ~ ( cR @ sK2_SY24 @ z ) )
= $false )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV13: a] :
( ( ( ~ ~ ( f @ SV13 @ sK1_SX0 )
| ~ ( cR @ sK4_SY31 @ z ) )
= $false )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV12: a] :
( ( ( ~ ~ ( f @ SV12 @ sK1_SX0 ) )
= $false )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
( ( ( ~ ( cR @ sK2_SY24 @ z ) )
= $false )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV13: a] :
( ( ( ~ ~ ( f @ SV13 @ sK1_SX0 ) )
= $false )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(75,plain,
( ( ( ~ ( cR @ sK4_SY31 @ z ) )
= $false )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV12: a] :
( ( ( ~ ( f @ SV12 @ sK1_SX0 ) )
= $true )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
( ( ( cR @ sK2_SY24 @ z )
= $true )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV13: a] :
( ( ( ~ ( f @ SV13 @ sK1_SX0 ) )
= $true )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
( ( ( cR @ sK4_SY31 @ z )
= $true )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV12: a] :
( ( ( f @ SV12 @ sK1_SX0 )
= $false )
| ( ( f @ sK2_SY24 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV13: a] :
( ( ( f @ SV13 @ sK1_SX0 )
= $false )
| ( ( f @ sK4_SY31 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,81,80,79,77,65,64,63,44,39]) ).
thf(83,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV104^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:40:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 0
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 0
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 ..
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 83 ****
% 0.08/0.24 %**** clause counter: 82 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------