%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU996^5 : 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 : n016.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 10:49:20 AM UTC 2026
% Result : Theorem 0.53s 0.28s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 60 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 179 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 750 ( 9 ~; 5 |; 45 &; 678 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 248 ( 0 ^; 248 !; 0 ?; 248 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_JOIN,type,
sK1_JOIN: a > a > a ).
thf(tp_sK2_SY27,type,
sK2_SY27: a > a > a ).
thf(tp_sK3_SX0,type,
sK3_SX0: a ).
thf(tp_sK4_SY94,type,
sK4_SY94: a ).
thf(tp_sK5_SY96,type,
sK5_SY96: a ).
thf(1,conjecture,
! [JOIN: a > a > a,MEET: a > a > a] :
( ( ! [Xx: a] :
( ( JOIN @ Xx @ Xx )
= Xx )
& ! [Xx: a] :
( ( MEET @ Xx @ Xx )
= Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
= ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
= ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ Xx @ Xy )
= ( JOIN @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( MEET @ Xx @ Xy )
= ( MEET @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a] :
( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
= ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( ( JOIN @ Xx @ Xz )
= Xz )
=> ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cMODULAR_THM_pme) ).
thf(2,negated_conjecture,
( ( ! [JOIN: a > a > a,MEET: a > a > a] :
( ( ! [Xx: a] :
( ( JOIN @ Xx @ Xx )
= Xx )
& ! [Xx: a] :
( ( MEET @ Xx @ Xx )
= Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
= ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
= ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ Xx @ Xy )
= ( JOIN @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( MEET @ Xx @ Xy )
= ( MEET @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a] :
( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
= ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( ( JOIN @ Xx @ Xz )
= Xz )
=> ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [JOIN: a > a > a,MEET: a > a > a] :
( ( ! [Xx: a] :
( ( JOIN @ Xx @ Xx )
= Xx )
& ! [Xx: a] :
( ( MEET @ Xx @ Xx )
= Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
= ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
= ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ Xx @ Xy )
= ( JOIN @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( MEET @ Xx @ Xy )
= ( MEET @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a] :
( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
= ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( ( JOIN @ Xx @ Xz )
= Xz )
=> ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
= ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY27: a > a > a] :
( ( ! [SY28: a] :
( ( sK1_JOIN @ SY28 @ SY28 )
= SY28 )
& ! [Xx: a] :
( ( SY27 @ Xx @ Xx )
= Xx )
& ! [SY30: a,SY31: a,SY32: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY30 @ SY31 ) @ SY32 )
= ( sK1_JOIN @ SY30 @ ( sK1_JOIN @ SY31 @ SY32 ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( SY27 @ ( SY27 @ Xx @ Xy ) @ Xz )
= ( SY27 @ Xx @ ( SY27 @ Xy @ Xz ) ) )
& ! [SY36: a,SY37: a] :
( ( sK1_JOIN @ SY36 @ SY37 )
= ( sK1_JOIN @ SY37 @ SY36 ) )
& ! [Xx: a,Xy: a] :
( ( SY27 @ Xx @ Xy )
= ( SY27 @ Xy @ Xx ) )
& ! [SY40: a,SY41: a] :
( ( sK1_JOIN @ ( SY27 @ SY40 @ SY41 ) @ SY41 )
= SY41 )
& ! [SY42: a,SY43: a] :
( ( SY27 @ ( sK1_JOIN @ SY42 @ SY43 ) @ SY43 )
= SY43 )
& ! [SY44: a,SY45: a,SY46: a] :
( ( sK1_JOIN @ SY44 @ ( SY27 @ SY45 @ SY46 ) )
= ( SY27 @ ( sK1_JOIN @ SY44 @ SY45 ) @ ( sK1_JOIN @ SY44 @ SY46 ) ) )
& ! [SY47: a,SY48: a,SY49: a] :
( ( SY27 @ SY47 @ ( sK1_JOIN @ SY48 @ SY49 ) )
= ( sK1_JOIN @ ( SY27 @ SY47 @ SY48 ) @ ( SY27 @ SY47 @ SY49 ) ) ) )
=> ! [SY50: a,SY51: a,SY52: a] :
( ( ( sK1_JOIN @ SY50 @ SY52 )
= SY52 )
=> ( ( sK1_JOIN @ SY50 @ ( SY27 @ SY51 @ SY52 ) )
= ( SY27 @ ( sK1_JOIN @ SY50 @ SY51 ) @ SY52 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY28: a] :
( ( sK1_JOIN @ SY28 @ SY28 )
= SY28 )
& ! [SY54: a] :
( ( sK2_SY27 @ SY54 @ SY54 )
= SY54 )
& ! [SY30: a,SY31: a,SY32: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY30 @ SY31 ) @ SY32 )
= ( sK1_JOIN @ SY30 @ ( sK1_JOIN @ SY31 @ SY32 ) ) )
& ! [SY58: a,SY59: a,SY60: a] :
( ( sK2_SY27 @ ( sK2_SY27 @ SY58 @ SY59 ) @ SY60 )
= ( sK2_SY27 @ SY58 @ ( sK2_SY27 @ SY59 @ SY60 ) ) )
& ! [SY36: a,SY37: a] :
( ( sK1_JOIN @ SY36 @ SY37 )
= ( sK1_JOIN @ SY37 @ SY36 ) )
& ! [SY63: a,SY64: a] :
( ( sK2_SY27 @ SY63 @ SY64 )
= ( sK2_SY27 @ SY64 @ SY63 ) )
& ! [SY65: a,SY66: a] :
( ( sK1_JOIN @ ( sK2_SY27 @ SY65 @ SY66 ) @ SY66 )
= SY66 )
& ! [SY67: a,SY68: a] :
( ( sK2_SY27 @ ( sK1_JOIN @ SY67 @ SY68 ) @ SY68 )
= SY68 )
& ! [SY69: a,SY70: a,SY71: a] :
( ( sK1_JOIN @ SY69 @ ( sK2_SY27 @ SY70 @ SY71 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY69 @ SY70 ) @ ( sK1_JOIN @ SY69 @ SY71 ) ) )
& ! [SY72: a,SY73: a,SY74: a] :
( ( sK2_SY27 @ SY72 @ ( sK1_JOIN @ SY73 @ SY74 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SY72 @ SY73 ) @ ( sK2_SY27 @ SY72 @ SY74 ) ) ) )
=> ! [SY75: a,SY76: a,SY77: a] :
( ( ( sK1_JOIN @ SY75 @ SY77 )
= SY77 )
=> ( ( sK1_JOIN @ SY75 @ ( sK2_SY27 @ SY76 @ SY77 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY75 @ SY76 ) @ SY77 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY28: a] :
( ( sK1_JOIN @ SY28 @ SY28 )
= SY28 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY54: a] :
( ( sK2_SY27 @ SY54 @ SY54 )
= SY54 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY30: a,SY31: a,SY32: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY30 @ SY31 ) @ SY32 )
= ( sK1_JOIN @ SY30 @ ( sK1_JOIN @ SY31 @ SY32 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SY58: a,SY59: a,SY60: a] :
( ( sK2_SY27 @ ( sK2_SY27 @ SY58 @ SY59 ) @ SY60 )
= ( sK2_SY27 @ SY58 @ ( sK2_SY27 @ SY59 @ SY60 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(10,plain,
( ( ! [SY36: a,SY37: a] :
( ( sK1_JOIN @ SY36 @ SY37 )
= ( sK1_JOIN @ SY37 @ SY36 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [SY63: a,SY64: a] :
( ( sK2_SY27 @ SY63 @ SY64 )
= ( sK2_SY27 @ SY64 @ SY63 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(12,plain,
( ( ! [SY65: a,SY66: a] :
( ( sK1_JOIN @ ( sK2_SY27 @ SY65 @ SY66 ) @ SY66 )
= SY66 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [SY67: a,SY68: a] :
( ( sK2_SY27 @ ( sK1_JOIN @ SY67 @ SY68 ) @ SY68 )
= SY68 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY69: a,SY70: a,SY71: a] :
( ( sK1_JOIN @ SY69 @ ( sK2_SY27 @ SY70 @ SY71 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY69 @ SY70 ) @ ( sK1_JOIN @ SY69 @ SY71 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [SY72: a,SY73: a,SY74: a] :
( ( sK2_SY27 @ SY72 @ ( sK1_JOIN @ SY73 @ SY74 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SY72 @ SY73 ) @ ( sK2_SY27 @ SY72 @ SY74 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [SY75: a,SY76: a,SY77: a] :
( ( ( sK1_JOIN @ SY75 @ SY77 )
= SY77 )
=> ( ( sK1_JOIN @ SY75 @ ( sK2_SY27 @ SY76 @ SY77 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY75 @ SY76 ) @ SY77 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(17,plain,
( ( ~ ! [SY75: a,SY76: a,SY77: a] :
( ( ( sK1_JOIN @ SY75 @ SY77 )
= SY77 )
=> ( ( sK1_JOIN @ SY75 @ ( sK2_SY27 @ SY76 @ SY77 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY75 @ SY76 ) @ SY77 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [SY72: a,SY73: a,SY74: a] :
( ( sK2_SY27 @ SY72 @ ( sK1_JOIN @ SY73 @ SY74 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SY72 @ SY73 ) @ ( sK2_SY27 @ SY72 @ SY74 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY69: a,SY70: a,SY71: a] :
( ( sK1_JOIN @ SY69 @ ( sK2_SY27 @ SY70 @ SY71 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY69 @ SY70 ) @ ( sK1_JOIN @ SY69 @ SY71 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [SY67: a,SY68: a] :
( ( sK2_SY27 @ ( sK1_JOIN @ SY67 @ SY68 ) @ SY68 )
= SY68 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [SY65: a,SY66: a] :
( ( sK1_JOIN @ ( sK2_SY27 @ SY65 @ SY66 ) @ SY66 )
= SY66 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [SY63: a,SY64: a] :
( ( sK2_SY27 @ SY63 @ SY64 )
= ( sK2_SY27 @ SY64 @ SY63 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [SY36: a,SY37: a] :
( ( sK1_JOIN @ SY36 @ SY37 )
= ( sK1_JOIN @ SY37 @ SY36 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [SY58: a,SY59: a,SY60: a] :
( ( sK2_SY27 @ ( sK2_SY27 @ SY58 @ SY59 ) @ SY60 )
= ( sK2_SY27 @ SY58 @ ( sK2_SY27 @ SY59 @ SY60 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [SY30: a,SY31: a,SY32: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY30 @ SY31 ) @ SY32 )
= ( sK1_JOIN @ SY30 @ ( sK1_JOIN @ SY31 @ SY32 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [SY54: a] :
( ( sK2_SY27 @ SY54 @ SY54 )
= SY54 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [SY28: a] :
( ( sK1_JOIN @ SY28 @ SY28 )
= SY28 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(28,plain,
( ( ~ ! [SY75: a,SY76: a,SY77: a] :
( ( ( sK1_JOIN @ SY75 @ SY77 )
= SY77 )
=> ( ( sK1_JOIN @ SY75 @ ( sK2_SY27 @ SY76 @ SY77 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SY75 @ SY76 ) @ SY77 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( ( sK1_JOIN @ SX0 @ SX2 )
!= SX2 )
| ( ( sK1_JOIN @ SX0 @ ( sK2_SY27 @ SX1 @ SX2 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(30,plain,
! [SV1: a] :
( ( ! [SY78: a,SY79: a] :
( ( sK2_SY27 @ SV1 @ ( sK1_JOIN @ SY78 @ SY79 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SV1 @ SY78 ) @ ( sK2_SY27 @ SV1 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(31,plain,
! [SV2: a] :
( ( ! [SY80: a,SY81: a] :
( ( sK1_JOIN @ SV2 @ ( sK2_SY27 @ SY80 @ SY81 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SV2 @ SY80 ) @ ( sK1_JOIN @ SV2 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(32,plain,
! [SV3: a] :
( ( ! [SY82: a] :
( ( sK2_SY27 @ ( sK1_JOIN @ SV3 @ SY82 ) @ SY82 )
= SY82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(33,plain,
! [SV4: a] :
( ( ! [SY83: a] :
( ( sK1_JOIN @ ( sK2_SY27 @ SV4 @ SY83 ) @ SY83 )
= SY83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(34,plain,
! [SV5: a] :
( ( ! [SY84: a] :
( ( sK2_SY27 @ SV5 @ SY84 )
= ( sK2_SY27 @ SY84 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(35,plain,
! [SV6: a] :
( ( ! [SY85: a] :
( ( sK1_JOIN @ SV6 @ SY85 )
= ( sK1_JOIN @ SY85 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(36,plain,
! [SV7: a] :
( ( ! [SY86: a,SY87: a] :
( ( sK2_SY27 @ ( sK2_SY27 @ SV7 @ SY86 ) @ SY87 )
= ( sK2_SY27 @ SV7 @ ( sK2_SY27 @ SY86 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(37,plain,
! [SV8: a] :
( ( ! [SY88: a,SY89: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV8 @ SY88 ) @ SY89 )
= ( sK1_JOIN @ SV8 @ ( sK1_JOIN @ SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(38,plain,
! [SV9: a] :
( ( ( sK2_SY27 @ SV9 @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(39,plain,
! [SV10: a] :
( ( ( sK1_JOIN @ SV10 @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(40,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( ( sK1_JOIN @ SX0 @ SX2 )
!= SX2 )
| ( ( sK1_JOIN @ SX0 @ ( sK2_SY27 @ SX1 @ SX2 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(41,plain,
! [SV11: a,SV1: a] :
( ( ! [SY90: a] :
( ( sK2_SY27 @ SV1 @ ( sK1_JOIN @ SV11 @ SY90 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SV1 @ SV11 ) @ ( sK2_SY27 @ SV1 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
! [SV12: a,SV2: a] :
( ( ! [SY91: a] :
( ( sK1_JOIN @ SV2 @ ( sK2_SY27 @ SV12 @ SY91 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SV2 @ SV12 ) @ ( sK1_JOIN @ SV2 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV13: a,SV3: a] :
( ( ( sK2_SY27 @ ( sK1_JOIN @ SV3 @ SV13 ) @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV14: a,SV4: a] :
( ( ( sK1_JOIN @ ( sK2_SY27 @ SV4 @ SV14 ) @ SV14 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV15: a,SV5: a] :
( ( ( sK2_SY27 @ SV5 @ SV15 )
= ( sK2_SY27 @ SV15 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV16: a,SV6: a] :
( ( ( sK1_JOIN @ SV6 @ SV16 )
= ( sK1_JOIN @ SV16 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV17: a,SV7: a] :
( ( ! [SY92: a] :
( ( sK2_SY27 @ ( sK2_SY27 @ SV7 @ SV17 ) @ SY92 )
= ( sK2_SY27 @ SV7 @ ( sK2_SY27 @ SV17 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV18: a,SV8: a] :
( ( ! [SY93: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV8 @ SV18 ) @ SY93 )
= ( sK1_JOIN @ SV8 @ ( sK1_JOIN @ SV18 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
( ( ! [SY94: a,SY95: a] :
( ( ( sK1_JOIN @ sK3_SX0 @ SY95 )
!= SY95 )
| ( ( sK1_JOIN @ sK3_SX0 @ ( sK2_SY27 @ SY94 @ SY95 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ sK3_SX0 @ SY94 ) @ SY95 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(50,plain,
! [SV19: a,SV11: a,SV1: a] :
( ( ( sK2_SY27 @ SV1 @ ( sK1_JOIN @ SV11 @ SV19 ) )
= ( sK1_JOIN @ ( sK2_SY27 @ SV1 @ SV11 ) @ ( sK2_SY27 @ SV1 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV20: a,SV12: a,SV2: a] :
( ( ( sK1_JOIN @ SV2 @ ( sK2_SY27 @ SV12 @ SV20 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ SV2 @ SV12 ) @ ( sK1_JOIN @ SV2 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV21: a,SV17: a,SV7: a] :
( ( ( sK2_SY27 @ ( sK2_SY27 @ SV7 @ SV17 ) @ SV21 )
= ( sK2_SY27 @ SV7 @ ( sK2_SY27 @ SV17 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV22: a,SV18: a,SV8: a] :
( ( ( sK1_JOIN @ ( sK1_JOIN @ SV8 @ SV18 ) @ SV22 )
= ( sK1_JOIN @ SV8 @ ( sK1_JOIN @ SV18 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
( ( ! [SY96: a] :
( ( ( sK1_JOIN @ sK3_SX0 @ SY96 )
!= SY96 )
| ( ( sK1_JOIN @ sK3_SX0 @ ( sK2_SY27 @ sK4_SY94 @ SY96 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ sK3_SX0 @ sK4_SY94 ) @ SY96 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(55,plain,
( ( ( ( sK1_JOIN @ sK3_SX0 @ sK5_SY96 )
!= sK5_SY96 )
| ( ( sK1_JOIN @ sK3_SX0 @ ( sK2_SY27 @ sK4_SY94 @ sK5_SY96 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ sK3_SX0 @ sK4_SY94 ) @ sK5_SY96 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(56,plain,
( ( ( sK1_JOIN @ sK3_SX0 @ sK5_SY96 )
!= sK5_SY96 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(57,plain,
( ( ( sK1_JOIN @ sK3_SX0 @ ( sK2_SY27 @ sK4_SY94 @ sK5_SY96 ) )
= ( sK2_SY27 @ ( sK1_JOIN @ sK3_SX0 @ sK4_SY94 ) @ sK5_SY96 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ( sK1_JOIN @ sK3_SX0 @ sK5_SY96 )
= sK5_SY96 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,58,57,53,52,51,50,46,45,44,43,39]) ).
thf(60,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU996^5 : 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
% 0.07/0.17 % Computer : n016.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:44:14 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.28
% 0.53/0.28 No.of.Axioms: 0
% 0.53/0.28
% 0.53/0.28 Length.of.Defs: 0
% 0.53/0.28
% 0.53/0.28 Contains.Choice.Funs: false
% 0.53/0.28 ..
% 0.53/0.28
% 0.53/0.28 ********************************
% 0.53/0.28 * All subproblems solved! *
% 0.53/0.28 ********************************
% 0.53/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:59,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.28
% 0.53/0.28 %**** Beginning of derivation protocol ****
% 0.53/0.28 % SZS output start CNFRefutation
% See solution above
% 0.53/0.28
% 0.53/0.28 %**** End of derivation protocol ****
% 0.53/0.28 %**** no. of clauses in derivation: 60 ****
% 0.53/0.28 %**** clause counter: 59 ****
% 0.53/0.28
% 0.53/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:59,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------