%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV001^5 : 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 : 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 10:49:21 AM UTC 2026
% Result : Theorem 17.00s 3.07s
% Output : CNFRefutation 17.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 93 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 237 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1024 ( 12 ~; 4 |; 35 &; 956 @)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 345 ( 0 ^; 345 !; 0 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_JOIN,type,
sK1_JOIN: a > a > a ).
thf(tp_sK2_SY24,type,
sK2_SY24: a > a > a ).
thf(tp_sK3_SX0,type,
sK3_SX0: a ).
thf(tp_sK4_SY79,type,
sK4_SY79: a ).
thf(tp_sK5_SY83,type,
sK5_SY83: a ).
thf(tp_sK6_SX0,type,
sK6_SX0: a ).
thf(tp_sK7_SY95,type,
sK7_SY95: a ).
thf(tp_sK8_SY99,type,
sK8_SY99: 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDISTRIB_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 ) ) ) ) ) )
= $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 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY24: a > a > a] :
( ( ! [SY25: a] :
( ( sK1_JOIN @ SY25 @ SY25 )
= SY25 )
& ! [Xx: a] :
( ( SY24 @ Xx @ Xx )
= Xx )
& ! [SY27: a,SY28: a,SY29: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY27 @ SY28 ) @ SY29 )
= ( sK1_JOIN @ SY27 @ ( sK1_JOIN @ SY28 @ SY29 ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( SY24 @ ( SY24 @ Xx @ Xy ) @ Xz )
= ( SY24 @ Xx @ ( SY24 @ Xy @ Xz ) ) )
& ! [SY33: a,SY34: a] :
( ( sK1_JOIN @ SY33 @ SY34 )
= ( sK1_JOIN @ SY34 @ SY33 ) )
& ! [Xx: a,Xy: a] :
( ( SY24 @ Xx @ Xy )
= ( SY24 @ Xy @ Xx ) )
& ! [SY37: a,SY38: a] :
( ( sK1_JOIN @ ( SY24 @ SY37 @ SY38 ) @ SY38 )
= SY38 )
& ! [SY39: a,SY40: a] :
( ( SY24 @ ( sK1_JOIN @ SY39 @ SY40 ) @ SY40 )
= SY40 ) )
=> ( ! [SY41: a,SY42: a,SY43: a] :
( ( sK1_JOIN @ SY41 @ ( SY24 @ SY42 @ SY43 ) )
= ( SY24 @ ( sK1_JOIN @ SY41 @ SY42 ) @ ( sK1_JOIN @ SY41 @ SY43 ) ) )
<=> ! [SY44: a,SY45: a,SY46: a] :
( ( SY24 @ SY44 @ ( sK1_JOIN @ SY45 @ SY46 ) )
= ( sK1_JOIN @ ( SY24 @ SY44 @ SY45 ) @ ( SY24 @ SY44 @ SY46 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY25: a] :
( ( sK1_JOIN @ SY25 @ SY25 )
= SY25 )
& ! [SY48: a] :
( ( sK2_SY24 @ SY48 @ SY48 )
= SY48 )
& ! [SY27: a,SY28: a,SY29: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY27 @ SY28 ) @ SY29 )
= ( sK1_JOIN @ SY27 @ ( sK1_JOIN @ SY28 @ SY29 ) ) )
& ! [SY52: a,SY53: a,SY54: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SY52 @ SY53 ) @ SY54 )
= ( sK2_SY24 @ SY52 @ ( sK2_SY24 @ SY53 @ SY54 ) ) )
& ! [SY33: a,SY34: a] :
( ( sK1_JOIN @ SY33 @ SY34 )
= ( sK1_JOIN @ SY34 @ SY33 ) )
& ! [SY57: a,SY58: a] :
( ( sK2_SY24 @ SY57 @ SY58 )
= ( sK2_SY24 @ SY58 @ SY57 ) )
& ! [SY59: a,SY60: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SY59 @ SY60 ) @ SY60 )
= SY60 )
& ! [SY61: a,SY62: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SY61 @ SY62 ) @ SY62 )
= SY62 ) )
=> ( ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) )
<=> ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY25: a] :
( ( sK1_JOIN @ SY25 @ SY25 )
= SY25 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY48: a] :
( ( sK2_SY24 @ SY48 @ SY48 )
= SY48 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY27: a,SY28: a,SY29: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY27 @ SY28 ) @ SY29 )
= ( sK1_JOIN @ SY27 @ ( sK1_JOIN @ SY28 @ SY29 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SY52: a,SY53: a,SY54: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SY52 @ SY53 ) @ SY54 )
= ( sK2_SY24 @ SY52 @ ( sK2_SY24 @ SY53 @ SY54 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(10,plain,
( ( ! [SY33: a,SY34: a] :
( ( sK1_JOIN @ SY33 @ SY34 )
= ( sK1_JOIN @ SY34 @ SY33 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [SY57: a,SY58: a] :
( ( sK2_SY24 @ SY57 @ SY58 )
= ( sK2_SY24 @ SY58 @ SY57 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(12,plain,
( ( ! [SY59: a,SY60: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SY59 @ SY60 ) @ SY60 )
= SY60 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [SY61: a,SY62: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SY61 @ SY62 ) @ SY62 )
= SY62 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) )
<=> ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) )
=> ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[14]) ).
thf(16,plain,
( ( ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) )
=> ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[14]) ).
thf(17,plain,
( ( ~ ( ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) )
=> ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) )
=> ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY61: a,SY62: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SY61 @ SY62 ) @ SY62 )
= SY62 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [SY59: a,SY60: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SY59 @ SY60 ) @ SY60 )
= SY60 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [SY57: a,SY58: a] :
( ( sK2_SY24 @ SY57 @ SY58 )
= ( sK2_SY24 @ SY58 @ SY57 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [SY33: a,SY34: a] :
( ( sK1_JOIN @ SY33 @ SY34 )
= ( sK1_JOIN @ SY34 @ SY33 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ! [SY52: a,SY53: a,SY54: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SY52 @ SY53 ) @ SY54 )
= ( sK2_SY24 @ SY52 @ ( sK2_SY24 @ SY53 @ SY54 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [SY27: a,SY28: a,SY29: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY27 @ SY28 ) @ SY29 )
= ( sK1_JOIN @ SY27 @ ( sK1_JOIN @ SY28 @ SY29 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [SY48: a] :
( ( sK2_SY24 @ SY48 @ SY48 )
= SY48 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [SY25: a] :
( ( sK1_JOIN @ SY25 @ SY25 )
= SY25 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(27,plain,
( ( ~ ( ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) )
=> ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( ~ ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) )
| ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(29,plain,
! [SV1: a] :
( ( ! [SY69: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SV1 @ SY69 ) @ SY69 )
= SY69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(30,plain,
! [SV2: a] :
( ( ! [SY70: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SV2 @ SY70 ) @ SY70 )
= SY70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(31,plain,
! [SV3: a] :
( ( ! [SY71: a] :
( ( sK2_SY24 @ SV3 @ SY71 )
= ( sK2_SY24 @ SY71 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(32,plain,
! [SV4: a] :
( ( ! [SY72: a] :
( ( sK1_JOIN @ SV4 @ SY72 )
= ( sK1_JOIN @ SY72 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(33,plain,
! [SV5: a] :
( ( ! [SY73: a,SY74: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SV5 @ SY73 ) @ SY74 )
= ( sK2_SY24 @ SV5 @ ( sK2_SY24 @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
! [SV6: a] :
( ( ! [SY75: a,SY76: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV6 @ SY75 ) @ SY76 )
= ( sK1_JOIN @ SV6 @ ( sK1_JOIN @ SY75 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV7: a] :
( ( ( sK2_SY24 @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV8: a] :
( ( ( sK1_JOIN @ SV8 @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) )
| ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV9: a,SV1: a] :
( ( ( sK2_SY24 @ ( sK1_JOIN @ SV1 @ SV9 ) @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV10: a,SV2: a] :
( ( ( sK1_JOIN @ ( sK2_SY24 @ SV2 @ SV10 ) @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV11: a,SV3: a] :
( ( ( sK2_SY24 @ SV3 @ SV11 )
= ( sK2_SY24 @ SV11 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV12: a,SV4: a] :
( ( ( sK1_JOIN @ SV4 @ SV12 )
= ( sK1_JOIN @ SV12 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV13: a,SV5: a] :
( ( ! [SY77: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SV5 @ SV13 ) @ SY77 )
= ( sK2_SY24 @ SV5 @ ( sK2_SY24 @ SV13 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV14: a,SV6: a] :
( ( ! [SY78: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV6 @ SV14 ) @ SY78 )
= ( sK1_JOIN @ SV6 @ ( sK1_JOIN @ SV14 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(46,plain,
! [SV15: a,SV13: a,SV5: a] :
( ( ( sK2_SY24 @ ( sK2_SY24 @ SV5 @ SV13 ) @ SV15 )
= ( sK2_SY24 @ SV5 @ ( sK2_SY24 @ SV13 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV16: a,SV14: a,SV6: a] :
( ( ( sK1_JOIN @ ( sK1_JOIN @ SV6 @ SV14 ) @ SV16 )
= ( sK1_JOIN @ SV6 @ ( sK1_JOIN @ SV14 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ! [SY79: a,SY80: a] :
( ( sK2_SY24 @ sK3_SX0 @ ( sK1_JOIN @ SY79 @ SY80 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ sK3_SX0 @ SY79 ) @ ( sK2_SY24 @ sK3_SX0 @ SY80 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(50,plain,
! [SV17: a] :
( ( ! [SY81: a,SY82: a] :
( ( sK1_JOIN @ SV17 @ ( sK2_SY24 @ SY81 @ SY82 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SV17 @ SY81 ) @ ( sK1_JOIN @ SV17 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(51,plain,
( ( ! [SY83: a] :
( ( sK2_SY24 @ sK3_SX0 @ ( sK1_JOIN @ sK4_SY79 @ SY83 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ sK3_SX0 @ sK4_SY79 ) @ ( sK2_SY24 @ sK3_SX0 @ SY83 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(52,plain,
! [SV18: a,SV17: a] :
( ( ! [SY84: a] :
( ( sK1_JOIN @ SV17 @ ( sK2_SY24 @ SV18 @ SY84 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SV17 @ SV18 ) @ ( sK1_JOIN @ SV17 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
( ( ( sK2_SY24 @ sK3_SX0 @ ( sK1_JOIN @ sK4_SY79 @ sK5_SY83 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ sK3_SX0 @ sK4_SY79 ) @ ( sK2_SY24 @ sK3_SX0 @ sK5_SY83 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV19: a,SV18: a,SV17: a] :
( ( ( sK1_JOIN @ SV17 @ ( sK2_SY24 @ SV18 @ SV19 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SV17 @ SV18 ) @ ( sK1_JOIN @ SV17 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(55,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,54,53,47,46,41,40,39,38,36]) ).
thf(56,plain,
( ( ! [SY61: a,SY62: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SY61 @ SY62 ) @ SY62 )
= SY62 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(57,plain,
( ( ! [SY59: a,SY60: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SY59 @ SY60 ) @ SY60 )
= SY60 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(58,plain,
( ( ! [SY57: a,SY58: a] :
( ( sK2_SY24 @ SY57 @ SY58 )
= ( sK2_SY24 @ SY58 @ SY57 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(59,plain,
( ( ! [SY33: a,SY34: a] :
( ( sK1_JOIN @ SY33 @ SY34 )
= ( sK1_JOIN @ SY34 @ SY33 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(60,plain,
( ( ! [SY52: a,SY53: a,SY54: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SY52 @ SY53 ) @ SY54 )
= ( sK2_SY24 @ SY52 @ ( sK2_SY24 @ SY53 @ SY54 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(61,plain,
( ( ! [SY27: a,SY28: a,SY29: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SY27 @ SY28 ) @ SY29 )
= ( sK1_JOIN @ SY27 @ ( sK1_JOIN @ SY28 @ SY29 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(62,plain,
( ( ! [SY48: a] :
( ( sK2_SY24 @ SY48 @ SY48 )
= SY48 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(63,plain,
( ( ! [SY25: a] :
( ( sK1_JOIN @ SY25 @ SY25 )
= SY25 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(64,plain,
( ( ~ ( ! [SY66: a,SY67: a,SY68: a] :
( ( sK2_SY24 @ SY66 @ ( sK1_JOIN @ SY67 @ SY68 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SY66 @ SY67 ) @ ( sK2_SY24 @ SY66 @ SY68 ) ) )
=> ! [SY63: a,SY64: a,SY65: a] :
( ( sK1_JOIN @ SY63 @ ( sK2_SY24 @ SY64 @ SY65 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SY63 @ SY64 ) @ ( sK1_JOIN @ SY63 @ SY65 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(65,plain,
( ( ~ ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) )
| ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
! [SV20: a] :
( ( ! [SY85: a] :
( ( sK2_SY24 @ ( sK1_JOIN @ SV20 @ SY85 ) @ SY85 )
= SY85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV21: a] :
( ( ! [SY86: a] :
( ( sK1_JOIN @ ( sK2_SY24 @ SV21 @ SY86 ) @ SY86 )
= SY86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV22: a] :
( ( ! [SY87: a] :
( ( sK2_SY24 @ SV22 @ SY87 )
= ( sK2_SY24 @ SY87 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV23: a] :
( ( ! [SY88: a] :
( ( sK1_JOIN @ SV23 @ SY88 )
= ( sK1_JOIN @ SY88 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV24: a] :
( ( ! [SY89: a,SY90: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SV24 @ SY89 ) @ SY90 )
= ( sK2_SY24 @ SV24 @ ( sK2_SY24 @ SY89 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV25: a] :
( ( ! [SY91: a,SY92: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV25 @ SY91 ) @ SY92 )
= ( sK1_JOIN @ SV25 @ ( sK1_JOIN @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV26: a] :
( ( ( sK2_SY24 @ SV26 @ SV26 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV27: a] :
( ( ( sK1_JOIN @ SV27 @ SV27 )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) )
| ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV28: a,SV20: a] :
( ( ( sK2_SY24 @ ( sK1_JOIN @ SV20 @ SV28 ) @ SV28 )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV29: a,SV21: a] :
( ( ( sK1_JOIN @ ( sK2_SY24 @ SV21 @ SV29 ) @ SV29 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV30: a,SV22: a] :
( ( ( sK2_SY24 @ SV22 @ SV30 )
= ( sK2_SY24 @ SV30 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV31: a,SV23: a] :
( ( ( sK1_JOIN @ SV23 @ SV31 )
= ( sK1_JOIN @ SV31 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV32: a,SV24: a] :
( ( ! [SY93: a] :
( ( sK2_SY24 @ ( sK2_SY24 @ SV24 @ SV32 ) @ SY93 )
= ( sK2_SY24 @ SV24 @ ( sK2_SY24 @ SV32 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV33: a,SV25: a] :
( ( ! [SY94: a] :
( ( sK1_JOIN @ ( sK1_JOIN @ SV25 @ SV33 ) @ SY94 )
= ( sK1_JOIN @ SV25 @ ( sK1_JOIN @ SV33 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(82,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( sK1_JOIN @ SX0 @ ( sK2_SY24 @ SX1 @ SX2 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ SX0 @ SX1 ) @ ( sK1_JOIN @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV34: a,SV32: a,SV24: a] :
( ( ( sK2_SY24 @ ( sK2_SY24 @ SV24 @ SV32 ) @ SV34 )
= ( sK2_SY24 @ SV24 @ ( sK2_SY24 @ SV32 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV35: a,SV33: a,SV25: a] :
( ( ( sK1_JOIN @ ( sK1_JOIN @ SV25 @ SV33 ) @ SV35 )
= ( sK1_JOIN @ SV25 @ ( sK1_JOIN @ SV33 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(85,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( sK2_SY24 @ SX0 @ ( sK1_JOIN @ SX1 @ SX2 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SX0 @ SX1 ) @ ( sK2_SY24 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
( ( ! [SY95: a,SY96: a] :
( ( sK1_JOIN @ sK6_SX0 @ ( sK2_SY24 @ SY95 @ SY96 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ sK6_SX0 @ SY95 ) @ ( sK1_JOIN @ sK6_SX0 @ SY96 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(87,plain,
! [SV36: a] :
( ( ! [SY97: a,SY98: a] :
( ( sK2_SY24 @ SV36 @ ( sK1_JOIN @ SY97 @ SY98 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SV36 @ SY97 ) @ ( sK2_SY24 @ SV36 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(88,plain,
( ( ! [SY99: a] :
( ( sK1_JOIN @ sK6_SX0 @ ( sK2_SY24 @ sK7_SY95 @ SY99 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ sK6_SX0 @ sK7_SY95 ) @ ( sK1_JOIN @ sK6_SX0 @ SY99 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(89,plain,
! [SV37: a,SV36: a] :
( ( ! [SY100: a] :
( ( sK2_SY24 @ SV36 @ ( sK1_JOIN @ SV37 @ SY100 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SV36 @ SV37 ) @ ( sK2_SY24 @ SV36 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(90,plain,
( ( ( sK1_JOIN @ sK6_SX0 @ ( sK2_SY24 @ sK7_SY95 @ sK8_SY99 ) )
= ( sK2_SY24 @ ( sK1_JOIN @ sK6_SX0 @ sK7_SY95 ) @ ( sK1_JOIN @ sK6_SX0 @ sK8_SY99 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(91,plain,
! [SV38: a,SV37: a,SV36: a] :
( ( ( sK2_SY24 @ SV36 @ ( sK1_JOIN @ SV37 @ SV38 ) )
= ( sK1_JOIN @ ( sK2_SY24 @ SV36 @ SV37 ) @ ( sK2_SY24 @ SV36 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(92,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,91,90,84,83,78,77,76,75,73]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV001^5 : 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
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:39:32 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.00/3.07
% 17.00/3.07 No.of.Axioms: 0
% 17.00/3.07
% 17.00/3.07 Length.of.Defs: 0
% 17.00/3.07
% 17.00/3.07 Contains.Choice.Funs: false
% 17.00/3.07 ...
% 17.00/3.07
% 17.00/3.07 ********************************
% 17.00/3.07 * All subproblems solved! *
% 17.00/3.07 ********************************
% 17.00/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 17.00/3.07
% 17.00/3.07 %**** Beginning of derivation protocol ****
% 17.00/3.07 % SZS output start CNFRefutation
% See solution above
% 17.00/3.07
% 17.00/3.07 %**** End of derivation protocol ****
% 17.00/3.07 %**** no. of clauses in derivation: 93 ****
% 17.00/3.07 %**** clause counter: 92 ****
% 17.00/3.07
% 17.00/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------