%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU901^5 : 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 : n002.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 10:49:12 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 72 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 384 ( 140 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 902 ( 46 ~; 42 |; 79 &; 615 @)
% ( 0 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 0 ^; 201 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_g,type,
g: $tType ).
thf(tp_sK1_Xh1,type,
sK1_Xh1: g > b ).
thf(tp_sK2_SY17,type,
sK2_SY17: b > a ).
thf(tp_sK3_SY33,type,
sK3_SY33: g > $o ).
thf(tp_sK4_SY48,type,
sK4_SY48: g > g ).
thf(tp_sK5_SY62,type,
sK5_SY62: b > $o ).
thf(tp_sK6_SY75,type,
sK6_SY75: b > b ).
thf(tp_sK7_SY87,type,
sK7_SY87: a > $o ).
thf(tp_sK8_SY98,type,
sK8_SY98: a > a ).
thf(tp_sK9_SY116,type,
sK9_SY116: g ).
thf(1,conjecture,
! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
( ( ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs1 @ ( Xf1 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs2 @ ( Xh1 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh1 @ ( Xf1 @ Xx ) )
= ( Xf2 @ ( Xh1 @ Xx ) ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: a] :
( ( Xs3 @ Xx )
=> ( Xs3 @ ( Xf3 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs3 @ ( Xh2 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( ( Xh2 @ ( Xf2 @ Xx ) )
= ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
=> ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM131D_pme) ).
thf(2,negated_conjecture,
( ( ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
( ( ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs1 @ ( Xf1 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs2 @ ( Xh1 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh1 @ ( Xf1 @ Xx ) )
= ( Xf2 @ ( Xh1 @ Xx ) ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: a] :
( ( Xs3 @ Xx )
=> ( Xs3 @ ( Xf3 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs3 @ ( Xh2 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( ( Xh2 @ ( Xf2 @ Xx ) )
= ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
=> ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
( ( ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs1 @ ( Xf1 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( Xs2 @ ( Xh1 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh1 @ ( Xf1 @ Xx ) )
= ( Xf2 @ ( Xh1 @ Xx ) ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs2 @ ( Xf2 @ Xx ) ) )
& ! [Xx: a] :
( ( Xs3 @ Xx )
=> ( Xs3 @ ( Xf3 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( Xs3 @ ( Xh2 @ Xx ) ) )
& ! [Xx: b] :
( ( Xs2 @ Xx )
=> ( ( Xh2 @ ( Xf2 @ Xx ) )
= ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
=> ! [Xx: g] :
( ( Xs1 @ Xx )
=> ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY17: b > a,SY18: g > $o,SY19: g > g,SY20: b > $o,SY21: b > b,SY22: a > $o,SY23: a > a] :
( ( ! [Xx: g] :
( ( SY18 @ Xx )
=> ( SY18 @ ( SY19 @ Xx ) ) )
& ! [Xx: b] :
( ( SY20 @ Xx )
=> ( SY20 @ ( SY21 @ Xx ) ) )
& ! [SY26: g] :
( ( SY18 @ SY26 )
=> ( SY20 @ ( sK1_Xh1 @ SY26 ) ) )
& ! [SY27: g] :
( ( SY18 @ SY27 )
=> ( ( sK1_Xh1 @ ( SY19 @ SY27 ) )
= ( SY21 @ ( sK1_Xh1 @ SY27 ) ) ) )
& ! [Xx: b] :
( ( SY20 @ Xx )
=> ( SY20 @ ( SY21 @ Xx ) ) )
& ! [Xx: a] :
( ( SY22 @ Xx )
=> ( SY22 @ ( SY23 @ Xx ) ) )
& ! [Xx: b] :
( ( SY20 @ Xx )
=> ( SY22 @ ( SY17 @ Xx ) ) )
& ! [Xx: b] :
( ( SY20 @ Xx )
=> ( ( SY17 @ ( SY21 @ Xx ) )
= ( SY23 @ ( SY17 @ Xx ) ) ) ) )
=> ! [SY32: g] :
( ( SY18 @ SY32 )
=> ( ( SY17 @ ( sK1_Xh1 @ ( SY19 @ SY32 ) ) )
= ( SY23 @ ( SY17 @ ( sK1_Xh1 @ SY32 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY33: g > $o,SY34: g > g,SY35: b > $o,SY36: b > b,SY37: a > $o,SY38: a > a] :
( ( ! [Xx: g] :
( ( SY33 @ Xx )
=> ( SY33 @ ( SY34 @ Xx ) ) )
& ! [Xx: b] :
( ( SY35 @ Xx )
=> ( SY35 @ ( SY36 @ Xx ) ) )
& ! [SY26: g] :
( ( SY33 @ SY26 )
=> ( SY35 @ ( sK1_Xh1 @ SY26 ) ) )
& ! [SY27: g] :
( ( SY33 @ SY27 )
=> ( ( sK1_Xh1 @ ( SY34 @ SY27 ) )
= ( SY36 @ ( sK1_Xh1 @ SY27 ) ) ) )
& ! [Xx: b] :
( ( SY35 @ Xx )
=> ( SY35 @ ( SY36 @ Xx ) ) )
& ! [Xx: a] :
( ( SY37 @ Xx )
=> ( SY37 @ ( SY38 @ Xx ) ) )
& ! [SY45: b] :
( ( SY35 @ SY45 )
=> ( SY37 @ ( sK2_SY17 @ SY45 ) ) )
& ! [SY46: b] :
( ( SY35 @ SY46 )
=> ( ( sK2_SY17 @ ( SY36 @ SY46 ) )
= ( SY38 @ ( sK2_SY17 @ SY46 ) ) ) ) )
=> ! [SY47: g] :
( ( SY33 @ SY47 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( SY34 @ SY47 ) ) )
= ( SY38 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY47 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY48: g > g,SY49: b > $o,SY50: b > b,SY51: a > $o,SY52: a > a] :
( ( ! [SY53: g] :
( ( sK3_SY33 @ SY53 )
=> ( sK3_SY33 @ ( SY48 @ SY53 ) ) )
& ! [Xx: b] :
( ( SY49 @ Xx )
=> ( SY49 @ ( SY50 @ Xx ) ) )
& ! [SY55: g] :
( ( sK3_SY33 @ SY55 )
=> ( SY49 @ ( sK1_Xh1 @ SY55 ) ) )
& ! [SY56: g] :
( ( sK3_SY33 @ SY56 )
=> ( ( sK1_Xh1 @ ( SY48 @ SY56 ) )
= ( SY50 @ ( sK1_Xh1 @ SY56 ) ) ) )
& ! [Xx: b] :
( ( SY49 @ Xx )
=> ( SY49 @ ( SY50 @ Xx ) ) )
& ! [Xx: a] :
( ( SY51 @ Xx )
=> ( SY51 @ ( SY52 @ Xx ) ) )
& ! [SY45: b] :
( ( SY49 @ SY45 )
=> ( SY51 @ ( sK2_SY17 @ SY45 ) ) )
& ! [SY46: b] :
( ( SY49 @ SY46 )
=> ( ( sK2_SY17 @ ( SY50 @ SY46 ) )
= ( SY52 @ ( sK2_SY17 @ SY46 ) ) ) ) )
=> ! [SY61: g] :
( ( sK3_SY33 @ SY61 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( SY48 @ SY61 ) ) )
= ( SY52 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY61 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY62: b > $o,SY63: b > b,SY64: a > $o,SY65: a > a] :
( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) )
& ! [Xx: b] :
( ( SY62 @ Xx )
=> ( SY62 @ ( SY63 @ Xx ) ) )
& ! [SY55: g] :
( ( sK3_SY33 @ SY55 )
=> ( SY62 @ ( sK1_Xh1 @ SY55 ) ) )
& ! [SY69: g] :
( ( sK3_SY33 @ SY69 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY69 ) )
= ( SY63 @ ( sK1_Xh1 @ SY69 ) ) ) )
& ! [Xx: b] :
( ( SY62 @ Xx )
=> ( SY62 @ ( SY63 @ Xx ) ) )
& ! [Xx: a] :
( ( SY64 @ Xx )
=> ( SY64 @ ( SY65 @ Xx ) ) )
& ! [SY45: b] :
( ( SY62 @ SY45 )
=> ( SY64 @ ( sK2_SY17 @ SY45 ) ) )
& ! [SY46: b] :
( ( SY62 @ SY46 )
=> ( ( sK2_SY17 @ ( SY63 @ SY46 ) )
= ( SY65 @ ( sK2_SY17 @ SY46 ) ) ) ) )
=> ! [SY74: g] :
( ( sK3_SY33 @ SY74 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY74 ) ) )
= ( SY65 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY74 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY75: b > b,SY76: a > $o,SY77: a > a] :
( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) )
& ! [SY79: b] :
( ( sK5_SY62 @ SY79 )
=> ( sK5_SY62 @ ( SY75 @ SY79 ) ) )
& ! [SY80: g] :
( ( sK3_SY33 @ SY80 )
=> ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) )
& ! [SY69: g] :
( ( sK3_SY33 @ SY69 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY69 ) )
= ( SY75 @ ( sK1_Xh1 @ SY69 ) ) ) )
& ! [SY82: b] :
( ( sK5_SY62 @ SY82 )
=> ( sK5_SY62 @ ( SY75 @ SY82 ) ) )
& ! [Xx: a] :
( ( SY76 @ Xx )
=> ( SY76 @ ( SY77 @ Xx ) ) )
& ! [SY84: b] :
( ( sK5_SY62 @ SY84 )
=> ( SY76 @ ( sK2_SY17 @ SY84 ) ) )
& ! [SY85: b] :
( ( sK5_SY62 @ SY85 )
=> ( ( sK2_SY17 @ ( SY75 @ SY85 ) )
= ( SY77 @ ( sK2_SY17 @ SY85 ) ) ) ) )
=> ! [SY74: g] :
( ( sK3_SY33 @ SY74 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY74 ) ) )
= ( SY77 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY74 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY87: a > $o,SY88: a > a] :
( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) )
& ! [SY90: b] :
( ( sK5_SY62 @ SY90 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) )
& ! [SY80: g] :
( ( sK3_SY33 @ SY80 )
=> ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) )
& ! [SY92: g] :
( ( sK3_SY33 @ SY92 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) )
& ! [SY93: b] :
( ( sK5_SY62 @ SY93 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) )
& ! [Xx: a] :
( ( SY87 @ Xx )
=> ( SY87 @ ( SY88 @ Xx ) ) )
& ! [SY84: b] :
( ( sK5_SY62 @ SY84 )
=> ( SY87 @ ( sK2_SY17 @ SY84 ) ) )
& ! [SY96: b] :
( ( sK5_SY62 @ SY96 )
=> ( ( sK2_SY17 @ ( sK6_SY75 @ SY96 ) )
= ( SY88 @ ( sK2_SY17 @ SY96 ) ) ) ) )
=> ! [SY74: g] :
( ( sK3_SY33 @ SY74 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY74 ) ) )
= ( SY88 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY74 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY98: a > a] :
( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) )
& ! [SY90: b] :
( ( sK5_SY62 @ SY90 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) )
& ! [SY80: g] :
( ( sK3_SY33 @ SY80 )
=> ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) )
& ! [SY92: g] :
( ( sK3_SY33 @ SY92 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) )
& ! [SY93: b] :
( ( sK5_SY62 @ SY93 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) )
& ! [SY104: a] :
( ( sK7_SY87 @ SY104 )
=> ( sK7_SY87 @ ( SY98 @ SY104 ) ) )
& ! [SY105: b] :
( ( sK5_SY62 @ SY105 )
=> ( sK7_SY87 @ ( sK2_SY17 @ SY105 ) ) )
& ! [SY96: b] :
( ( sK5_SY62 @ SY96 )
=> ( ( sK2_SY17 @ ( sK6_SY75 @ SY96 ) )
= ( SY98 @ ( sK2_SY17 @ SY96 ) ) ) ) )
=> ! [SY74: g] :
( ( sK3_SY33 @ SY74 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY74 ) ) )
= ( SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY74 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) )
& ! [SY90: b] :
( ( sK5_SY62 @ SY90 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) )
& ! [SY80: g] :
( ( sK3_SY33 @ SY80 )
=> ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) )
& ! [SY92: g] :
( ( sK3_SY33 @ SY92 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) )
& ! [SY93: b] :
( ( sK5_SY62 @ SY93 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) )
& ! [SY113: a] :
( ( sK7_SY87 @ SY113 )
=> ( sK7_SY87 @ ( sK8_SY98 @ SY113 ) ) )
& ! [SY105: b] :
( ( sK5_SY62 @ SY105 )
=> ( sK7_SY87 @ ( sK2_SY17 @ SY105 ) ) )
& ! [SY115: b] :
( ( sK5_SY62 @ SY115 )
=> ( ( sK2_SY17 @ ( sK6_SY75 @ SY115 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SY115 ) ) ) ) )
=> ! [SY116: g] :
( ( sK3_SY33 @ SY116 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY116 ) ) )
= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY116 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY66: g] :
( ( sK3_SY33 @ SY66 )
=> ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY90: b] :
( ( sK5_SY62 @ SY90 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SY80: g] :
( ( sK3_SY33 @ SY80 )
=> ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SY92: g] :
( ( sK3_SY33 @ SY92 )
=> ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SY93: b] :
( ( sK5_SY62 @ SY93 )
=> ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SY113: a] :
( ( sK7_SY87 @ SY113 )
=> ( sK7_SY87 @ ( sK8_SY98 @ SY113 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [SY105: b] :
( ( sK5_SY62 @ SY105 )
=> ( sK7_SY87 @ ( sK2_SY17 @ SY105 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SY115: b] :
( ( sK5_SY62 @ SY115 )
=> ( ( sK2_SY17 @ ( sK6_SY75 @ SY115 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SY115 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [SY116: g] :
( ( sK3_SY33 @ SY116 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY116 ) ) )
= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY116 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(21,plain,
( ( ~ ! [SY116: g] :
( ( sK3_SY33 @ SY116 )
=> ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ SY116 ) ) )
= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ SY116 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ( sK3_SY33 @ sK9_SY116 )
& ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(23,plain,
( ( ! [SY66: g] :
( ~ ( sK3_SY33 @ SY66 )
| ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(24,plain,
( ( ! [SY90: b] :
( ~ ( sK5_SY62 @ SY90 )
| ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(25,plain,
( ( ! [SY80: g] :
( ~ ( sK3_SY33 @ SY80 )
| ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(26,plain,
( ( ! [SY92: g] :
( ~ ( sK3_SY33 @ SY92 )
| ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(27,plain,
( ( ! [SY93: b] :
( ~ ( sK5_SY62 @ SY93 )
| ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(28,plain,
( ( ! [SY113: a] :
( ~ ( sK7_SY87 @ SY113 )
| ( sK7_SY87 @ ( sK8_SY98 @ SY113 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(29,plain,
( ( ! [SY105: b] :
( ~ ( sK5_SY62 @ SY105 )
| ( sK7_SY87 @ ( sK2_SY17 @ SY105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(30,plain,
( ( ! [SY115: b] :
( ~ ( sK5_SY62 @ SY115 )
| ( ( sK2_SY17 @ ( sK6_SY75 @ SY115 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(31,plain,
( ( ! [SY115: b] :
( ~ ( sK5_SY62 @ SY115 )
| ( ( sK2_SY17 @ ( sK6_SY75 @ SY115 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SY115 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [SY105: b] :
( ~ ( sK5_SY62 @ SY105 )
| ( sK7_SY87 @ ( sK2_SY17 @ SY105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(33,plain,
( ( ! [SY113: a] :
( ~ ( sK7_SY87 @ SY113 )
| ( sK7_SY87 @ ( sK8_SY98 @ SY113 ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [SY93: b] :
( ~ ( sK5_SY62 @ SY93 )
| ( sK5_SY62 @ ( sK6_SY75 @ SY93 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(35,plain,
( ( ! [SY92: g] :
( ~ ( sK3_SY33 @ SY92 )
| ( ( sK1_Xh1 @ ( sK4_SY48 @ SY92 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SY92 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(36,plain,
( ( ! [SY80: g] :
( ~ ( sK3_SY33 @ SY80 )
| ( sK5_SY62 @ ( sK1_Xh1 @ SY80 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [SY90: b] :
( ~ ( sK5_SY62 @ SY90 )
| ( sK5_SY62 @ ( sK6_SY75 @ SY90 ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(38,plain,
( ( ! [SY66: g] :
( ~ ( sK3_SY33 @ SY66 )
| ( sK3_SY33 @ ( sK4_SY48 @ SY66 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ( sK3_SY33 @ sK9_SY116 )
& ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(40,plain,
( ( ~ ( ~ ( sK3_SY33 @ sK9_SY116 )
| ~ ( ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
! [SV1: b] :
( ( ~ ( sK5_SY62 @ SV1 )
| ( ( sK2_SY17 @ ( sK6_SY75 @ SV1 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV2: b] :
( ( ~ ( sK5_SY62 @ SV2 )
| ( sK7_SY87 @ ( sK2_SY17 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV3: a] :
( ( ~ ( sK7_SY87 @ SV3 )
| ( sK7_SY87 @ ( sK8_SY98 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV4: b] :
( ( ~ ( sK5_SY62 @ SV4 )
| ( sK5_SY62 @ ( sK6_SY75 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV5: g] :
( ( ~ ( sK3_SY33 @ SV5 )
| ( ( sK1_Xh1 @ ( sK4_SY48 @ SV5 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV6: g] :
( ( ~ ( sK3_SY33 @ SV6 )
| ( sK5_SY62 @ ( sK1_Xh1 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV7: b] :
( ( ~ ( sK5_SY62 @ SV7 )
| ( sK5_SY62 @ ( sK6_SY75 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV8: g] :
( ( ~ ( sK3_SY33 @ SV8 )
| ( sK3_SY33 @ ( sK4_SY48 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
( ( ~ ( sK3_SY33 @ sK9_SY116 )
| ~ ( ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: b] :
( ( ( ~ ( sK5_SY62 @ SV1 ) )
= $true )
| ( ( ( sK2_SY17 @ ( sK6_SY75 @ SV1 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV2: b] :
( ( ( ~ ( sK5_SY62 @ SV2 ) )
= $true )
| ( ( sK7_SY87 @ ( sK2_SY17 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV3: a] :
( ( ( ~ ( sK7_SY87 @ SV3 ) )
= $true )
| ( ( sK7_SY87 @ ( sK8_SY98 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV4: b] :
( ( ( ~ ( sK5_SY62 @ SV4 ) )
= $true )
| ( ( sK5_SY62 @ ( sK6_SY75 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV5: g] :
( ( ( ~ ( sK3_SY33 @ SV5 ) )
= $true )
| ( ( ( sK1_Xh1 @ ( sK4_SY48 @ SV5 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV6: g] :
( ( ( ~ ( sK3_SY33 @ SV6 ) )
= $true )
| ( ( sK5_SY62 @ ( sK1_Xh1 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV7: b] :
( ( ( ~ ( sK5_SY62 @ SV7 ) )
= $true )
| ( ( sK5_SY62 @ ( sK6_SY75 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV8: g] :
( ( ( ~ ( sK3_SY33 @ SV8 ) )
= $true )
| ( ( sK3_SY33 @ ( sK4_SY48 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ( sK3_SY33 @ sK9_SY116 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(59,plain,
( ( ~ ( ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(60,plain,
! [SV1: b] :
( ( ( sK5_SY62 @ SV1 )
= $false )
| ( ( ( sK2_SY17 @ ( sK6_SY75 @ SV1 ) )
= ( sK8_SY98 @ ( sK2_SY17 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV2: b] :
( ( ( sK5_SY62 @ SV2 )
= $false )
| ( ( sK7_SY87 @ ( sK2_SY17 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV3: a] :
( ( ( sK7_SY87 @ SV3 )
= $false )
| ( ( sK7_SY87 @ ( sK8_SY98 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV4: b] :
( ( ( sK5_SY62 @ SV4 )
= $false )
| ( ( sK5_SY62 @ ( sK6_SY75 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV5: g] :
( ( ( sK3_SY33 @ SV5 )
= $false )
| ( ( ( sK1_Xh1 @ ( sK4_SY48 @ SV5 ) )
= ( sK6_SY75 @ ( sK1_Xh1 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV6: g] :
( ( ( sK3_SY33 @ SV6 )
= $false )
| ( ( sK5_SY62 @ ( sK1_Xh1 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV7: b] :
( ( ( sK5_SY62 @ SV7 )
= $false )
| ( ( sK5_SY62 @ ( sK6_SY75 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV8: g] :
( ( ( sK3_SY33 @ SV8 )
= $false )
| ( ( sK3_SY33 @ ( sK4_SY48 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(68,plain,
( ( sK3_SY33 @ sK9_SY116 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(69,plain,
( ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
!= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(70,plain,
( ( ( sK2_SY17 @ ( sK1_Xh1 @ ( sK4_SY48 @ sK9_SY116 ) ) )
= ( sK8_SY98 @ ( sK2_SY17 @ ( sK1_Xh1 @ sK9_SY116 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(71,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,70,68,67,66,65,64,63,62,61]) ).
thf(72,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU901^5 : 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
% 0.11/0.18 % Computer : n002.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 15:40:27 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.24
% 0.11/0.24 No.of.Axioms: 0
% 0.11/0.24
% 0.11/0.24 Length.of.Defs: 0
% 0.11/0.24
% 0.11/0.24 Contains.Choice.Funs: false
% 0.11/0.24 ...
% 0.11/0.24
% 0.11/0.24 ********************************
% 0.11/0.24 * All subproblems solved! *
% 0.11/0.24 ********************************
% 0.11/0.24 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:71,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.24
% 0.11/0.24 %**** Beginning of derivation protocol ****
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24
% 0.11/0.24 %**** End of derivation protocol ****
% 0.11/0.24 %**** no. of clauses in derivation: 72 ****
% 0.11/0.24 %**** clause counter: 71 ****
% 0.11/0.24
% 0.11/0.24 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:71,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------