%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO334^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:08:04 AM UTC 2026
% Result : Theorem 0.31s 0.29s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 60 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 159 ( 82 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 702 ( 36 ~; 34 |; 18 &; 567 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 213 ( 0 ^; 205 !; 8 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_c_stara,type,
c_stara: a > a > a ).
thf(tp_c_starb,type,
c_starb: b > b > b ).
thf(tp_c_starc,type,
c_starc: c > c > c ).
thf(tp_sK1_Xf,type,
sK1_Xf: a > b ).
thf(tp_sK2_SY17,type,
sK2_SY17: a > c ).
thf(tp_sK3_SY33,type,
sK3_SY33: b > c ).
thf(tp_sK4_SX0,type,
sK4_SX0: b ).
thf(tp_sK5_SY64,type,
sK5_SY64: b > a ).
thf(tp_sK6_SY71,type,
sK6_SY71: b ).
thf(tp_sK7_SY74,type,
sK7_SY74: c > $o ).
thf(1,conjecture,
! [Xf: a > b,Xg: a > c,Xh: b > c] :
( ( ! [Xx: a,Xq: c > $o] :
( ( Xq @ ( Xh @ ( Xf @ Xx ) ) )
=> ( Xq @ ( Xg @ Xx ) ) )
& ! [Xy: b] :
? [Xx: a] :
! [Xq: b > $o] :
( ( Xq @ ( Xf @ Xx ) )
=> ( Xq @ Xy ) )
& ! [Xx: a,Xy: a,Xq: b > $o] :
( ( Xq @ ( Xf @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) ) )
& ! [Xx: a,Xy: a,Xq: c > $o] :
( ( Xq @ ( Xg @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) ) )
=> ! [Xx: b,Xy: b,Xq: c > $o] :
( ( Xq @ ( Xh @ ( c_starb @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM270_INST) ).
thf(2,negated_conjecture,
( ( ! [Xf: a > b,Xg: a > c,Xh: b > c] :
( ( ! [Xx: a,Xq: c > $o] :
( ( Xq @ ( Xh @ ( Xf @ Xx ) ) )
=> ( Xq @ ( Xg @ Xx ) ) )
& ! [Xy: b] :
? [Xx: a] :
! [Xq: b > $o] :
( ( Xq @ ( Xf @ Xx ) )
=> ( Xq @ Xy ) )
& ! [Xx: a,Xy: a,Xq: b > $o] :
( ( Xq @ ( Xf @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) ) )
& ! [Xx: a,Xy: a,Xq: c > $o] :
( ( Xq @ ( Xg @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) ) )
=> ! [Xx: b,Xy: b,Xq: c > $o] :
( ( Xq @ ( Xh @ ( c_starb @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xf: a > b,Xg: a > c,Xh: b > c] :
( ( ! [Xx: a,Xq: c > $o] :
( ( Xq @ ( Xh @ ( Xf @ Xx ) ) )
=> ( Xq @ ( Xg @ Xx ) ) )
& ! [Xy: b] :
? [Xx: a] :
! [Xq: b > $o] :
( ( Xq @ ( Xf @ Xx ) )
=> ( Xq @ Xy ) )
& ! [Xx: a,Xy: a,Xq: b > $o] :
( ( Xq @ ( Xf @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) ) )
& ! [Xx: a,Xy: a,Xq: c > $o] :
( ( Xq @ ( Xg @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) ) )
=> ! [Xx: b,Xy: b,Xq: c > $o] :
( ( Xq @ ( Xh @ ( c_starb @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY17: a > c,SY18: b > c] :
( ( ! [SY19: a,SY20: c > $o] :
( ( SY20 @ ( SY18 @ ( sK1_Xf @ SY19 ) ) )
=> ( SY20 @ ( SY17 @ SY19 ) ) )
& ! [SY21: b] :
? [SY22: a] :
! [SY23: b > $o] :
( ( SY23 @ ( sK1_Xf @ SY22 ) )
=> ( SY23 @ SY21 ) )
& ! [SY24: a,SY25: a,SY26: b > $o] :
( ( SY26 @ ( sK1_Xf @ ( c_stara @ SY24 @ SY25 ) ) )
=> ( SY26 @ ( c_starb @ ( sK1_Xf @ SY24 ) @ ( sK1_Xf @ SY25 ) ) ) )
& ! [Xx: a,Xy: a,Xq: c > $o] :
( ( Xq @ ( SY17 @ ( c_stara @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( SY17 @ Xx ) @ ( SY17 @ Xy ) ) ) ) )
=> ! [Xx: b,Xy: b,Xq: c > $o] :
( ( Xq @ ( SY18 @ ( c_starb @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( SY18 @ Xx ) @ ( SY18 @ Xy ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY33: b > c] :
( ( ! [SY34: a,SY35: c > $o] :
( ( SY35 @ ( SY33 @ ( sK1_Xf @ SY34 ) ) )
=> ( SY35 @ ( sK2_SY17 @ SY34 ) ) )
& ! [SY21: b] :
? [SY22: a] :
! [SY23: b > $o] :
( ( SY23 @ ( sK1_Xf @ SY22 ) )
=> ( SY23 @ SY21 ) )
& ! [SY24: a,SY25: a,SY26: b > $o] :
( ( SY26 @ ( sK1_Xf @ ( c_stara @ SY24 @ SY25 ) ) )
=> ( SY26 @ ( c_starb @ ( sK1_Xf @ SY24 ) @ ( sK1_Xf @ SY25 ) ) ) )
& ! [SY42: a,SY43: a,SY44: c > $o] :
( ( SY44 @ ( sK2_SY17 @ ( c_stara @ SY42 @ SY43 ) ) )
=> ( SY44 @ ( c_starc @ ( sK2_SY17 @ SY42 ) @ ( sK2_SY17 @ SY43 ) ) ) ) )
=> ! [Xx: b,Xy: b,Xq: c > $o] :
( ( Xq @ ( SY33 @ ( c_starb @ Xx @ Xy ) ) )
=> ( Xq @ ( c_starc @ ( SY33 @ Xx ) @ ( SY33 @ Xy ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY48: a,SY49: c > $o] :
( ( SY49 @ ( sK3_SY33 @ ( sK1_Xf @ SY48 ) ) )
=> ( SY49 @ ( sK2_SY17 @ SY48 ) ) )
& ! [SY21: b] :
? [SY22: a] :
! [SY23: b > $o] :
( ( SY23 @ ( sK1_Xf @ SY22 ) )
=> ( SY23 @ SY21 ) )
& ! [SY24: a,SY25: a,SY26: b > $o] :
( ( SY26 @ ( sK1_Xf @ ( c_stara @ SY24 @ SY25 ) ) )
=> ( SY26 @ ( c_starb @ ( sK1_Xf @ SY24 ) @ ( sK1_Xf @ SY25 ) ) ) )
& ! [SY42: a,SY43: a,SY44: c > $o] :
( ( SY44 @ ( sK2_SY17 @ ( c_stara @ SY42 @ SY43 ) ) )
=> ( SY44 @ ( c_starc @ ( sK2_SY17 @ SY42 ) @ ( sK2_SY17 @ SY43 ) ) ) ) )
=> ! [SY59: b,SY60: b,SY61: c > $o] :
( ( SY61 @ ( sK3_SY33 @ ( c_starb @ SY59 @ SY60 ) ) )
=> ( SY61 @ ( c_starc @ ( sK3_SY33 @ SY59 ) @ ( sK3_SY33 @ SY60 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY48: a,SY49: c > $o] :
( ( SY49 @ ( sK3_SY33 @ ( sK1_Xf @ SY48 ) ) )
=> ( SY49 @ ( sK2_SY17 @ SY48 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY21: b] :
? [SY22: a] :
! [SY23: b > $o] :
( ( SY23 @ ( sK1_Xf @ SY22 ) )
=> ( SY23 @ SY21 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY24: a,SY25: a,SY26: b > $o] :
( ( SY26 @ ( sK1_Xf @ ( c_stara @ SY24 @ SY25 ) ) )
=> ( SY26 @ ( c_starb @ ( sK1_Xf @ SY24 ) @ ( sK1_Xf @ SY25 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SY42: a,SY43: a,SY44: c > $o] :
( ( SY44 @ ( sK2_SY17 @ ( c_stara @ SY42 @ SY43 ) ) )
=> ( SY44 @ ( c_starc @ ( sK2_SY17 @ SY42 ) @ ( sK2_SY17 @ SY43 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [SY59: b,SY60: b,SY61: c > $o] :
( ( SY61 @ ( sK3_SY33 @ ( c_starb @ SY59 @ SY60 ) ) )
=> ( SY61 @ ( c_starc @ ( sK3_SY33 @ SY59 ) @ ( sK3_SY33 @ SY60 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ ! [SY59: b,SY60: b,SY61: c > $o] :
( ( SY61 @ ( sK3_SY33 @ ( c_starb @ SY59 @ SY60 ) ) )
=> ( SY61 @ ( c_starc @ ( sK3_SY33 @ SY59 ) @ ( sK3_SY33 @ SY60 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY42: a,SY43: a,SY44: c > $o] :
( ( SY44 @ ( sK2_SY17 @ ( c_stara @ SY42 @ SY43 ) ) )
=> ( SY44 @ ( c_starc @ ( sK2_SY17 @ SY42 ) @ ( sK2_SY17 @ SY43 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SY24: a,SY25: a,SY26: b > $o] :
( ( SY26 @ ( sK1_Xf @ ( c_stara @ SY24 @ SY25 ) ) )
=> ( SY26 @ ( c_starb @ ( sK1_Xf @ SY24 ) @ ( sK1_Xf @ SY25 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [SY21: b] :
? [SY22: a] :
! [SY23: b > $o] :
( ( SY23 @ ( sK1_Xf @ SY22 ) )
=> ( SY23 @ SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [SY48: a,SY49: c > $o] :
( ( SY49 @ ( sK3_SY33 @ ( sK1_Xf @ SY48 ) ) )
=> ( SY49 @ ( sK2_SY17 @ SY48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(17,plain,
( ( ~ ! [SY59: b,SY60: b,SY61: c > $o] :
( ( SY61 @ ( sK3_SY33 @ ( c_starb @ SY59 @ SY60 ) ) )
=> ( SY61 @ ( c_starc @ ( sK3_SY33 @ SY59 ) @ ( sK3_SY33 @ SY60 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: a,SX1: a,SX2: c > $o] :
( ~ ( SX2 @ ( sK2_SY17 @ ( c_stara @ SX0 @ SX1 ) ) )
| ( SX2 @ ( c_starc @ ( sK2_SY17 @ SX0 ) @ ( sK2_SY17 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SX0: b] :
~ ! [SX1: a] :
~ ! [SX2: b > $o] :
( ~ ( SX2 @ ( sK1_Xf @ SX1 ) )
| ( SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: a,SX1: a,SX2: b > $o] :
( ~ ( SX2 @ ( sK1_Xf @ ( c_stara @ SX0 @ SX1 ) ) )
| ( SX2 @ ( c_starb @ ( sK1_Xf @ SX0 ) @ ( sK1_Xf @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(21,plain,
( ( ! [SX0: a,SX1: c > $o] :
( ~ ( SX1 @ ( sK3_SY33 @ ( sK1_Xf @ SX0 ) ) )
| ( SX1 @ ( sK2_SY17 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(22,plain,
( ( ~ ! [SX0: b,SX1: b,SX2: c > $o] :
( ~ ( SX2 @ ( sK3_SY33 @ ( c_starb @ SX0 @ SX1 ) ) )
| ( SX2 @ ( c_starc @ ( sK3_SY33 @ SX0 ) @ ( sK3_SY33 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
! [SV1: a] :
( ( ! [SY62: a,SY63: c > $o] :
( ~ ( SY63 @ ( sK2_SY17 @ ( c_stara @ SV1 @ SY62 ) ) )
| ( SY63 @ ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV2: b] :
( ( ~ ! [SY64: a] :
~ ! [SY65: b > $o] :
( ~ ( SY65 @ ( sK1_Xf @ SY64 ) )
| ( SY65 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV3: a] :
( ( ! [SY66: a,SY67: b > $o] :
( ~ ( SY67 @ ( sK1_Xf @ ( c_stara @ SV3 @ SY66 ) ) )
| ( SY67 @ ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV4: a] :
( ( ! [SY68: c > $o] :
( ~ ( SY68 @ ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
| ( SY68 @ ( sK2_SY17 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [SX0: b,SX1: b,SX2: c > $o] :
( ~ ( SX2 @ ( sK3_SY33 @ ( c_starb @ SX0 @ SX1 ) ) )
| ( SX2 @ ( c_starc @ ( sK3_SY33 @ SX0 ) @ ( sK3_SY33 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV5: a,SV1: a] :
( ( ! [SY69: c > $o] :
( ~ ( SY69 @ ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
| ( SY69 @ ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: b] :
( ( ! [SY64: a] :
~ ! [SY65: b > $o] :
( ~ ( SY65 @ ( sK1_Xf @ SY64 ) )
| ( SY65 @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV6: a,SV3: a] :
( ( ! [SY70: b > $o] :
( ~ ( SY70 @ ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
| ( SY70 @ ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV4: a,SV7: c > $o] :
( ( ~ ( SV7 @ ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
| ( SV7 @ ( sK2_SY17 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [SY71: b,SY72: c > $o] :
( ~ ( SY72 @ ( sK3_SY33 @ ( c_starb @ sK4_SX0 @ SY71 ) ) )
| ( SY72 @ ( c_starc @ ( sK3_SY33 @ sK4_SX0 ) @ ( sK3_SY33 @ SY71 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(33,plain,
! [SV5: a,SV1: a,SV8: c > $o] :
( ( ~ ( SV8 @ ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
| ( SV8 @ ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: b] :
( ( ~ ! [SY73: b > $o] :
( ~ ( SY73 @ ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
| ( SY73 @ SV2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(35,plain,
! [SV6: a,SV3: a,SV9: b > $o] :
( ( ~ ( SV9 @ ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
| ( SV9 @ ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV4: a,SV7: c > $o] :
( ( ( ~ ( SV7 @ ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) ) )
= $true )
| ( ( SV7 @ ( sK2_SY17 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
( ( ! [SY74: c > $o] :
( ~ ( SY74 @ ( sK3_SY33 @ ( c_starb @ sK4_SX0 @ sK6_SY71 ) ) )
| ( SY74 @ ( c_starc @ ( sK3_SY33 @ sK4_SX0 ) @ ( sK3_SY33 @ sK6_SY71 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(38,plain,
! [SV5: a,SV1: a,SV8: c > $o] :
( ( ( ~ ( SV8 @ ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) ) )
= $true )
| ( ( SV8 @ ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV2: b] :
( ( ! [SY73: b > $o] :
( ~ ( SY73 @ ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
| ( SY73 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV6: a,SV3: a,SV9: b > $o] :
( ( ( ~ ( SV9 @ ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) ) )
= $true )
| ( ( SV9 @ ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV4: a,SV7: c > $o] :
( ( ( SV7 @ ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
= $false )
| ( ( SV7 @ ( sK2_SY17 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( sK7_SY74 @ ( sK3_SY33 @ ( c_starb @ sK4_SX0 @ sK6_SY71 ) ) )
| ( sK7_SY74 @ ( c_starc @ ( sK3_SY33 @ sK4_SX0 ) @ ( sK3_SY33 @ sK6_SY71 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(43,plain,
! [SV5: a,SV1: a,SV8: c > $o] :
( ( ( SV8 @ ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
= $false )
| ( ( SV8 @ ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV2: b,SV10: b > $o] :
( ( ~ ( SV10 @ ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
| ( SV10 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV6: a,SV3: a,SV9: b > $o] :
( ( ( SV9 @ ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
= $false )
| ( ( SV9 @ ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
( ( ~ ( sK7_SY74 @ ( sK3_SY33 @ ( c_starb @ sK4_SX0 @ sK6_SY71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
( ( sK7_SY74 @ ( c_starc @ ( sK3_SY33 @ sK4_SX0 ) @ ( sK3_SY33 @ sK6_SY71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: b,SV10: b > $o] :
( ( ( ~ ( SV10 @ ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) ) )
= $true )
| ( ( SV10 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( sK7_SY74 @ ( sK3_SY33 @ ( c_starb @ sK4_SX0 @ sK6_SY71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV2: b,SV10: b > $o] :
( ( ( SV10 @ ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
= $false )
| ( ( SV10 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV4: a] :
( ( ( ( sK3_SY33 @ ( sK1_Xf @ SV4 ) )
= ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
= $false )
| ( ( ( sK2_SY17 @ SV4 )
= ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[41:[bind(SV7,$thf( ^ [SV11: c] : ( SV11 = ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) ) ))]]) ).
thf(52,plain,
! [SV4: a] :
( ( ( sK2_SY17 @ SV4 )
= ( sK3_SY33 @ ( sK1_Xf @ SV4 ) ) )
= $true ),
inference(sim,[status(thm)],[51]) ).
thf(53,plain,
! [SV5: a,SV1: a] :
( ( ( ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) )
= ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
= $false )
| ( ( ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) )
= ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[43:[bind(SV8,$thf( ^ [SV12: c] : ( SV12 = ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) ) ))]]) ).
thf(54,plain,
! [SV5: a,SV1: a] :
( ( ( c_starc @ ( sK2_SY17 @ SV1 ) @ ( sK2_SY17 @ SV5 ) )
= ( sK2_SY17 @ ( c_stara @ SV1 @ SV5 ) ) )
= $true ),
inference(sim,[status(thm)],[53]) ).
thf(55,plain,
! [SV6: a,SV3: a] :
( ( ( ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) )
= ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
= $false )
| ( ( ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) )
= ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[45:[bind(SV9,$thf( ^ [SV13: b] : ( SV13 = ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) ) ))]]) ).
thf(56,plain,
! [SV6: a,SV3: a] :
( ( ( c_starb @ ( sK1_Xf @ SV3 ) @ ( sK1_Xf @ SV6 ) )
= ( sK1_Xf @ ( c_stara @ SV3 @ SV6 ) ) )
= $true ),
inference(sim,[status(thm)],[55]) ).
thf(57,plain,
! [SV2: b] :
( ( ( ( sK1_Xf @ ( sK5_SY64 @ SV2 ) )
= ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
= $false )
| ( ( SV2
= ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[50:[bind(SV10,$thf( ^ [SV14: b] : ( SV14 = ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) ) ))]]) ).
thf(58,plain,
! [SV2: b] :
( ( SV2
= ( sK1_Xf @ ( sK5_SY64 @ SV2 ) ) )
= $true ),
inference(sim,[status(thm)],[57]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,58,56,54,52,49]) ).
thf(60,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO334^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.20 % Computer : n003.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Oct 6 17:36:39 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.29
% 0.31/0.29 No.of.Axioms: 0
% 0.31/0.29
% 0.31/0.29 Length.of.Defs: 0
% 0.31/0.29
% 0.31/0.29 Contains.Choice.Funs: false
% 0.31/0.29 ..
% 0.31/0.29
% 0.31/0.29 ********************************
% 0.31/0.29 * All subproblems solved! *
% 0.31/0.29 ********************************
% 0.31/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:59,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.31/0.29
% 0.31/0.29 %**** Beginning of derivation protocol ****
% 0.31/0.29 % SZS output start CNFRefutation
% See solution above
% 0.31/0.29
% 0.31/0.29 %**** End of derivation protocol ****
% 0.31/0.29 %**** no. of clauses in derivation: 60 ****
% 0.31/0.29 %**** clause counter: 59 ****
% 0.31/0.29
% 0.31/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:59,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------