%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN386+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n001.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 11:05:41 AM UTC 2026
% Result : Theorem 0.10s 0.21s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 64 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 355 ( 83 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 782 ( 149 ~; 84 |; 11 &; 508 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 275 ( 0 ^; 243 !; 32 ?; 275 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_big_d,type,
big_d: $i > $i > $i > $o ).
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_big_s,type,
big_s: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i > $i ).
thf(tp_sK3_SY22,type,
sK3_SY22: $i > $i ).
thf(tp_sK4_SY26,type,
sK4_SY26: $i > $i ).
thf(tp_sK5_SY34,type,
sK5_SY34: $i > $i ).
thf(tp_sK6_SY45,type,
sK6_SY45: $i > $i > $i ).
thf(tp_sK7_SY47,type,
sK7_SY47: $i > $i > $i ).
thf(1,conjecture,
( ( ! [X: $i] :
? [Y: $i] : ( big_f @ X @ Y )
& ? [X: $i] :
! [E: $i] :
? [N: $i] :
! [W: $i] :
( ( big_s @ N @ W )
=> ( big_d @ W @ X @ E ) )
& ! [E: $i] :
? [D: $i] :
! [A: $i,B: $i] :
( ( big_d @ A @ B @ D )
=> ! [Y: $i,Z: $i] :
( ( ( big_f @ A @ Y )
& ( big_f @ B @ Z ) )
=> ( big_d @ Y @ Z @ E ) ) ) )
=> ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2138) ).
thf(2,negated_conjecture,
( ( ( ! [X: $i] :
? [Y: $i] : ( big_f @ X @ Y )
& ? [X: $i] :
! [E: $i] :
? [N: $i] :
! [W: $i] :
( ( big_s @ N @ W )
=> ( big_d @ W @ X @ E ) )
& ! [E: $i] :
? [D: $i] :
! [A: $i,B: $i] :
( ( big_d @ A @ B @ D )
=> ! [Y: $i,Z: $i] :
( ( ( big_f @ A @ Y )
& ( big_f @ B @ Z ) )
=> ( big_d @ Y @ Z @ E ) ) ) )
=> ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [X: $i] :
? [Y: $i] : ( big_f @ X @ Y )
& ? [X: $i] :
! [E: $i] :
? [N: $i] :
! [W: $i] :
( ( big_s @ N @ W )
=> ( big_d @ W @ X @ E ) )
& ! [E: $i] :
? [D: $i] :
! [A: $i,B: $i] :
( ( big_d @ A @ B @ D )
=> ! [Y: $i,Z: $i] :
( ( ( big_f @ A @ Y )
& ( big_f @ B @ Z ) )
=> ( big_d @ Y @ Z @ E ) ) ) )
=> ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
? [Y: $i] : ( big_f @ X @ Y ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [X: $i] :
! [E: $i] :
? [N: $i] :
! [W: $i] :
( ( big_s @ N @ W )
=> ( big_d @ W @ X @ E ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [E: $i] :
? [D: $i] :
! [A: $i,B: $i] :
( ( big_d @ A @ B @ D )
=> ! [Y: $i,Z: $i] :
( ( ( big_f @ A @ Y )
& ( big_f @ B @ Z ) )
=> ( big_d @ Y @ Z @ E ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [E: $i] :
? [D: $i] :
! [A: $i,B: $i] :
( ( big_d @ A @ B @ D )
=> ! [Y: $i,Z: $i] :
( ( ( big_f @ A @ Y )
& ( big_f @ B @ Z ) )
=> ( big_d @ Y @ Z @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ? [X: $i] :
! [E: $i] :
? [N: $i] :
! [W: $i] :
( ( big_s @ N @ W )
=> ( big_d @ W @ X @ E ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [X: $i] :
? [Y: $i] : ( big_f @ X @ Y ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ? [Y: $i] :
! [E: $i] :
? [M: $i] :
! [W: $i] :
( ( big_s @ M @ W )
=> ! [Z: $i] :
( ( big_f @ W @ Z )
=> ( big_d @ Z @ Y @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( big_s @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( big_f @ SX3 @ SX4 )
| ( big_d @ SX4 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i,SX3: $i] :
( ~ ( big_d @ SX2 @ SX3 @ SX1 )
| ! [SX4: $i,SX5: $i] :
( ~ ~ ( ~ ( big_f @ SX2 @ SX4 )
| ~ ( big_f @ SX3 @ SX5 ) )
| ( big_d @ SX4 @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( big_f @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(16,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( big_s @ SX2 @ SX3 )
| ( big_d @ SX3 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( big_s @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( big_f @ SX3 @ SX4 )
| ( big_d @ SX4 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ! [SY17: $i] :
~ ! [SY18: $i,SY19: $i] :
( ~ ( big_d @ SY18 @ SY19 @ SY17 )
| ! [SY20: $i,SY21: $i] :
( ~ ~ ( ~ ( big_f @ SY18 @ SY20 )
| ~ ( big_f @ SY19 @ SY21 ) )
| ( big_d @ SY20 @ SY21 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ~ ! [SY22: $i] :
~ ( big_f @ SV2 @ SY22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( big_s @ SX2 @ SX3 )
| ( big_d @ SX3 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( big_s @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( big_f @ SX3 @ SX4 )
| ( big_d @ SX4 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
~ ! [SY18: $i,SY19: $i] :
( ~ ( big_d @ SY18 @ SY19 @ SY17 )
| ! [SY20: $i,SY21: $i] :
( ~ ~ ( ~ ( big_f @ SY18 @ SY20 )
| ~ ( big_f @ SY19 @ SY21 ) )
| ( big_d @ SY20 @ SY21 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY22: $i] :
~ ( big_f @ SV2 @ SY22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ! [SY23: $i] :
~ ! [SY24: $i] :
~ ! [SY25: $i] :
( ~ ( big_s @ SY24 @ SY25 )
| ( big_d @ SY25 @ sK1_SX0 @ SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(25,plain,
! [SV3: $i] :
( ( ~ ! [SY26: $i] :
~ ! [SY27: $i] :
~ ! [SY28: $i] :
( ~ ( big_s @ SY27 @ SY28 )
| ! [SY29: $i] :
( ~ ( big_f @ SY28 @ SY29 )
| ( big_d @ SY29 @ SV3 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( big_d @ SY30 @ SY31 @ ( sK2_SY17 @ SV1 ) )
| ! [SY20: $i,SY21: $i] :
( ~ ~ ( ~ ( big_f @ SY30 @ SY20 )
| ~ ( big_f @ SY31 @ SY21 ) )
| ( big_d @ SY20 @ SY21 @ SV1 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ~ ( big_f @ SV2 @ ( sK3_SY22 @ SV2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(28,plain,
( ( ! [SY23: $i] :
~ ! [SY24: $i] :
~ ! [SY25: $i] :
( ~ ( big_s @ SY24 @ SY25 )
| ( big_d @ SY25 @ sK1_SX0 @ SY23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
~ ! [SY27: $i] :
~ ! [SY28: $i] :
( ~ ( big_s @ SY27 @ SY28 )
| ! [SY29: $i] :
( ~ ( big_f @ SY28 @ SY29 )
| ( big_d @ SY29 @ SV3 @ SY26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( big_d @ SY30 @ SY31 @ ( sK2_SY17 @ SV1 ) )
| ! [SY20: $i,SY21: $i] :
( ~ ~ ( ~ ( big_f @ SY30 @ SY20 )
| ~ ( big_f @ SY31 @ SY21 ) )
| ( big_d @ SY20 @ SY21 @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $i] :
( ( big_f @ SV2 @ ( sK3_SY22 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i] :
( ( ~ ! [SY34: $i] :
~ ! [SY35: $i] :
( ~ ( big_s @ SY34 @ SY35 )
| ( big_d @ SY35 @ sK1_SX0 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i] :
( ( ~ ! [SY36: $i] :
~ ! [SY37: $i] :
( ~ ( big_s @ SY36 @ SY37 )
| ! [SY38: $i] :
( ~ ( big_f @ SY37 @ SY38 )
| ( big_d @ SY38 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(34,plain,
! [SV1: $i,SV5: $i] :
( ( ! [SY39: $i] :
( ~ ( big_d @ SV5 @ SY39 @ ( sK2_SY17 @ SV1 ) )
| ! [SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( big_f @ SV5 @ SY40 )
| ~ ( big_f @ SY39 @ SY41 ) )
| ( big_d @ SY40 @ SY41 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY34: $i] :
~ ! [SY35: $i] :
( ~ ( big_s @ SY34 @ SY35 )
| ( big_d @ SY35 @ sK1_SX0 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i] :
( ( ! [SY36: $i] :
~ ! [SY37: $i] :
( ~ ( big_s @ SY36 @ SY37 )
| ! [SY38: $i] :
( ~ ( big_f @ SY37 @ SY38 )
| ( big_d @ SY38 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i,SV6: $i,SV5: $i] :
( ( ~ ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
| ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ( big_f @ SV5 @ SY42 )
| ~ ( big_f @ SV6 @ SY43 ) )
| ( big_d @ SY42 @ SY43 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i] :
( ( ~ ! [SY44: $i] :
( ~ ( big_s @ ( sK5_SY34 @ SV4 ) @ SY44 )
| ( big_d @ SY44 @ sK1_SX0 @ SV4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(39,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ! [SY45: $i] :
( ~ ( big_s @ SV7 @ SY45 )
| ! [SY38: $i] :
( ~ ( big_f @ SY45 @ SY38 )
| ( big_d @ SY38 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: $i,SV6: $i,SV5: $i] :
( ( ( ~ ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) ) )
= $true )
| ( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ( big_f @ SV5 @ SY42 )
| ~ ( big_f @ SV6 @ SY43 ) )
| ( big_d @ SY42 @ SY43 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY44: $i] :
( ~ ( big_s @ ( sK5_SY34 @ SV4 ) @ SY44 )
| ( big_d @ SY44 @ sK1_SX0 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i,SV7: $i] :
( ( ! [SY45: $i] :
( ~ ( big_s @ SV7 @ SY45 )
| ! [SY38: $i] :
( ~ ( big_f @ SY45 @ SY38 )
| ( big_d @ SY38 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV1: $i,SV6: $i,SV5: $i] :
( ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false )
| ( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ( big_f @ SV5 @ SY42 )
| ~ ( big_f @ SV6 @ SY43 ) )
| ( big_d @ SY42 @ SY43 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( big_s @ ( sK5_SY34 @ SV4 ) @ SV8 )
| ( big_d @ SV8 @ sK1_SX0 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( big_s @ SV7 @ ( sK6_SY45 @ SV3 @ SV7 ) )
| ! [SY47: $i] :
( ~ ( big_f @ ( sK6_SY45 @ SV3 @ SV7 ) @ SY47 )
| ( big_d @ SY47 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(46,plain,
! [SV1: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ! [SY48: $i] :
( ~ ~ ( ~ ( big_f @ SV5 @ SV9 )
| ~ ( big_f @ SV6 @ SY48 ) )
| ( big_d @ SV9 @ SY48 @ SV1 ) ) )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( big_s @ ( sK5_SY34 @ SV4 ) @ SV8 ) )
= $true )
| ( ( big_d @ SV8 @ sK1_SX0 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV7: $i] :
( ( ~ ( big_s @ SV7 @ ( sK6_SY45 @ SV3 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY47: $i] :
( ~ ( big_f @ ( sK6_SY45 @ SV3 @ SV7 ) @ SY47 )
| ( big_d @ SY47 @ SV3 @ ( sK4_SY26 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( big_f @ SV5 @ SV9 )
| ~ ( big_f @ SV6 @ SV10 ) )
| ( big_d @ SV9 @ SV10 @ SV1 ) )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV8: $i,SV4: $i] :
( ( ( big_s @ ( sK5_SY34 @ SV4 ) @ SV8 )
= $false )
| ( ( big_d @ SV8 @ sK1_SX0 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV3: $i,SV7: $i] :
( ( big_s @ SV7 @ ( sK6_SY45 @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( big_f @ ( sK6_SY45 @ SV3 @ SV7 ) @ ( sK7_SY47 @ SV7 @ SV3 ) )
| ( big_d @ ( sK7_SY47 @ SV7 @ SV3 ) @ SV3 @ ( sK4_SY26 @ SV3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(54,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( big_f @ SV5 @ SV9 )
| ~ ( big_f @ SV6 @ SV10 ) ) )
= $true )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( big_f @ ( sK6_SY45 @ SV3 @ SV7 ) @ ( sK7_SY47 @ SV7 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV3: $i,SV7: $i] :
( ( big_d @ ( sK7_SY47 @ SV7 @ SV3 ) @ SV3 @ ( sK4_SY26 @ SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ( big_f @ SV5 @ SV9 )
| ~ ( big_f @ SV6 @ SV10 ) ) )
= $false )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV7: $i,SV3: $i] :
( ( big_f @ ( sK6_SY45 @ SV3 @ SV7 ) @ ( sK7_SY47 @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( big_f @ SV5 @ SV9 )
| ~ ( big_f @ SV6 @ SV10 ) )
= $true )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( big_f @ SV5 @ SV9 ) )
= $true )
| ( ( ~ ( big_f @ SV6 @ SV10 ) )
= $true )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(61,plain,
! [SV1: $i,SV10: $i,SV6: $i,SV9: $i,SV5: $i] :
( ( ( big_f @ SV5 @ SV9 )
= $false )
| ( ( ~ ( big_f @ SV6 @ SV10 ) )
= $true )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV1: $i,SV9: $i,SV5: $i,SV10: $i,SV6: $i] :
( ( ( big_f @ SV6 @ SV10 )
= $false )
| ( ( big_f @ SV5 @ SV9 )
= $false )
| ( ( big_d @ SV9 @ SV10 @ SV1 )
= $true )
| ( ( big_d @ SV5 @ SV6 @ ( sK2_SY17 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,62,58,56,52,51]) ).
thf(64,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN386+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.10/0.17 % Computer : n001.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 17:25:54 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.21
% 0.10/0.21 No.of.Axioms: 0
% 0.10/0.21
% 0.10/0.21 Length.of.Defs: 0
% 0.10/0.21
% 0.10/0.21 Contains.Choice.Funs: false
% 0.10/0.21 ..
% 0.10/0.21
% 0.10/0.21 ********************************
% 0.10/0.21 * All subproblems solved! *
% 0.10/0.21 ********************************
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:63,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.21
% 0.10/0.21 %**** Beginning of derivation protocol ****
% 0.10/0.21 % SZS output start CNFRefutation
% See solution above
% 0.10/0.21
% 0.10/0.21 %**** End of derivation protocol ****
% 0.10/0.21 %**** no. of clauses in derivation: 64 ****
% 0.10/0.21 %**** clause counter: 63 ****
% 0.10/0.21
% 0.10/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:63,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------