%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN088-1.010 : TPTP v9.3.1. Released v1.0.0.
% 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 : n008.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 11:02:56 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.24s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 23
% Syntax : Number of formulae : 105 ( 84 unt; 0 typ; 0 def)
% Number of atoms : 835 ( 200 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1334 ( 244 ~; 330 |; 0 &; 760 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-10 aty)
% Number of variables : 330 ( 0 ^; 330 !; 0 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_p,type,
p: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_q_1,type,
q_1: $i > $o ).
thf(tp_q_10,type,
q_10: $i > $o ).
thf(tp_q_2,type,
q_2: $i > $o ).
thf(tp_q_3,type,
q_3: $i > $o ).
thf(tp_q_4,type,
q_4: $i > $o ).
thf(tp_q_5,type,
q_5: $i > $o ).
thf(tp_q_6,type,
q_6: $i > $o ).
thf(tp_q_7,type,
q_7: $i > $o ).
thf(tp_q_8,type,
q_8: $i > $o ).
thf(tp_q_9,type,
q_9: $i > $o ).
thf(1,axiom,
q_10 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_21) ).
thf(2,axiom,
q_10 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_20) ).
thf(3,axiom,
q_9 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_19) ).
thf(4,axiom,
q_9 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_18) ).
thf(5,axiom,
q_8 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_17) ).
thf(6,axiom,
q_8 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_16) ).
thf(7,axiom,
q_7 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_15) ).
thf(8,axiom,
q_7 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_14) ).
thf(9,axiom,
q_6 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_13) ).
thf(10,axiom,
q_6 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_12) ).
thf(11,axiom,
q_5 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_11) ).
thf(12,axiom,
q_5 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_10) ).
thf(13,axiom,
q_4 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_9) ).
thf(14,axiom,
q_4 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_8) ).
thf(15,axiom,
q_3 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_7) ).
thf(16,axiom,
q_3 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_6) ).
thf(17,axiom,
q_2 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_5) ).
thf(18,axiom,
q_2 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_4) ).
thf(19,axiom,
q_1 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_3) ).
thf(20,axiom,
q_1 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_2) ).
thf(21,axiom,
! [X_1: $i,X_2: $i,X_3: $i,X_4: $i,X_5: $i,X_6: $i,X_7: $i,X_8: $i,X_9: $i,X_10: $i] :
( ( p @ X_1 @ X_2 @ X_3 @ X_4 @ X_5 @ X_6 @ X_7 @ X_8 @ X_9 @ X_10 )
| ~ ( q_1 @ X_1 )
| ~ ( q_2 @ X_2 )
| ~ ( q_3 @ X_3 )
| ~ ( q_4 @ X_4 )
| ~ ( q_5 @ X_5 )
| ~ ( q_6 @ X_6 )
| ~ ( q_7 @ X_7 )
| ~ ( q_8 @ X_8 )
| ~ ( q_9 @ X_9 )
| ~ ( q_10 @ X_10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_1) ).
thf(22,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(23,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,negated_conjecture,
~ ( p @ a @ a @ a @ a @ a @ a @ a @ a @ a @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_goal_1) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[23]) ).
thf(26,plain,
( ( q_10 @ b )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( q_10 @ a )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,plain,
( ( q_9 @ b )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(29,plain,
( ( q_9 @ a )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,plain,
( ( q_8 @ b )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(31,plain,
( ( q_8 @ a )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(32,plain,
( ( q_7 @ b )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( q_7 @ a )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( q_6 @ b )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( q_6 @ a )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( q_5 @ b )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( q_5 @ a )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( q_4 @ b )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( q_4 @ a )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( q_3 @ b )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( q_3 @ a )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( q_2 @ b )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( q_2 @ a )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( q_1 @ b )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( q_1 @ a )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [X_1: $i,X_2: $i,X_3: $i,X_4: $i,X_5: $i,X_6: $i,X_7: $i,X_8: $i,X_9: $i,X_10: $i] :
( ( p @ X_1 @ X_2 @ X_3 @ X_4 @ X_5 @ X_6 @ X_7 @ X_8 @ X_9 @ X_10 )
| ~ ( q_1 @ X_1 )
| ~ ( q_2 @ X_2 )
| ~ ( q_3 @ X_3 )
| ~ ( q_4 @ X_4 )
| ~ ( q_5 @ X_5 )
| ~ ( q_6 @ X_6 )
| ~ ( q_7 @ X_7 )
| ~ ( q_8 @ X_8 )
| ~ ( q_9 @ X_9 )
| ~ ( q_10 @ X_10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ~ ( p @ a @ a @ a @ a @ a @ a @ a @ a @ a @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( ~ ( p @ a @ a @ a @ a @ a @ a @ a @ a @ a @ a ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( ! [X_1: $i,X_2: $i,X_3: $i,X_4: $i,X_5: $i,X_6: $i,X_7: $i,X_8: $i,X_9: $i,X_10: $i] :
( ( p @ X_1 @ X_2 @ X_3 @ X_4 @ X_5 @ X_6 @ X_7 @ X_8 @ X_9 @ X_10 )
| ~ ( q_1 @ X_1 )
| ~ ( q_2 @ X_2 )
| ~ ( q_3 @ X_3 )
| ~ ( q_4 @ X_4 )
| ~ ( q_5 @ X_5 )
| ~ ( q_6 @ X_6 )
| ~ ( q_7 @ X_7 )
| ~ ( q_8 @ X_8 )
| ~ ( q_9 @ X_9 )
| ~ ( q_10 @ X_10 ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( q_1 @ a )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( q_1 @ b )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( q_2 @ a )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( q_2 @ b )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( q_3 @ a )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( q_3 @ b )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( q_4 @ a )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( q_4 @ b )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( q_5 @ a )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( q_5 @ b )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( q_6 @ a )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(62,plain,
( ( q_6 @ b )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(63,plain,
( ( q_7 @ a )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(64,plain,
( ( q_7 @ b )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(65,plain,
( ( q_8 @ a )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(66,plain,
( ( q_8 @ b )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,plain,
( ( q_9 @ a )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(68,plain,
( ( q_9 @ b )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(69,plain,
( ( q_10 @ a )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(70,plain,
( ( q_10 @ b )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(71,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,plain,
( ( p @ a @ a @ a @ a @ a @ a @ a @ a @ a @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY10: $i,SY11: $i,SY12: $i,SY13: $i,SY14: $i,SY15: $i,SY16: $i,SY17: $i,SY18: $i] :
( ( p @ SV1 @ SY10 @ SY11 @ SY12 @ SY13 @ SY14 @ SY15 @ SY16 @ SY17 @ SY18 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SY10 )
| ~ ( q_3 @ SY11 )
| ~ ( q_4 @ SY12 )
| ~ ( q_5 @ SY13 )
| ~ ( q_6 @ SY14 )
| ~ ( q_7 @ SY15 )
| ~ ( q_8 @ SY16 )
| ~ ( q_9 @ SY17 )
| ~ ( q_10 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(74,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY19: $i,SY20: $i,SY21: $i,SY22: $i,SY23: $i,SY24: $i,SY25: $i,SY26: $i] :
( ( p @ SV1 @ SV2 @ SY19 @ SY20 @ SY21 @ SY22 @ SY23 @ SY24 @ SY25 @ SY26 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SY19 )
| ~ ( q_4 @ SY20 )
| ~ ( q_5 @ SY21 )
| ~ ( q_6 @ SY22 )
| ~ ( q_7 @ SY23 )
| ~ ( q_8 @ SY24 )
| ~ ( q_9 @ SY25 )
| ~ ( q_10 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i,SY30: $i,SY31: $i,SY32: $i,SY33: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SY27 @ SY28 @ SY29 @ SY30 @ SY31 @ SY32 @ SY33 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SY27 )
| ~ ( q_5 @ SY28 )
| ~ ( q_6 @ SY29 )
| ~ ( q_7 @ SY30 )
| ~ ( q_8 @ SY31 )
| ~ ( q_9 @ SY32 )
| ~ ( q_10 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(77,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY34: $i,SY35: $i,SY36: $i,SY37: $i,SY38: $i,SY39: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SY34 @ SY35 @ SY36 @ SY37 @ SY38 @ SY39 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SY34 )
| ~ ( q_6 @ SY35 )
| ~ ( q_7 @ SY36 )
| ~ ( q_8 @ SY37 )
| ~ ( q_9 @ SY38 )
| ~ ( q_10 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(78,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i,SY43: $i,SY44: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SY40 @ SY41 @ SY42 @ SY43 @ SY44 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SY40 )
| ~ ( q_7 @ SY41 )
| ~ ( q_8 @ SY42 )
| ~ ( q_9 @ SY43 )
| ~ ( q_10 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(79,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i,SY48: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SY45 @ SY46 @ SY47 @ SY48 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SY45 )
| ~ ( q_8 @ SY46 )
| ~ ( q_9 @ SY47 )
| ~ ( q_10 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(80,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SY49 @ SY50 @ SY51 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SY49 )
| ~ ( q_9 @ SY50 )
| ~ ( q_10 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(81,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SY52 @ SY53 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SY52 )
| ~ ( q_10 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(82,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY54: $i] :
( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SY54 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(83,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
| ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(84,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true )
| ( ( ~ ( q_1 @ SV1 )
| ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(85,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( q_1 @ SV1 ) )
= $true )
| ( ( ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(86,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( q_1 @ SV1 )
= $false )
| ( ( ~ ( q_2 @ SV2 )
| ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(87,plain,
! [SV1: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( q_2 @ SV2 ) )
= $true )
| ( ( ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(88,plain,
! [SV1: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i] :
( ( ( q_2 @ SV2 )
= $false )
| ( ( ~ ( q_3 @ SV3 )
| ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(89,plain,
! [SV1: $i,SV2: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i] :
( ( ( ~ ( q_3 @ SV3 ) )
= $true )
| ( ( ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(90,plain,
! [SV1: $i,SV2: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i] :
( ( ( q_3 @ SV3 )
= $false )
| ( ( ~ ( q_4 @ SV4 )
| ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(91,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( q_4 @ SV4 ) )
= $true )
| ( ( ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(92,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( q_4 @ SV4 )
= $false )
| ( ( ~ ( q_5 @ SV5 )
| ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(93,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i] :
( ( ( ~ ( q_5 @ SV5 ) )
= $true )
| ( ( ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(94,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i] :
( ( ( q_5 @ SV5 )
= $false )
| ( ( ~ ( q_6 @ SV6 )
| ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(95,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i] :
( ( ( ~ ( q_6 @ SV6 ) )
= $true )
| ( ( ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(96,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i] :
( ( ( q_6 @ SV6 )
= $false )
| ( ( ~ ( q_7 @ SV7 )
| ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(97,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i] :
( ( ( ~ ( q_7 @ SV7 ) )
= $true )
| ( ( ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(98,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i] :
( ( ( q_7 @ SV7 )
= $false )
| ( ( ~ ( q_8 @ SV8 )
| ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV7: $i,SV10: $i,SV9: $i,SV8: $i] :
( ( ( ~ ( q_8 @ SV8 ) )
= $true )
| ( ( ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_7 @ SV7 )
= $false )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(100,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV7: $i,SV10: $i,SV9: $i,SV8: $i] :
( ( ( q_8 @ SV8 )
= $false )
| ( ( ~ ( q_9 @ SV9 )
| ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_7 @ SV7 )
= $false )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(101,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV7: $i,SV8: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( q_9 @ SV9 ) )
= $true )
| ( ( ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_8 @ SV8 )
= $false )
| ( ( q_7 @ SV7 )
= $false )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(102,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV7: $i,SV8: $i,SV10: $i,SV9: $i] :
( ( ( q_9 @ SV9 )
= $false )
| ( ( ~ ( q_10 @ SV10 ) )
= $true )
| ( ( q_8 @ SV8 )
= $false )
| ( ( q_7 @ SV7 )
= $false )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(103,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i,SV6: $i,SV7: $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( q_10 @ SV10 )
= $false )
| ( ( q_9 @ SV9 )
= $false )
| ( ( q_8 @ SV8 )
= $false )
| ( ( q_7 @ SV7 )
= $false )
| ( ( q_6 @ SV6 )
= $false )
| ( ( q_5 @ SV5 )
= $false )
| ( ( q_4 @ SV4 )
= $false )
| ( ( q_3 @ SV3 )
= $false )
| ( ( q_2 @ SV2 )
= $false )
| ( ( q_1 @ SV1 )
= $false )
| ( ( p @ SV1 @ SV2 @ SV3 @ SV4 @ SV5 @ SV6 @ SV7 @ SV8 @ SV9 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,103,74,72,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN088-1.010 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.18 % Computer : n008.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Oct 6 17:16:54 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.24
% 0.13/0.24 No.of.Axioms: 22
% 0.13/0.24
% 0.13/0.24 Length.of.Defs: 0
% 0.13/0.24
% 0.13/0.24 Contains.Choice.Funs: false
% 0.13/0.24 ...
% 0.13/0.24
% 0.13/0.24 ********************************
% 0.13/0.24 * All subproblems solved! *
% 0.13/0.24 ********************************
% 0.13/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.24
% 0.13/0.24 %**** Beginning of derivation protocol ****
% 0.13/0.24 % SZS output start CNFRefutation
% See solution above
% 0.13/0.24
% 0.13/0.24 %**** End of derivation protocol ****
% 0.13/0.24 %**** no. of clauses in derivation: 105 ****
% 0.13/0.24 %**** clause counter: 104 ****
% 0.13/0.24
% 0.13/0.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:22,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------