%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n018.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 11:02:30 AM UTC 2026
% Result : Unsatisfiable 0.40s 0.33s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 105 ( 95 unt; 0 typ; 0 def)
% Number of atoms : 309 ( 209 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 549 ( 23 ~; 20 |; 0 &; 506 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 206 ( 0 ^; 206 !; 0 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_drop,type,
drop: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_eq3,type,
eq3: $i > $i > $i ).
thf(tp_impl,type,
impl: $i > $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_prop_drop_inj2,type,
prop_drop_inj2: $i > $i > $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(3,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(5,axiom,
! [X: $i] :
( ( eq3 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(6,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(7,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(8,axiom,
! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(9,axiom,
! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(11,axiom,
( ( eq3 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(12,axiom,
( ( eq3 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(13,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( prop_drop_inj2 @ X @ Y @ Z )
= ( impl @ ( eq @ ( drop @ X @ Y ) @ ( drop @ X @ Z ) ) @ ( eq @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(14,axiom,
! [Y: $i] :
( ( drop @ z @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(15,axiom,
! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(16,axiom,
! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(17,axiom,
! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(18,axiom,
! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(19,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(20,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,negated_conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( eq3 @ ( prop_drop_inj2 @ X @ Y @ Z ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(22,plain,
$false = $false,
inference(unfold_def,[status(thm)],[20]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( prop_drop_inj2 @ X @ Y @ Z )
= ( impl @ ( eq @ ( drop @ X @ Y ) @ ( drop @ X @ Z ) ) @ ( eq @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [Y: $i] :
( ( drop @ z @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq3 @ ( prop_drop_inj2 @ X @ Y @ Z ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(42,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(44,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq3 @ ( prop_drop_inj2 @ X @ Y @ Z ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq3 @ ( prop_drop_inj2 @ X @ Y @ Z ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(48,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(49,plain,
( ( ! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(50,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(51,plain,
( ( ! [Y: $i] :
( ( drop @ z @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( prop_drop_inj2 @ X @ Y @ Z )
= ( impl @ ( eq @ ( drop @ X @ Y ) @ ( drop @ X @ Z ) ) @ ( eq @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(53,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(54,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(59,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(62,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(65,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[42]) ).
thf(66,plain,
! [SV1: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ( eq3 @ ( prop_drop_inj2 @ SV1 @ SY32 @ SY33 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(67,plain,
! [SV2: $i] :
( ( ( impl @ btrue @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(68,plain,
! [SV3: $i] :
( ( ( impl @ bfalse @ SV3 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(69,plain,
! [SV4: $i] :
( ( ( drop @ ( s @ SV4 ) @ nil )
= nil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(70,plain,
! [SV5: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ( drop @ ( s @ SV5 ) @ ( cons @ SY34 @ SY35 ) )
= ( drop @ SV5 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( drop @ z @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(72,plain,
! [SV7: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( prop_drop_inj2 @ SV7 @ SY36 @ SY37 )
= ( impl @ ( eq @ ( drop @ SV7 @ SY36 ) @ ( drop @ SV7 @ SY37 ) ) @ ( eq @ SY36 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(73,plain,
! [SV8: $i] :
( ( ! [SY38: $i] :
( ( eq2 @ ( s @ SV8 ) @ ( s @ SY38 ) )
= ( eq2 @ SV8 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(74,plain,
! [SV9: $i] :
( ( ( eq2 @ ( s @ SV9 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(75,plain,
! [SV10: $i] :
( ( ( eq2 @ z @ ( s @ SV10 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV11: $i] :
( ( ( eq @ SV11 @ SV11 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV12: $i] :
( ( ( eq2 @ SV12 @ SV12 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV13: $i] :
( ( ( eq3 @ SV13 @ SV13 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV14: $i] :
( ( ! [SY39: $i] :
( ( ( eq2 @ SV14 @ SY39 )
!= bfalse )
| ! [SY40: $i,SY41: $i] :
( ( eq @ ( cons @ SV14 @ SY40 ) @ ( cons @ SY39 @ SY41 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV15: $i] :
( ( ! [SY42: $i] :
( ( ( eq2 @ SV15 @ SY42 )
!= btrue )
| ! [SY43: $i,SY44: $i] :
( ( eq @ ( cons @ SV15 @ SY43 ) @ ( cons @ SY42 @ SY44 ) )
= ( eq @ SY43 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV16: $i] :
( ( ! [SY45: $i] :
( ( eq @ nil @ ( cons @ SV16 @ SY45 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV17: $i] :
( ( ! [SY46: $i] :
( ( eq @ ( cons @ SV17 @ SY46 ) @ nil )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(84,plain,
! [SV18: $i,SV1: $i] :
( ( ! [SY47: $i] :
( ( eq3 @ ( prop_drop_inj2 @ SV1 @ SV18 @ SY47 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
! [SV19: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ( drop @ ( s @ SV5 ) @ ( cons @ SV19 @ SY48 ) )
= ( drop @ SV5 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY49: $i] :
( ( prop_drop_inj2 @ SV7 @ SV20 @ SY49 )
= ( impl @ ( eq @ ( drop @ SV7 @ SV20 ) @ ( drop @ SV7 @ SY49 ) ) @ ( eq @ SV20 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV21: $i,SV8: $i] :
( ( ( eq2 @ ( s @ SV8 ) @ ( s @ SV21 ) )
= ( eq2 @ SV8 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV22: $i,SV14: $i] :
( ( ( ( eq2 @ SV14 @ SV22 )
!= bfalse )
| ! [SY50: $i,SY51: $i] :
( ( eq @ ( cons @ SV14 @ SY50 ) @ ( cons @ SV22 @ SY51 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV23: $i,SV15: $i] :
( ( ( ( eq2 @ SV15 @ SV23 )
!= btrue )
| ! [SY52: $i,SY53: $i] :
( ( eq @ ( cons @ SV15 @ SY52 ) @ ( cons @ SV23 @ SY53 ) )
= ( eq @ SY52 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV24: $i,SV16: $i] :
( ( ( eq @ nil @ ( cons @ SV16 @ SV24 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV25: $i,SV17: $i] :
( ( ( eq @ ( cons @ SV17 @ SV25 ) @ nil )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV26: $i,SV18: $i,SV1: $i] :
( ( ( eq3 @ ( prop_drop_inj2 @ SV1 @ SV18 @ SV26 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV27: $i,SV19: $i,SV5: $i] :
( ( ( drop @ ( s @ SV5 ) @ ( cons @ SV19 @ SV27 ) )
= ( drop @ SV5 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV28: $i,SV20: $i,SV7: $i] :
( ( ( prop_drop_inj2 @ SV7 @ SV20 @ SV28 )
= ( impl @ ( eq @ ( drop @ SV7 @ SV20 ) @ ( drop @ SV7 @ SV28 ) ) @ ( eq @ SV20 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV22: $i,SV14: $i] :
( ( ( ( eq2 @ SV14 @ SV22 )
!= bfalse )
= $true )
| ( ( ! [SY50: $i,SY51: $i] :
( ( eq @ ( cons @ SV14 @ SY50 ) @ ( cons @ SV22 @ SY51 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV23: $i,SV15: $i] :
( ( ( ( eq2 @ SV15 @ SV23 )
!= btrue )
= $true )
| ( ( ! [SY52: $i,SY53: $i] :
( ( eq @ ( cons @ SV15 @ SY52 ) @ ( cons @ SV23 @ SY53 ) )
= ( eq @ SY52 @ SY53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV26: $i,SV18: $i,SV1: $i] :
( ( ( eq3 @ ( prop_drop_inj2 @ SV1 @ SV18 @ SV26 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV22: $i,SV14: $i] :
( ( ( ( eq2 @ SV14 @ SV22 )
= bfalse )
= $false )
| ( ( ! [SY50: $i,SY51: $i] :
( ( eq @ ( cons @ SV14 @ SY50 ) @ ( cons @ SV22 @ SY51 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(99,plain,
! [SV23: $i,SV15: $i] :
( ( ( ( eq2 @ SV15 @ SV23 )
= btrue )
= $false )
| ( ( ! [SY52: $i,SY53: $i] :
( ( eq @ ( cons @ SV15 @ SY52 ) @ ( cons @ SV23 @ SY53 ) )
= ( eq @ SY52 @ SY53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV22: $i,SV29: $i,SV14: $i] :
( ( ( ! [SY54: $i] :
( ( eq @ ( cons @ SV14 @ SV29 ) @ ( cons @ SV22 @ SY54 ) )
= bfalse ) )
= $true )
| ( ( ( eq2 @ SV14 @ SV22 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV23: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY55: $i] :
( ( eq @ ( cons @ SV15 @ SV30 ) @ ( cons @ SV23 @ SY55 ) )
= ( eq @ SV30 @ SY55 ) ) )
= $true )
| ( ( ( eq2 @ SV15 @ SV23 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV31: $i,SV22: $i,SV29: $i,SV14: $i] :
( ( ( ( eq @ ( cons @ SV14 @ SV29 ) @ ( cons @ SV22 @ SV31 ) )
= bfalse )
= $true )
| ( ( ( eq2 @ SV14 @ SV22 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV32: $i,SV23: $i,SV30: $i,SV15: $i] :
( ( ( ( eq @ ( cons @ SV15 @ SV30 ) @ ( cons @ SV23 @ SV32 ) )
= ( eq @ SV30 @ SV32 ) )
= $true )
| ( ( ( eq2 @ SV15 @ SV23 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,103,102,97,94,93,91,90,87,83,78,77,76,75,74,71,69,68,67,54]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22 % Computer : n018.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 17:12:52 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.33
% 0.40/0.33 No.of.Axioms: 19
% 0.40/0.33
% 0.40/0.33 Length.of.Defs: 0
% 0.40/0.33
% 0.40/0.33 Contains.Choice.Funs: false
% 0.40/0.33 ...
% 0.40/0.33
% 0.40/0.33 ********************************
% 0.40/0.33 * All subproblems solved! *
% 0.40/0.33 ********************************
% 0.40/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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)
% 0.40/0.33
% 0.40/0.33 %**** Beginning of derivation protocol ****
% 0.40/0.33 % SZS output start CNFRefutation
% See solution above
% 0.40/0.33
% 0.40/0.33 %**** End of derivation protocol ****
% 0.40/0.33 %**** no. of clauses in derivation: 105 ****
% 0.40/0.33 %**** clause counter: 104 ****
% 0.40/0.33
% 0.40/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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)
%------------------------------------------------------------------------------