%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX207+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 : n020.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 11:02:33 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 142 ( 139 unt; 0 typ; 0 def)
% Number of atoms : 384 ( 266 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 438 ( 68 ~; 6 |; 0 &; 360 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 172 ( 0 ^; 164 !; 8 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aP,type,
aP: $i > $i ).
thf(tp_append,type,
append: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bP,type,
bP: $i > $i ).
thf(tp_c2,type,
c2: $i > $i > $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_linC,type,
linC: $i > $i ).
thf(tp_linP,type,
linP: $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_pA,type,
pA: $i ).
thf(tp_pB,type,
pB: $i ).
thf(tp_pE,type,
pE: $i ).
thf(tp_proj1AP,type,
proj1AP: $i > $i ).
thf(tp_proj1BP,type,
proj1BP: $i > $i ).
thf(tp_proj1C,type,
proj1C: $i > $i ).
thf(tp_proj2C,type,
proj2C: $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(1,axiom,
! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(2,axiom,
( ( linP @ pE )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(3,axiom,
( ( linP @ pB )
= ( cons @ b @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(4,axiom,
( ( linP @ pA )
= ( cons @ a @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(5,axiom,
! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(6,axiom,
! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(7,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(8,axiom,
! [Y: $i] :
( ( append @ nil @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(9,axiom,
! [X: $i,X2: $i] :
( ( proj2C @ ( c2 @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(10,axiom,
! [X: $i,X2: $i] :
( ( proj1C @ ( c2 @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(11,axiom,
pB != pE,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(12,axiom,
pA != pE,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(13,axiom,
pA != pB,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(14,axiom,
! [X: $i] :
( ( bP @ X )
!= pE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(15,axiom,
! [X: $i] :
( ( bP @ X )
!= pB ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(16,axiom,
! [X: $i] :
( ( bP @ X )
!= pA ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(17,axiom,
! [X: $i] :
( ( aP @ X )
!= pE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(18,axiom,
! [X: $i] :
( ( aP @ X )
!= pB ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(19,axiom,
! [X: $i] :
( ( aP @ X )
!= pA ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(20,axiom,
! [X: $i,X2: $i] :
( ( aP @ X )
!= ( bP @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(21,axiom,
! [X: $i] :
( ( proj1BP @ ( bP @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(22,axiom,
! [X: $i] :
( ( proj1AP @ ( aP @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(23,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(24,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(25,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(26,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(27,conjecture,
? [U: $i,V: $i] :
~ ( ( ( linC @ U )
= ( linC @ V ) )
=> ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_027) ).
thf(28,negated_conjecture,
( ( ? [U: $i,V: $i] :
~ ( ( ( linC @ U )
= ( linC @ V ) )
=> ( U = V ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[27]) ).
thf(29,plain,
( ( ? [U: $i,V: $i] :
~ ( ( ( linC @ U )
= ( linC @ V ) )
=> ( U = V ) ) )
= $false ),
inference(unfold_def,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(31,plain,
( ( ( linP @ pE )
= nil )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(32,plain,
( ( ( linP @ pB )
= ( cons @ b @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(33,plain,
( ( ( linP @ pA )
= ( cons @ a @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(34,plain,
( ( ! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(35,plain,
( ( ! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(37,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2C @ ( c2 @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1C @ ( c2 @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( pB != pE )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(41,plain,
( ( pA != pE )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( pA != pB )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pE ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pB ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pA ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pE ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pB ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pA ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [X: $i,X2: $i] :
( ( aP @ X )
!= ( bP @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( proj1BP @ ( bP @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( proj1AP @ ( aP @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(52,plain,
( ( a != b )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(54,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(56,plain,
( ( ~ ? [U: $i,V: $i] :
~ ( ( ( linC @ U )
= ( linC @ V ) )
=> ( U = V ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(57,plain,
( ( ! [U: $i,V: $i] :
( ( ( linC @ U )
!= ( linC @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(58,plain,
( ( pB != pE )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(59,plain,
( ( pA != pE )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(60,plain,
( ( pA != pB )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pE ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pB ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pA ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pE ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(65,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pB ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(66,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pA ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(67,plain,
( ( ! [X: $i,X2: $i] :
( ( aP @ X )
!= ( bP @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(68,plain,
( ( a != b )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(69,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(70,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(71,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(73,plain,
( ( a != b )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(74,plain,
( ( ! [X: $i] :
( ( proj1AP @ ( aP @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [X: $i] :
( ( proj1BP @ ( bP @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ! [X: $i,X2: $i] :
( ( aP @ X )
!= ( bP @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(77,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pA ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pB ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(79,plain,
( ( ! [X: $i] :
( ( aP @ X )
!= pE ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(80,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pA ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(81,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pB ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(82,plain,
( ( ! [X: $i] :
( ( bP @ X )
!= pE ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( pA != pB )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(84,plain,
( ( pA != pE )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(85,plain,
( ( pB != pE )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(86,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1C @ ( c2 @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(87,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2C @ ( c2 @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(88,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(89,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(90,plain,
( ( ! [P: $i] :
( ( linP @ ( aP @ P ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ P ) @ ( cons @ a @ nil ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(91,plain,
( ( ! [Q: $i] :
( ( linP @ ( bP @ Q ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ Q ) @ ( cons @ b @ nil ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(92,plain,
( ( ( linP @ pA )
= ( cons @ a @ nil ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(93,plain,
( ( ( linP @ pB )
= ( cons @ b @ nil ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(94,plain,
( ( ( linP @ pE )
= nil )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(95,plain,
( ( ! [P: $i,Q: $i] :
( ( linC @ ( c2 @ P @ Q ) )
= ( append @ ( linP @ P ) @ ( linP @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] :
( ( ( linC @ U )
!= ( linC @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(97,plain,
! [SV1: $i] :
( ( ! [SY30: $i] :
( ( head @ ( cons @ SV1 @ SY30 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(98,plain,
! [SV2: $i] :
( ( ! [SY31: $i] :
( ( tail @ ( cons @ SV2 @ SY31 ) )
= SY31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(99,plain,
! [SV3: $i] :
( ( ! [SY32: $i] :
( nil
!= ( cons @ SV3 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(100,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(101,plain,
! [SV4: $i] :
( ( ( proj1AP @ ( aP @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( proj1BP @ ( bP @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(103,plain,
! [SV6: $i] :
( ( ! [SY33: $i] :
( ( aP @ SV6 )
!= ( bP @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(104,plain,
! [SV7: $i] :
( ( ( aP @ SV7 )
!= pA )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(105,plain,
! [SV8: $i] :
( ( ( aP @ SV8 )
!= pB )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(106,plain,
! [SV9: $i] :
( ( ( aP @ SV9 )
!= pE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(107,plain,
! [SV10: $i] :
( ( ( bP @ SV10 )
!= pA )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(108,plain,
! [SV11: $i] :
( ( ( bP @ SV11 )
!= pB )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(109,plain,
! [SV12: $i] :
( ( ( bP @ SV12 )
!= pE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(110,plain,
( ( pA = pB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(111,plain,
( ( pA = pE )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(112,plain,
( ( pB = pE )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(113,plain,
! [SV13: $i] :
( ( ! [SY34: $i] :
( ( proj1C @ ( c2 @ SV13 @ SY34 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(114,plain,
! [SV14: $i] :
( ( ! [SY35: $i] :
( ( proj2C @ ( c2 @ SV14 @ SY35 ) )
= SY35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(115,plain,
! [SV15: $i] :
( ( ( append @ nil @ SV15 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(116,plain,
! [SV16: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( append @ ( cons @ SY36 @ SY37 ) @ SV16 )
= ( cons @ SY36 @ ( append @ SY37 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(117,plain,
! [SV17: $i] :
( ( ( linP @ ( aP @ SV17 ) )
= ( append @ ( cons @ a @ nil ) @ ( append @ ( linP @ SV17 ) @ ( cons @ a @ nil ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(118,plain,
! [SV18: $i] :
( ( ( linP @ ( bP @ SV18 ) )
= ( append @ ( cons @ b @ nil ) @ ( append @ ( linP @ SV18 ) @ ( cons @ b @ nil ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(119,plain,
! [SV19: $i] :
( ( ! [SY38: $i] :
( ( linC @ ( c2 @ SV19 @ SY38 ) )
= ( append @ ( linP @ SV19 ) @ ( linP @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(120,plain,
! [SV20: $i] :
( ( ! [SY39: $i] :
( ( ( linC @ SV20 )
!= ( linC @ SY39 ) )
| ( SV20 = SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(121,plain,
! [SV21: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV21 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(122,plain,
! [SV22: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV22 ) )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(123,plain,
! [SV23: $i,SV3: $i] :
( ( nil
!= ( cons @ SV3 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(124,plain,
! [SV24: $i,SV6: $i] :
( ( ( aP @ SV6 )
!= ( bP @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(125,plain,
! [SV7: $i] :
( ( ( aP @ SV7 )
= pA )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(126,plain,
! [SV8: $i] :
( ( ( aP @ SV8 )
= pB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(127,plain,
! [SV9: $i] :
( ( ( aP @ SV9 )
= pE )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(128,plain,
! [SV10: $i] :
( ( ( bP @ SV10 )
= pA )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(129,plain,
! [SV11: $i] :
( ( ( bP @ SV11 )
= pB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(130,plain,
! [SV12: $i] :
( ( ( bP @ SV12 )
= pE )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(131,plain,
! [SV25: $i,SV13: $i] :
( ( ( proj1C @ ( c2 @ SV13 @ SV25 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV26: $i,SV14: $i] :
( ( ( proj2C @ ( c2 @ SV14 @ SV26 ) )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV16: $i,SV27: $i] :
( ( ! [SY40: $i] :
( ( append @ ( cons @ SV27 @ SY40 ) @ SV16 )
= ( cons @ SV27 @ ( append @ SY40 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV28: $i,SV19: $i] :
( ( ( linC @ ( c2 @ SV19 @ SV28 ) )
= ( append @ ( linP @ SV19 ) @ ( linP @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV29: $i,SV20: $i] :
( ( ( ( linC @ SV20 )
!= ( linC @ SV29 ) )
| ( SV20 = SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV23: $i,SV3: $i] :
( ( nil
= ( cons @ SV3 @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV24: $i,SV6: $i] :
( ( ( aP @ SV6 )
= ( bP @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(138,plain,
! [SV16: $i,SV30: $i,SV27: $i] :
( ( ( append @ ( cons @ SV27 @ SV30 ) @ SV16 )
= ( cons @ SV27 @ ( append @ SV30 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV29: $i,SV20: $i] :
( ( ( ( linC @ SV20 )
!= ( linC @ SV29 ) )
= $true )
| ( ( SV20 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV29: $i,SV20: $i] :
( ( ( ( linC @ SV20 )
= ( linC @ SV29 ) )
= $false )
| ( ( SV20 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(141,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,140,138,137,136,134,132,131,130,129,128,127,126,125,122,121,118,117,115,112,111,110,102,101,100,94,93]) ).
thf(142,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 17:12:21 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26
% 0.10/0.26 No.of.Axioms: 26
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 0
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: false
% 0.10/0.26 ...
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,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:141,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.26
% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 142 ****
% 0.10/0.26 %**** clause counter: 141 ****
% 0.10/0.26
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,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:141,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------