%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN075-1 : 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 : n009.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 11:02:53 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 106 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 635 ( 327 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1080 ( 142 ~; 217 |; 0 &; 721 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 231 ( 0 ^; 231 !; 0 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_big_f,type,
big_f: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_h,type,
h: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( X != a )
| ( Y != b )
| ( big_f @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( Y = b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( X = a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(7,negated_conjecture,
! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(8,negated_conjecture,
! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(9,negated_conjecture,
! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(10,negated_conjecture,
! [Y: $i,X: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( f @ X )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(11,negated_conjecture,
! [Y: $i,X: $i,Z: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
= ( g @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(12,negated_conjecture,
! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
!= ( g @ X ) )
| ( ( f @ X )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] :
( ( X != a )
| ( Y != b )
| ( big_f @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( Y = b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( X = a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( ! [Y: $i,X: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( f @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
= ( g @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
!= ( g @ X ) )
| ( ( f @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [Y: $i,X: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
!= ( g @ X ) )
| ( ( f @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(26,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( big_f @ Y @ ( f @ X ) )
| ( Y
= ( g @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [Y: $i,X: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( f @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( Y
!= ( g @ X ) )
| ( big_f @ Y @ ( f @ X ) )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( big_f @ ( h @ X @ Z ) @ ( f @ X ) )
| ( ( h @ X @ Z )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [X: $i,Z: $i] :
( ( ( f @ X )
!= X )
| ( ( h @ X @ Z )
!= Z )
| ~ ( big_f @ ( h @ X @ Z ) @ ( f @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( X = a ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( big_f @ X @ Y )
| ( Y = b ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( X != a )
| ( Y != b )
| ( big_f @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( g @ SX1 ) )
| ( big_f @ SX0 @ ( f @ SX1 ) )
| ( ( h @ SX1 @ SX2 )
!= SX2 )
| ~ ( big_f @ ( h @ SX1 @ SX2 ) @ ( f @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( g @ SX1 ) )
| ( big_f @ SX0 @ ( f @ SX1 ) )
| ( big_f @ ( h @ SX1 @ SX2 ) @ ( f @ SX1 ) )
| ( ( h @ SX1 @ SX2 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != a )
| ( SX1 != b )
| ( big_f @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( f @ SX0 )
!= SX0 )
| ( ( h @ SX0 @ SX1 )
!= SX1 )
| ~ ( big_f @ ( h @ SX0 @ SX1 ) @ ( f @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( g @ SX1 ) )
| ( big_f @ SX0 @ ( f @ SX1 ) )
| ( ( f @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( f @ SX0 )
!= SX0 )
| ( big_f @ ( h @ SX0 @ SX1 ) @ ( f @ SX0 ) )
| ( ( h @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( big_f @ SX0 @ ( f @ SX1 ) )
| ( SX0
!= ( g @ SX1 ) )
| ( ( f @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(43,plain,
! [SV1: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( big_f @ SV1 @ ( f @ SY23 ) )
| ( SV1
= ( g @ SY23 ) )
| ( big_f @ ( h @ SY23 @ SY24 ) @ ( f @ SY23 ) )
| ~ ( big_f @ ( h @ SY23 @ SY24 ) @ ( f @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(44,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ~ ( big_f @ SV2 @ SY25 )
| ( SV2 = a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(45,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( ~ ( big_f @ SV3 @ SY26 )
| ( SY26 = b ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(46,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV4: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ( SV4
!= ( g @ SY27 ) )
| ( big_f @ SV4 @ ( f @ SY27 ) )
| ( ( h @ SY27 @ SY28 )
!= SY28 )
| ~ ( big_f @ ( h @ SY27 @ SY28 ) @ ( f @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ( SV5
!= ( g @ SY29 ) )
| ( big_f @ SV5 @ ( f @ SY29 ) )
| ( big_f @ ( h @ SY29 @ SY30 ) @ ( f @ SY29 ) )
| ( ( h @ SY29 @ SY30 )
= SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV6: $i] :
( ( ! [SY31: $i] :
( ( SV6 != a )
| ( SY31 != b )
| ( big_f @ SV6 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
! [SV7: $i] :
( ( ! [SY32: $i] :
( ( ( f @ SV7 )
!= SV7 )
| ( ( h @ SV7 @ SY32 )
!= SY32 )
| ~ ( big_f @ ( h @ SV7 @ SY32 ) @ ( f @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(51,plain,
! [SV8: $i] :
( ( ! [SY33: $i] :
( ( SV8
!= ( g @ SY33 ) )
| ( big_f @ SV8 @ ( f @ SY33 ) )
| ( ( f @ SY33 )
= SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
! [SV9: $i] :
( ( ! [SY34: $i] :
( ( ( f @ SV9 )
!= SV9 )
| ( big_f @ ( h @ SV9 @ SY34 ) @ ( f @ SV9 ) )
| ( ( h @ SV9 @ SY34 )
= SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(53,plain,
! [SV10: $i] :
( ( ! [SY35: $i] :
( ~ ( big_f @ SV10 @ ( f @ SY35 ) )
| ( SV10
!= ( g @ SY35 ) )
| ( ( f @ SY35 )
= SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV11: $i,SV1: $i] :
( ( ! [SY36: $i] :
( ~ ( big_f @ SV1 @ ( f @ SV11 ) )
| ( SV1
= ( g @ SV11 ) )
| ( big_f @ ( h @ SV11 @ SY36 ) @ ( f @ SV11 ) )
| ~ ( big_f @ ( h @ SV11 @ SY36 ) @ ( f @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( big_f @ SV2 @ SV12 )
| ( SV2 = a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV13: $i,SV3: $i] :
( ( ~ ( big_f @ SV3 @ SV13 )
| ( SV13 = b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY37: $i] :
( ( SV4
!= ( g @ SV14 ) )
| ( big_f @ SV4 @ ( f @ SV14 ) )
| ( ( h @ SV14 @ SY37 )
!= SY37 )
| ~ ( big_f @ ( h @ SV14 @ SY37 ) @ ( f @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY38: $i] :
( ( SV5
!= ( g @ SV15 ) )
| ( big_f @ SV5 @ ( f @ SV15 ) )
| ( big_f @ ( h @ SV15 @ SY38 ) @ ( f @ SV15 ) )
| ( ( h @ SV15 @ SY38 )
= SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV16: $i,SV6: $i] :
( ( ( SV6 != a )
| ( SV16 != b )
| ( big_f @ SV6 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( f @ SV7 )
!= SV7 )
| ( ( h @ SV7 @ SV17 )
!= SV17 )
| ~ ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV18: $i,SV8: $i] :
( ( ( SV8
!= ( g @ SV18 ) )
| ( big_f @ SV8 @ ( f @ SV18 ) )
| ( ( f @ SV18 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV19: $i,SV9: $i] :
( ( ( ( f @ SV9 )
!= SV9 )
| ( big_f @ ( h @ SV9 @ SV19 ) @ ( f @ SV9 ) )
| ( ( h @ SV9 @ SV19 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( big_f @ SV10 @ ( f @ SV20 ) )
| ( SV10
!= ( g @ SV20 ) )
| ( ( f @ SV20 )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV21: $i,SV11: $i,SV1: $i] :
( ( ~ ( big_f @ SV1 @ ( f @ SV11 ) )
| ( SV1
= ( g @ SV11 ) )
| ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
| ~ ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( big_f @ SV2 @ SV12 ) )
= $true )
| ( ( SV2 = a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV13: $i,SV3: $i] :
( ( ( ~ ( big_f @ SV3 @ SV13 ) )
= $true )
| ( ( SV13 = b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( SV4
!= ( g @ SV14 ) )
| ( big_f @ SV4 @ ( f @ SV14 ) )
| ( ( h @ SV14 @ SV22 )
!= SV22 )
| ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( SV5
!= ( g @ SV15 ) )
| ( big_f @ SV5 @ ( f @ SV15 ) )
| ( big_f @ ( h @ SV15 @ SV23 ) @ ( f @ SV15 ) )
| ( ( h @ SV15 @ SV23 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV16: $i,SV6: $i] :
( ( ( SV6 != a )
= $true )
| ( ( ( SV16 != b )
| ( big_f @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( f @ SV7 )
!= SV7 )
= $true )
| ( ( ( ( h @ SV7 @ SV17 )
!= SV17 )
| ~ ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV18: $i,SV8: $i] :
( ( ( SV8
!= ( g @ SV18 ) )
= $true )
| ( ( ( big_f @ SV8 @ ( f @ SV18 ) )
| ( ( f @ SV18 )
= SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV19: $i,SV9: $i] :
( ( ( ( f @ SV9 )
!= SV9 )
= $true )
| ( ( ( big_f @ ( h @ SV9 @ SV19 ) @ ( f @ SV9 ) )
| ( ( h @ SV9 @ SV19 )
= SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( big_f @ SV10 @ ( f @ SV20 ) ) )
= $true )
| ( ( ( SV10
!= ( g @ SV20 ) )
| ( ( f @ SV20 )
= SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV21: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( big_f @ SV1 @ ( f @ SV11 ) ) )
= $true )
| ( ( ( SV1
= ( g @ SV11 ) )
| ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
| ~ ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV12: $i,SV2: $i] :
( ( ( big_f @ SV2 @ SV12 )
= $false )
| ( ( SV2 = a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV13: $i,SV3: $i] :
( ( ( big_f @ SV3 @ SV13 )
= $false )
| ( ( SV13 = b )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( SV4
!= ( g @ SV14 ) )
= $true )
| ( ( ( big_f @ SV4 @ ( f @ SV14 ) )
| ( ( h @ SV14 @ SV22 )
!= SV22 )
| ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( SV5
!= ( g @ SV15 ) )
= $true )
| ( ( ( big_f @ SV5 @ ( f @ SV15 ) )
| ( big_f @ ( h @ SV15 @ SV23 ) @ ( f @ SV15 ) )
| ( ( h @ SV15 @ SV23 )
= SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV16: $i,SV6: $i] :
( ( ( SV6 = a )
= $false )
| ( ( ( SV16 != b )
| ( big_f @ SV6 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( f @ SV7 )
= SV7 )
= $false )
| ( ( ( ( h @ SV7 @ SV17 )
!= SV17 )
| ~ ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV18: $i,SV8: $i] :
( ( ( SV8
= ( g @ SV18 ) )
= $false )
| ( ( ( big_f @ SV8 @ ( f @ SV18 ) )
| ( ( f @ SV18 )
= SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV19: $i,SV9: $i] :
( ( ( ( f @ SV9 )
= SV9 )
= $false )
| ( ( ( big_f @ ( h @ SV9 @ SV19 ) @ ( f @ SV9 ) )
| ( ( h @ SV9 @ SV19 )
= SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV20: $i,SV10: $i] :
( ( ( big_f @ SV10 @ ( f @ SV20 ) )
= $false )
| ( ( ( SV10
!= ( g @ SV20 ) )
| ( ( f @ SV20 )
= SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV21: $i,SV11: $i,SV1: $i] :
( ( ( big_f @ SV1 @ ( f @ SV11 ) )
= $false )
| ( ( ( SV1
= ( g @ SV11 ) )
| ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
| ~ ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( SV4
= ( g @ SV14 ) )
= $false )
| ( ( ( big_f @ SV4 @ ( f @ SV14 ) )
| ( ( h @ SV14 @ SV22 )
!= SV22 )
| ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( SV5
= ( g @ SV15 ) )
= $false )
| ( ( ( big_f @ SV5 @ ( f @ SV15 ) )
| ( big_f @ ( h @ SV15 @ SV23 ) @ ( f @ SV15 ) )
| ( ( h @ SV15 @ SV23 )
= SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV6: $i,SV16: $i] :
( ( ( SV16 != b )
= $true )
| ( ( big_f @ SV6 @ SV16 )
= $true )
| ( ( SV6 = a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( h @ SV7 @ SV17 )
!= SV17 )
= $true )
| ( ( ~ ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) ) )
= $true )
| ( ( ( f @ SV7 )
= SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV18: $i,SV8: $i] :
( ( ( big_f @ SV8 @ ( f @ SV18 ) )
= $true )
| ( ( ( f @ SV18 )
= SV18 )
= $true )
| ( ( SV8
= ( g @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV19: $i,SV9: $i] :
( ( ( big_f @ ( h @ SV9 @ SV19 ) @ ( f @ SV9 ) )
= $true )
| ( ( ( h @ SV9 @ SV19 )
= SV19 )
= $true )
| ( ( ( f @ SV9 )
= SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV20: $i,SV10: $i] :
( ( ( SV10
!= ( g @ SV20 ) )
= $true )
| ( ( ( f @ SV20 )
= SV20 )
= $true )
| ( ( big_f @ SV10 @ ( f @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV21: $i,SV11: $i,SV1: $i] :
( ( ( SV1
= ( g @ SV11 ) )
= $true )
| ( ( ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
| ~ ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) ) )
= $true )
| ( ( big_f @ SV1 @ ( f @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV22: $i,SV14: $i,SV4: $i] :
( ( ( big_f @ SV4 @ ( f @ SV14 ) )
= $true )
| ( ( ( ( h @ SV14 @ SV22 )
!= SV22 )
| ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true )
| ( ( SV4
= ( g @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV23: $i,SV15: $i,SV5: $i] :
( ( ( big_f @ SV5 @ ( f @ SV15 ) )
= $true )
| ( ( ( big_f @ ( h @ SV15 @ SV23 ) @ ( f @ SV15 ) )
| ( ( h @ SV15 @ SV23 )
= SV23 ) )
= $true )
| ( ( SV5
= ( g @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV6: $i,SV16: $i] :
( ( ( SV16 = b )
= $false )
| ( ( big_f @ SV6 @ SV16 )
= $true )
| ( ( SV6 = a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( h @ SV7 @ SV17 )
= SV17 )
= $false )
| ( ( ~ ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) ) )
= $true )
| ( ( ( f @ SV7 )
= SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV20: $i,SV10: $i] :
( ( ( SV10
= ( g @ SV20 ) )
= $false )
| ( ( ( f @ SV20 )
= SV20 )
= $true )
| ( ( big_f @ SV10 @ ( f @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV1: $i,SV21: $i,SV11: $i] :
( ( ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
= $true )
| ( ( ~ ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) ) )
= $true )
| ( ( SV1
= ( g @ SV11 ) )
= $true )
| ( ( big_f @ SV1 @ ( f @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV4: $i,SV22: $i,SV14: $i] :
( ( ( ( h @ SV14 @ SV22 )
!= SV22 )
= $true )
| ( ( ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true )
| ( ( big_f @ SV4 @ ( f @ SV14 ) )
= $true )
| ( ( SV4
= ( g @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV5: $i,SV23: $i,SV15: $i] :
( ( ( big_f @ ( h @ SV15 @ SV23 ) @ ( f @ SV15 ) )
= $true )
| ( ( ( h @ SV15 @ SV23 )
= SV23 )
= $true )
| ( ( big_f @ SV5 @ ( f @ SV15 ) )
= $true )
| ( ( SV5
= ( g @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV17: $i,SV7: $i] :
( ( ( big_f @ ( h @ SV7 @ SV17 ) @ ( f @ SV7 ) )
= $false )
| ( ( ( h @ SV7 @ SV17 )
= SV17 )
= $false )
| ( ( ( f @ SV7 )
= SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV1: $i,SV21: $i,SV11: $i] :
( ( ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
= $false )
| ( ( big_f @ ( h @ SV11 @ SV21 ) @ ( f @ SV11 ) )
= $true )
| ( ( SV1
= ( g @ SV11 ) )
= $true )
| ( ( big_f @ SV1 @ ( f @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV4: $i,SV22: $i,SV14: $i] :
( ( ( ( h @ SV14 @ SV22 )
= SV22 )
= $false )
| ( ( ~ ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) ) )
= $true )
| ( ( big_f @ SV4 @ ( f @ SV14 ) )
= $true )
| ( ( SV4
= ( g @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV4: $i,SV22: $i,SV14: $i] :
( ( ( big_f @ ( h @ SV14 @ SV22 ) @ ( f @ SV14 ) )
= $false )
| ( ( ( h @ SV14 @ SV22 )
= SV22 )
= $false )
| ( ( big_f @ SV4 @ ( f @ SV14 ) )
= $true )
| ( ( SV4
= ( g @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(105,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,104,102,101,100,97,95,90,89,76,75]) ).
thf(106,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN075-1 : 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
% 0.10/0.18 % Computer : n009.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 17:16:32 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.23
% 0.10/0.23 No.of.Axioms: 10
% 0.10/0.23
% 0.10/0.23 Length.of.Defs: 0
% 0.10/0.23
% 0.10/0.23 Contains.Choice.Funs: false
% 0.10/0.23 ...
% 0.10/0.23
% 0.10/0.23 ********************************
% 0.10/0.23 * All subproblems solved! *
% 0.10/0.23 ********************************
% 0.10/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:105,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.23
% 0.10/0.23 %**** Beginning of derivation protocol ****
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23
% 0.10/0.23 %**** End of derivation protocol ****
% 0.10/0.23 %**** no. of clauses in derivation: 106 ****
% 0.10/0.23 %**** clause counter: 105 ****
% 0.10/0.23
% 0.10/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:105,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------