%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM008+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/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 10:12:00 AM UTC 2026
% Result : Theorem 30.08s 5.21s
% Output : CNFRefutation 30.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 132 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 879 ( 234 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1503 ( 360 ~; 228 |; 27 &; 864 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 316 ( 0 ^; 307 !; 9 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_goal,type,
goal: $o ).
thf(tp_rewrite,type,
rewrite: $i > $i > $o ).
thf(tp_sK1_SY37,type,
sK1_SY37: $i > $i > $i ).
thf(tp_sK2_SY42,type,
sK2_SY42: $i > $i > $i > $i ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i > $i > $i > $i ).
thf(tp_transitive_reflexive_rewrite,type,
transitive_reflexive_rewrite: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( transitive_reflexive_rewrite @ A @ B )
=> ( ( equalish @ A @ B )
| ? [C: $i] :
( ( rewrite @ A @ C )
& ( transitive_reflexive_rewrite @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_or_rewrite) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ a @ A )
& ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ih_cfl) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ A @ B )
& ( rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lo_cfl) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ B @ C ) )
=> ( transitive_reflexive_rewrite @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( rewrite @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_in_transitive_reflexive_rewrite) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(8,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(9,axiom,
( ( transitive_reflexive_rewrite @ a @ b )
& ( transitive_reflexive_rewrite @ a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).
thf(10,axiom,
! [A: $i] :
( ( ( transitive_reflexive_rewrite @ b @ A )
& ( transitive_reflexive_rewrite @ c @ A ) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',found) ).
thf(11,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(12,negated_conjecture,
goal = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
goal = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( transitive_reflexive_rewrite @ A @ B )
=> ( ( equalish @ A @ B )
| ? [C: $i] :
( ( rewrite @ A @ C )
& ( transitive_reflexive_rewrite @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ a @ A )
& ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ A @ B )
& ( rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ B @ C ) )
=> ( transitive_reflexive_rewrite @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( rewrite @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [A: $i] : ( equalish @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ( transitive_reflexive_rewrite @ a @ b )
& ( transitive_reflexive_rewrite @ a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( ( transitive_reflexive_rewrite @ b @ A )
& ( transitive_reflexive_rewrite @ c @ A ) )
=> goal ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ goal ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( ( transitive_reflexive_rewrite @ b @ A )
& ( transitive_reflexive_rewrite @ c @ A ) )
=> goal ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(26,plain,
( ( ( transitive_reflexive_rewrite @ a @ b )
& ( transitive_reflexive_rewrite @ a @ c ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [A: $i] : ( equalish @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( rewrite @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ B @ C ) )
=> ( transitive_reflexive_rewrite @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ A @ B )
& ( rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ a @ A )
& ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( transitive_reflexive_rewrite @ A @ B )
=> ( ( equalish @ A @ B )
| ? [C: $i] :
( ( rewrite @ A @ C )
& ( transitive_reflexive_rewrite @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ~ goal ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equalish @ SX0 @ SX1 )
| ( transitive_reflexive_rewrite @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( ~ ( transitive_reflexive_rewrite @ a @ b )
| ~ ( transitive_reflexive_rewrite @ a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( rewrite @ a @ SX0 )
| ~ ( transitive_reflexive_rewrite @ SX0 @ SX1 ) )
| ~ ( transitive_reflexive_rewrite @ SX0 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SX1 @ SX3 )
| ~ ( transitive_reflexive_rewrite @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equalish @ SX0 @ SX1 )
| ( equalish @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( transitive_reflexive_rewrite @ SX0 @ SX1 )
| ( equalish @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( rewrite @ SX0 @ SX2 )
| ~ ( transitive_reflexive_rewrite @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SX0 @ SX1 )
| ~ ( transitive_reflexive_rewrite @ SX1 @ SX2 ) )
| ( transitive_reflexive_rewrite @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rewrite @ SX0 @ SX1 )
| ( transitive_reflexive_rewrite @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(43,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( transitive_reflexive_rewrite @ b @ SX0 )
| ~ ( transitive_reflexive_rewrite @ c @ SX0 ) )
| goal ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rewrite @ SX0 @ SX1 )
| ~ ( rewrite @ SX0 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SX1 @ SX3 )
| ~ ( transitive_reflexive_rewrite @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(45,plain,
! [SV1: $i] :
( ( equalish @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(46,plain,
goal = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV2: $i] :
( ( ! [SY22: $i] :
( ~ ( equalish @ SV2 @ SY22 )
| ( transitive_reflexive_rewrite @ SV2 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
( ( ~ ( transitive_reflexive_rewrite @ a @ b )
| ~ ( transitive_reflexive_rewrite @ a @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(49,plain,
! [SV3: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ~ ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SY23 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SY24 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SY23 @ SX3 )
| ~ ( transitive_reflexive_rewrite @ SY24 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(50,plain,
! [SV4: $i] :
( ( ! [SY26: $i] :
( ~ ( equalish @ SV4 @ SY26 )
| ( equalish @ SY26 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(51,plain,
! [SV5: $i] :
( ( ! [SY27: $i] :
( ~ ( transitive_reflexive_rewrite @ SV5 @ SY27 )
| ( equalish @ SV5 @ SY27 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY28 )
| ~ ( transitive_reflexive_rewrite @ SY28 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(52,plain,
! [SV6: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV6 @ SY29 )
| ~ ( transitive_reflexive_rewrite @ SY29 @ SY30 ) )
| ( transitive_reflexive_rewrite @ SV6 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(53,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
( ~ ( rewrite @ SV7 @ SY31 )
| ( transitive_reflexive_rewrite @ SV7 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ b @ SV8 )
| ~ ( transitive_reflexive_rewrite @ c @ SV8 ) )
| goal )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV9: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ~ ( ~ ( rewrite @ SV9 @ SY32 )
| ~ ( rewrite @ SV9 @ SY33 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SY32 @ SX3 )
| ~ ( transitive_reflexive_rewrite @ SY33 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV10 )
| ( transitive_reflexive_rewrite @ SV2 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
( ( ~ ( transitive_reflexive_rewrite @ a @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ( transitive_reflexive_rewrite @ a @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(59,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SY35 ) )
| ~ ! [SY36: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY36 )
| ~ ( transitive_reflexive_rewrite @ SY35 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV12 )
| ( equalish @ SV12 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ( transitive_reflexive_rewrite @ SV5 @ SV13 )
| ( equalish @ SV5 @ SV13 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY37 )
| ~ ( transitive_reflexive_rewrite @ SY37 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 )
| ~ ( transitive_reflexive_rewrite @ SV14 @ SY38 ) )
| ( transitive_reflexive_rewrite @ SV6 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( rewrite @ SV7 @ SV15 )
| ( transitive_reflexive_rewrite @ SV7 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ b @ SV8 )
| ~ ( transitive_reflexive_rewrite @ c @ SV8 ) ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( rewrite @ SV9 @ SV16 )
| ~ ( rewrite @ SV9 @ SY39 ) )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY40 )
| ~ ( transitive_reflexive_rewrite @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV10 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(67,plain,
( ( transitive_reflexive_rewrite @ a @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(68,plain,
( ( transitive_reflexive_rewrite @ a @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(69,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
| ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV12 ) )
= $true )
| ( ( equalish @ SV12 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV5 @ SV13 ) )
= $true )
| ( ( ( equalish @ SV5 @ SV13 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY37 )
| ~ ( transitive_reflexive_rewrite @ SY37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 )
| ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) )
| ( transitive_reflexive_rewrite @ SV6 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( rewrite @ SV7 @ SV15 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( transitive_reflexive_rewrite @ b @ SV8 )
| ~ ( transitive_reflexive_rewrite @ c @ SV8 ) ) )
= $false )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ~ ~ ( ~ ( rewrite @ SV9 @ SV16 )
| ~ ( rewrite @ SV9 @ SV19 ) )
| ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV10: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV10 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV12: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV12 )
= $false )
| ( ( equalish @ SV12 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV13: $i,SV5: $i] :
( ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false )
| ( ( ( equalish @ SV5 @ SV13 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY37 )
| ~ ( transitive_reflexive_rewrite @ SY37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 )
| ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV15: $i,SV7: $i] :
( ( ( rewrite @ SV7 @ SV15 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV8: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ b @ SV8 )
| ~ ( transitive_reflexive_rewrite @ c @ SV8 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( rewrite @ SV9 @ SV16 )
| ~ ( rewrite @ SV9 @ SV19 ) ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) ) )
= $false )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV13: $i,SV5: $i] :
( ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY37 )
| ~ ( transitive_reflexive_rewrite @ SY37 @ SV13 ) ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 )
| ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV8: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ b @ SV8 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ c @ SV8 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( ~ ( rewrite @ SV9 @ SV16 )
| ~ ( rewrite @ SV9 @ SV19 ) ) )
= $false )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(90,plain,
! [SV13: $i,SV5: $i] :
( ( ( ! [SY37: $i] :
~ ~ ( ~ ( rewrite @ SV5 @ SY37 )
| ~ ( transitive_reflexive_rewrite @ SY37 @ SV13 ) ) )
= $false )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 )
| ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(92,plain,
! [SV8: $i] :
( ( ( transitive_reflexive_rewrite @ b @ SV8 )
= $false )
| ( ( ~ ( transitive_reflexive_rewrite @ c @ SV8 ) )
= $true )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( rewrite @ SV9 @ SV16 )
| ~ ( rewrite @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rewrite @ SV5 @ ( sK1_SY37 @ SV13 @ SV5 ) )
| ~ ( transitive_reflexive_rewrite @ ( sK1_SY37 @ SV13 @ SV5 ) @ SV13 ) ) )
= $false )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(96,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV6 @ SV14 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV8: $i] :
( ( ( transitive_reflexive_rewrite @ c @ SV8 )
= $false )
| ( ( transitive_reflexive_rewrite @ b @ SV8 )
= $false )
| ( goal = $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( rewrite @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ( rewrite @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) ) )
= $false )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( ~ ( rewrite @ SV5 @ ( sK1_SY37 @ SV13 @ SV5 ) )
| ~ ( transitive_reflexive_rewrite @ ( sK1_SY37 @ SV13 @ SV5 ) @ SV13 ) ) )
= $true )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( transitive_reflexive_rewrite @ SV6 @ SV14 )
= $false )
| ( ( ~ ( transitive_reflexive_rewrite @ SV14 @ SV18 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( ~ ( rewrite @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( rewrite @ a @ SV3 )
| ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( rewrite @ SV5 @ ( sK1_SY37 @ SV13 @ SV5 ) )
| ~ ( transitive_reflexive_rewrite @ ( sK1_SY37 @ SV13 @ SV5 ) @ SV13 ) )
= $false )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV6: $i,SV18: $i,SV14: $i] :
( ( ( transitive_reflexive_rewrite @ SV14 @ SV18 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV14 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV16: $i,SV19: $i,SV9: $i] :
( ( ( rewrite @ SV9 @ SV19 )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( rewrite @ a @ SV3 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( rewrite @ SV5 @ ( sK1_SY37 @ SV13 @ SV5 ) ) )
= $false )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV5: $i,SV13: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ ( sK1_SY37 @ SV13 @ SV5 ) @ SV13 ) )
= $false )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(110,plain,
! [SV9: $i,SV19: $i,SV16: $i] :
( ( ( ! [SY42: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ SY42 )
| ~ ( transitive_reflexive_rewrite @ SV19 @ SY42 ) ) )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( rewrite @ a @ SV3 )
= $false )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV13: $i,SV5: $i] :
( ( ( rewrite @ SV5 @ ( sK1_SY37 @ SV13 @ SV5 ) )
= $true )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV5: $i,SV13: $i] :
( ( ( transitive_reflexive_rewrite @ ( sK1_SY37 @ SV13 @ SV5 ) @ SV13 )
= $true )
| ( ( equalish @ SV5 @ SV13 )
= $true )
| ( ( transitive_reflexive_rewrite @ SV5 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(114,plain,
! [SV19: $i,SV9: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) )
| ~ ( transitive_reflexive_rewrite @ SV19 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) ) ) )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(115,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( ~ ( transitive_reflexive_rewrite @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV19: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( ~ ( transitive_reflexive_rewrite @ SV16 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) )
| ~ ( transitive_reflexive_rewrite @ SV19 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) ) ) )
= $true )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(117,plain,
! [SV11: $i,SV17: $i,SV3: $i] :
( ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV19: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV16 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) )
| ~ ( transitive_reflexive_rewrite @ SV19 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) ) )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV3: $i,SV17: $i,SV11: $i] :
( ( ( ! [SY41: $i] :
~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ SY41 )
| ~ ( transitive_reflexive_rewrite @ SV17 @ SY41 ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(120,plain,
! [SV19: $i,SV9: $i,SV16: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV16 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) ) )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(121,plain,
! [SV16: $i,SV9: $i,SV19: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV19 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) ) )
= $false )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(122,plain,
! [SV17: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV17 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(123,plain,
! [SV19: $i,SV9: $i,SV16: $i] :
( ( ( transitive_reflexive_rewrite @ SV16 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) )
= $true )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(124,plain,
! [SV16: $i,SV9: $i,SV19: $i] :
( ( ( transitive_reflexive_rewrite @ SV19 @ ( sK2_SY42 @ SV9 @ SV19 @ SV16 ) )
= $true )
| ( ( rewrite @ SV9 @ SV16 )
= $false )
| ( ( rewrite @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(125,plain,
! [SV17: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( transitive_reflexive_rewrite @ SV11 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV17 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) ) ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(126,plain,
! [SV17: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV11 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) )
| ~ ( transitive_reflexive_rewrite @ SV17 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(127,plain,
! [SV17: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV11 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(128,plain,
! [SV11: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( transitive_reflexive_rewrite @ SV17 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) ) )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(129,plain,
! [SV17: $i,SV3: $i,SV11: $i] :
( ( ( transitive_reflexive_rewrite @ SV11 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(130,plain,
! [SV11: $i,SV3: $i,SV17: $i] :
( ( ( transitive_reflexive_rewrite @ SV17 @ ( sK3_SY41 @ SV3 @ SV17 @ SV11 ) )
= $true )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV11 )
= $false )
| ( ( rewrite @ a @ SV3 )
= $false )
| ( ( transitive_reflexive_rewrite @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(131,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,130,129,124,123,113,112,105,97,81,78,76,68,67,46]) ).
thf(132,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 18:37:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.08/5.21
% 30.08/5.21 No.of.Axioms: 10
% 30.08/5.21
% 30.08/5.21 Length.of.Defs: 0
% 30.08/5.21
% 30.08/5.21 Contains.Choice.Funs: false
% 30.08/5.21 ...
% 30.08/5.21
% 30.08/5.21 ********************************
% 30.08/5.21 * All subproblems solved! *
% 30.08/5.21 ********************************
% 30.08/5.21 % SZS status Theorem for /export/starexec/sandbox/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:131,loop_count:0,foatp_calls:1,translation:fof_full)
% 30.08/5.21
% 30.08/5.21 %**** Beginning of derivation protocol ****
% 30.08/5.21 % SZS output start CNFRefutation
% See solution above
% 30.08/5.21
% 30.08/5.21 %**** End of derivation protocol ****
% 30.08/5.21 %**** no. of clauses in derivation: 132 ****
% 30.08/5.21 %**** clause counter: 131 ****
% 30.08/5.21
% 30.08/5.21 % SZS status Theorem for /export/starexec/sandbox/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:131,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------