%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n004.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 10:36:57 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 5
% Syntax : Number of formulae : 87 ( 43 unt; 0 typ; 4 def)
% Number of atoms : 819 ( 554 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 1966 ( 971 ~; 368 |; 39 &; 580 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 411 ( 11 ^; 380 !; 20 ?; 411 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c1,type,
c1: $i ).
thf(tp_cCKB_FIN,type,
cCKB_FIN: ( $i > $i > $o ) > $o ).
thf(tp_cCKB_INF,type,
cCKB_INF: ( $i > $i > $o ) > $o ).
thf(tp_cCKB_INJ,type,
cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
thf(tp_cCKB_XPL,type,
cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $i > $i > $i > $o ).
thf(tp_sK2_SY49,type,
sK2_SY49: $i ).
thf(tp_sK3_SY61,type,
sK3_SY61: $i ).
thf(tp_sK4_SY100,type,
sK4_SY100: $i > $i > $i ).
thf(tp_sK5_SY102,type,
sK5_SY102: $i > $i > $i ).
thf(cCKB_FIN,definition,
( cCKB_FIN
= ( ^ [Xk: $i > $i > $o] :
~ ( cCKB_INF @ Xk ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_FIN_def) ).
thf(cCKB_INF,definition,
( cCKB_INF
= ( ^ [Xk: $i > $i > $o] :
? [Xh: $i > $i > $i > $i > $o,Xm: $i,Xn: $i] :
( ( cCKB_INJ @ Xh )
& ( cCKB_XPL @ Xh @ Xk @ Xm @ Xn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_INF_def) ).
thf(cCKB_INJ,definition,
( cCKB_INJ
= ( ^ [Xh: $i > $i > $i > $i > $o] :
! [Xx1: $i,Xy1: $i,Xx2: $i,Xy2: $i,Xu: $i,Xv: $i] :
( ( ( Xh @ Xx1 @ Xy1 @ Xu @ Xv )
& ( Xh @ Xx2 @ Xy2 @ Xu @ Xv ) )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_INJ_def) ).
thf(cCKB_XPL,definition,
( cCKB_XPL
= ( ^ [Xh: $i > $i > $i > $i > $o,Xk: $i > $i > $o,Xm: $i,Xn: $i] :
( ( Xk @ Xm @ Xn )
& ! [Xx: $i,Xy: $i] :
( ( Xk @ Xx @ Xy )
=> ? [Xu: $i,Xv: $i] :
( ( Xh @ Xx @ Xy @ Xu @ Xv )
& ( Xk @ Xu @ Xv )
& ~ ( ( Xu = Xm )
& ( Xv = Xn ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_XPL_def) ).
thf(1,conjecture,
( cCKB_FIN
@ ^ [Xu: $i,Xv: $i] :
( ( Xu = c1 )
& ( Xv = c1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cL3000) ).
thf(2,negated_conjecture,
( ( cCKB_FIN
@ ^ [Xu: $i,Xv: $i] :
( ( Xu = c1 )
& ( Xv = c1 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ? [SY2: $i > $i > $i > $i > $o,SY3: $i,SY4: $i] :
( ! [SY5: $i,SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
( ( ( SY2 @ SY5 @ SY6 @ SY9 @ SY10 )
& ( SY2 @ SY7 @ SY8 @ SY9 @ SY10 ) )
=> ( ( SY5 = SY7 )
& ( SY6 = SY8 ) ) )
& ( SY3 = c1 )
& ( SY4 = c1 )
& ! [SY32: $i,SY33: $i] :
( ( ( SY32 = c1 )
& ( SY33 = c1 ) )
=> ? [SY34: $i,SY35: $i] :
( ( SY2 @ SY32 @ SY33 @ SY34 @ SY35 )
& ( SY34 = c1 )
& ( SY35 = c1 )
& ~ ( ( SY34 = SY3 )
& ( SY35 = SY4 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cCKB_FIN,cCKB_INF,cCKB_INJ,cCKB_XPL]) ).
thf(4,plain,
( ( ? [SY2: $i > $i > $i > $i > $o,SY3: $i,SY4: $i] :
( ! [SY5: $i,SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
( ( ( SY2 @ SY5 @ SY6 @ SY9 @ SY10 )
& ( SY2 @ SY7 @ SY8 @ SY9 @ SY10 ) )
=> ( ( SY5 = SY7 )
& ( SY6 = SY8 ) ) )
& ( SY3 = c1 )
& ( SY4 = c1 )
& ! [SY32: $i,SY33: $i] :
( ( ( SY32 = c1 )
& ( SY33 = c1 ) )
=> ? [SY34: $i,SY35: $i] :
( ( SY2 @ SY32 @ SY33 @ SY34 @ SY35 )
& ( SY34 = c1 )
& ( SY35 = c1 )
& ~ ( ( SY34 = SY3 )
& ( SY35 = SY4 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [SY2: $i > $i > $i > $i > $o,SY3: $i,SY4: $i] :
( ! [SY5: $i,SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
( ( ( SY2 @ SY5 @ SY6 @ SY9 @ SY10 )
& ( SY2 @ SY7 @ SY8 @ SY9 @ SY10 ) )
=> ( ( SY5 = SY7 )
& ( SY6 = SY8 ) ) )
& ( SY3 = c1 )
& ( SY4 = c1 )
& ! [SY32: $i,SY33: $i] :
( ( ( SY32 = c1 )
& ( SY33 = c1 ) )
=> ? [SY34: $i,SY35: $i] :
( ( SY2 @ SY32 @ SY33 @ SY34 @ SY35 )
& ( SY34 = c1 )
& ( SY35 = c1 )
& ~ ( ( SY34 = SY3 )
& ( SY35 = SY4 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ! [SX0: $i > $i > $i > $i > $o] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ! [SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ( SX0 @ SX3 @ SX4 @ SX7 @ SX8 )
| ~ ( SX0 @ SX5 @ SX6 @ SX7 @ SX8 ) )
| ~ ( ( SX3 != SX5 )
| ( SX4 != SX6 ) ) )
| ~ ~ ( ~ ~ ( ( SX1 != c1 )
| ( SX2 != c1 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ( SX3 != c1 )
| ( SX4 != c1 ) )
| ~ ! [SX5: $i] :
~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( SX0 @ SX3 @ SX4 @ SX5 @ SX6 )
| ~ ~ ( ( SX5 != c1 )
| ( SX6 != c1 ) ) )
| ~ ~ ~ ( ( SX5 != SX1 )
| ( SX6 != SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,cCKB_FIN,cCKB_INF,cCKB_INJ,cCKB_XPL]) ).
thf(7,plain,
( ( ! [SX0: $i > $i > $i > $i > $o] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ! [SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ( SX0 @ SX3 @ SX4 @ SX7 @ SX8 )
| ~ ( SX0 @ SX5 @ SX6 @ SX7 @ SX8 ) )
| ~ ( ( SX3 != SX5 )
| ( SX4 != SX6 ) ) )
| ~ ~ ( ~ ~ ( ( SX1 != c1 )
| ( SX2 != c1 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ( SX3 != c1 )
| ( SX4 != c1 ) )
| ~ ! [SX5: $i] :
~ ~ ! [SX6: $i] :
~ ~ ( ~ ~ ( ~ ( SX0 @ SX3 @ SX4 @ SX5 @ SX6 )
| ~ ~ ( ( SX5 != c1 )
| ( SX6 != c1 ) ) )
| ~ ~ ~ ( ( SX5 != SX1 )
| ( SX6 != SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( SY49 != c1 )
| ( SY50 != c1 ) )
| ~ ! [SY57: $i,SY58: $i] :
( ~ ~ ( ( SY57 != c1 )
| ( SY58 != c1 ) )
| ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY57 @ SY58 @ SY59 @ SY60 )
| ~ ~ ( ( SY59 != c1 )
| ( SY60 != c1 ) ) )
| ~ ~ ~ ( ( SY59 != SY49 )
| ( SY60 != SY50 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ~ ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( SY49 != c1 )
| ( SY50 != c1 ) )
| ~ ! [SY57: $i,SY58: $i] :
( ~ ~ ( ( SY57 != c1 )
| ( SY58 != c1 ) )
| ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY57 @ SY58 @ SY59 @ SY60 )
| ~ ~ ( ( SY59 != c1 )
| ( SY60 != c1 ) ) )
| ~ ~ ~ ( ( SY59 != SY49 )
| ( SY60 != SY50 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( SY49 != c1 )
| ( SY50 != c1 ) )
| ~ ! [SY57: $i,SY58: $i] :
( ~ ~ ( ( SY57 != c1 )
| ( SY58 != c1 ) )
| ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY57 @ SY58 @ SY59 @ SY60 )
| ~ ~ ( ( SY59 != c1 )
| ( SY60 != c1 ) ) )
| ~ ~ ~ ( ( SY59 != SY49 )
| ( SY60 != SY50 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( SY61 != c1 ) )
| ~ ! [SY68: $i,SY69: $i] :
( ~ ~ ( ( SY68 != c1 )
| ( SY69 != c1 ) )
| ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY68 @ SY69 @ SY70 @ SY71 )
| ~ ~ ( ( SY70 != c1 )
| ( SY71 != c1 ) ) )
| ~ ~ ~ ( ( SY70 != sK2_SY49 )
| ( SY71 != SY61 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ~ ! [SY61: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( SY61 != c1 ) )
| ~ ! [SY68: $i,SY69: $i] :
( ~ ~ ( ( SY68 != c1 )
| ( SY69 != c1 ) )
| ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY68 @ SY69 @ SY70 @ SY71 )
| ~ ~ ( ( SY70 != c1 )
| ( SY71 != c1 ) ) )
| ~ ~ ~ ( ( SY70 != sK2_SY49 )
| ( SY71 != SY61 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY61: $i] :
~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( SY61 != c1 ) )
| ~ ! [SY68: $i,SY69: $i] :
( ~ ~ ( ( SY68 != c1 )
| ( SY69 != c1 ) )
| ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY68 @ SY69 @ SY70 @ SY71 )
| ~ ~ ( ( SY70 != c1 )
| ( SY71 != c1 ) ) )
| ~ ~ ~ ( ( SY70 != sK2_SY49 )
| ( SY71 != SY61 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( ~ ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) )
| ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
( ( ~ ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SY51 @ SY52 @ SY55 @ SY56 )
| ~ ( sK1_SX0 @ SY53 @ SY54 @ SY55 @ SY56 ) )
| ~ ( ( SY51 != SY53 )
| ( SY52 != SY54 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i,SY85: $i,SY86: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SY82 @ SY85 @ SY86 )
| ~ ( sK1_SX0 @ SY83 @ SY84 @ SY85 @ SY86 ) )
| ~ ( ( SV1 != SY83 )
| ( SY82 != SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
| ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SY89 @ SY90 )
| ~ ( sK1_SX0 @ SY87 @ SY88 @ SY89 @ SY90 ) )
| ~ ( ( SV1 != SY87 )
| ( SV2 != SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SY92 @ SY93 )
| ~ ( sK1_SX0 @ SV3 @ SY91 @ SY92 @ SY93 ) )
| ~ ( ( SV1 != SV3 )
| ( SV2 != SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SY78: $i,SY79: $i] :
( ~ ~ ( ( SY78 != c1 )
| ( SY79 != c1 ) )
| ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SY78 @ SY79 @ SY80 @ SY81 )
| ~ ~ ( ( SY80 != c1 )
| ( SY81 != c1 ) ) )
| ~ ~ ~ ( ( SY80 != sK2_SY49 )
| ( SY81 != sK3_SY61 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SY94 @ SY95 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SY94 @ SY95 ) )
| ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( sK2_SY49 != c1 )
| ( sK3_SY61 != c1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV5: $i] :
( ( ! [SY96: $i] :
( ~ ~ ( ( SV5 != c1 )
| ( SY96 != c1 ) )
| ~ ! [SY97: $i] :
~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SY96 @ SY97 @ SY98 )
| ~ ~ ( ( SY97 != c1 )
| ( SY98 != c1 ) ) )
| ~ ~ ~ ( ( SY97 != sK2_SY49 )
| ( SY98 != sK3_SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i,SV3: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ! [SY99: $i] :
( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SY99 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SY99 ) )
| ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( sK2_SY49 != c1 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( sK3_SY61 != c1 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV7: $i,SV5: $i] :
( ( ~ ~ ( ( SV5 != c1 )
| ( SV7 != c1 ) )
| ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) )
| ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( sK2_SY49 = c1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( sK3_SY61 = c1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != c1 )
| ( SV7 != c1 ) ) )
= $true )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) ) )
= $true )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != c1 )
| ( SV7 != c1 ) ) )
= $false )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) ) )
= $false )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV7: $i,SV5: $i] :
( ( ( ( SV5 != c1 )
| ( SV7 != c1 ) )
= $true )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
| ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV7: $i,SV5: $i] :
( ( ( SV5 != c1 )
= $true )
| ( ( SV7 != c1 )
= $true )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV7: $i,SV5: $i] :
( ( ( SV5 = c1 )
= $false )
| ( ( SV7 != c1 )
= $true )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: $i,SV3: $i,SV8: $i,SV6: $i,SV2: $i,SV1: $i] :
( ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV5: $i,SV7: $i] :
( ( ( SV7 = c1 )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV2: $i,SV1: $i,SV8: $i,SV6: $i,SV4: $i,SV3: $i] :
( ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( ( SV1 != SV3 )
| ( SV2 != SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV7: $i,SV5: $i] :
( ( ( ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ SY100 @ SY101 )
| ~ ~ ( ( SY100 != c1 )
| ( SY101 != c1 ) ) )
| ~ ~ ~ ( ( SY100 != sK2_SY49 )
| ( SY101 != sK3_SY61 ) ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV8: $i,SV6: $i,SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( ( SV1 != SV3 )
| ( SV2 != SV4 ) )
= $false )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ SY102 )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( SY102 != c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( SY102 != sK3_SY61 ) ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV4: $i,SV8: $i,SV6: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( SV1 != SV3 )
= $false )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV3: $i,SV8: $i,SV6: $i,SV1: $i,SV4: $i,SV2: $i] :
( ( ( SV2 != SV4 )
= $false )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ! [SY102: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ SY102 )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( SY102 != c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( SY102 != sK3_SY61 ) ) ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: $i,SV8: $i,SV6: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( SV1 = SV3 )
= $true )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV3: $i,SV8: $i,SV6: $i,SV1: $i,SV4: $i,SV2: $i] :
( ( ( SV2 = SV4 )
= $true )
| ( ( sK1_SX0 @ SV1 @ SV2 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SX0 @ SV3 @ SV4 @ SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV7: $i,SV5: $i] :
( ( ( ! [SY102: $i] :
~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ SY102 )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( SY102 != c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( SY102 != sK3_SY61 ) ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(61,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(62,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
| ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(64,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(65,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(67,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
| ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(69,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(70,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(72,plain,
! [SV7: $i,SV5: $i] :
( ( ( sK1_SX0 @ SV5 @ SV7 @ ( sK4_SY100 @ SV7 @ SV5 ) @ ( sK5_SY102 @ SV7 @ SV5 ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) ) )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= sK2_SY49 )
= $true )
| ( ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
| ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 ) )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK4_SY100 @ SV7 @ SV5 )
= sK2_SY49 )
= $false )
| ( ( ( sK5_SY102 @ SV7 @ SV5 )
!= sK3_SY61 )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(77,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK4_SY100 @ SV7 @ SV5 )
!= c1 )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(78,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK5_SY102 @ SV7 @ SV5 )
!= c1 )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK5_SY102 @ SV7 @ SV5 )
= sK3_SY61 )
= $false )
| ( ( ( sK4_SY100 @ SV7 @ SV5 )
= sK2_SY49 )
= $false )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK4_SY100 @ SV7 @ SV5 )
= c1 )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(81,plain,
! [SV5: $i,SV7: $i] :
( ( ( ( sK5_SY102 @ SV7 @ SV5 )
= c1 )
= $true )
| ( ( SV5 = c1 )
= $false )
| ( ( SV7 = c1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(82,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,81,80,79,72,58,57,38]) ).
thf(83,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:00:09 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24
% 0.09/0.24 No.of.Axioms: 0
% 0.09/0.24
% 0.09/0.24 Length.of.Defs: 969
% 0.09/0.24
% 0.09/0.24 Contains.Choice.Funs: false
% 0.09/0.24 ....
% 0.09/0.24
% 0.09/0.24 ********************************
% 0.09/0.24 * All subproblems solved! *
% 0.09/0.24 ********************************
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:82,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.24
% 0.09/0.24 %**** Beginning of derivation protocol ****
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24
% 0.09/0.24 %**** End of derivation protocol ****
% 0.09/0.24 %**** no. of clauses in derivation: 83 ****
% 0.09/0.24 %**** clause counter: 82 ****
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:82,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------