%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET848-2 : 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 : n011.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 10:42:07 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 73 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 778 ( 44 ~; 48 |; 0 &; 686 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 132 ( 0 ^; 132 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Union,type,
c_Union: $i > $i > $i ).
thf(tp_c_Zorn_OTFin,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(tp_c_Zorn_Ochain,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(tp_c_Zorn_Omaxchain,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(tp_c_Zorn_Osucc,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(1,axiom,
! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_minus @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_Osucc @ V_S @ V_c @ T_a )
!= V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
thf(2,axiom,
! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
thf(3,axiom,
! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
thf(4,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(5,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a )
= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,negated_conjecture,
~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_minus @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_Osucc @ V_S @ V_c @ T_a )
!= V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a )
= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( ~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_minus @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_Osucc @ V_S @ V_c @ T_a )
!= V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(21,plain,
( ( ~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(22,plain,
( ( ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a )
= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(25,plain,
( ( ! [V_Y: $i,V_S: $i,T_a: $i] :
( ~ ( c_lessequals @ V_Y @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) )
| ( c_in @ ( c_Union @ V_Y @ ( tc_set @ T_a ) ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(26,plain,
( ( ! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [V_c: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_minus @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ T_a ) ) ) ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_Osucc @ V_S @ V_c @ T_a )
!= V_c ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(28,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(29,plain,
( ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( c_in @ SV1 @ SY15 @ SY16 )
| ! [SY17: $i] :
( ( c_in @ SV1 @ SY17 @ SY16 )
| ( c_in @ SV1 @ ( c_minus @ SY15 @ SY17 @ ( tc_set @ SY16 ) ) @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY18: $i] : ( c_lessequals @ SV2 @ SV2 @ ( tc_set @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ( c_lessequals @ SV3 @ ( c_Zorn_OTFin @ SY19 @ SY20 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY20 ) ) ) )
| ( c_in @ ( c_Union @ SV3 @ ( tc_set @ SY20 ) ) @ ( c_Zorn_OTFin @ SY19 @ SY20 ) @ ( tc_set @ ( tc_set @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV4: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( c_in @ SV4 @ ( c_Zorn_OTFin @ SY21 @ SY22 ) @ ( tc_set @ ( tc_set @ SY22 ) ) )
| ( c_in @ SV4 @ ( c_Zorn_Ochain @ SY21 @ SY22 ) @ ( tc_set @ ( tc_set @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV5: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SY23 @ SY24 ) @ ( c_Zorn_Omaxchain @ SY23 @ SY24 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY24 ) ) ) ) @ ( tc_set @ ( tc_set @ SY24 ) ) )
| ( ( c_Zorn_Osucc @ SY23 @ SV5 @ SY24 )
!= SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY25: $i] :
( ~ ( c_in @ SV1 @ SV6 @ SY25 )
| ! [SY26: $i] :
( ( c_in @ SV1 @ SY26 @ SY25 )
| ( c_in @ SV1 @ ( c_minus @ SV6 @ SY26 @ ( tc_set @ SY25 ) ) @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV7: $i,SV2: $i] :
( ( c_lessequals @ SV2 @ SV2 @ ( tc_set @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY27: $i] :
( ~ ( c_lessequals @ SV3 @ ( c_Zorn_OTFin @ SV8 @ SY27 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY27 ) ) ) )
| ( c_in @ ( c_Union @ SV3 @ ( tc_set @ SY27 ) ) @ ( c_Zorn_OTFin @ SV8 @ SY27 ) @ ( tc_set @ ( tc_set @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( c_in @ SV4 @ ( c_Zorn_OTFin @ SV9 @ SY28 ) @ ( tc_set @ ( tc_set @ SY28 ) ) )
| ( c_in @ SV4 @ ( c_Zorn_Ochain @ SV9 @ SY28 ) @ ( tc_set @ ( tc_set @ SY28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY29: $i] :
( ~ ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SV10 @ SY29 ) @ ( c_Zorn_Omaxchain @ SV10 @ SY29 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SY29 ) ) ) ) @ ( tc_set @ ( tc_set @ SY29 ) ) )
| ( ( c_Zorn_Osucc @ SV10 @ SV5 @ SY29 )
!= SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ SV6 @ SV11 )
| ! [SY30: $i] :
( ( c_in @ SV1 @ SY30 @ SV11 )
| ( c_in @ SV1 @ ( c_minus @ SV6 @ SY30 @ ( tc_set @ SV11 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ~ ( c_lessequals @ SV3 @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV12 ) ) ) )
| ( c_in @ ( c_Union @ SV3 @ ( tc_set @ SV12 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ ( c_Zorn_OTFin @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) )
| ( c_in @ SV4 @ ( c_Zorn_Ochain @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SV10 @ SV14 ) @ ( c_Zorn_Omaxchain @ SV10 @ SV14 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV14 ) ) ) ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
| ( ( c_Zorn_Osucc @ SV10 @ SV5 @ SV14 )
!= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ SV6 @ SV11 ) )
= $true )
| ( ( ! [SY30: $i] :
( ( c_in @ SV1 @ SY30 @ SV11 )
| ( c_in @ SV1 @ ( c_minus @ SV6 @ SY30 @ ( tc_set @ SV11 ) ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( c_lessequals @ SV3 @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV12 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Union @ SV3 @ ( tc_set @ SV12 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ ( c_Zorn_OTFin @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) ) )
= $true )
| ( ( c_in @ SV4 @ ( c_Zorn_Ochain @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SV10 @ SV14 ) @ ( c_Zorn_Omaxchain @ SV10 @ SV14 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV14 ) ) ) ) @ ( tc_set @ ( tc_set @ SV14 ) ) ) )
= $true )
| ( ( ( c_Zorn_Osucc @ SV10 @ SV5 @ SV14 )
!= SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ SV1 @ SV6 @ SV11 )
= $false )
| ( ( ! [SY30: $i] :
( ( c_in @ SV1 @ SY30 @ SV11 )
| ( c_in @ SV1 @ ( c_minus @ SV6 @ SY30 @ ( tc_set @ SV11 ) ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( c_lessequals @ SV3 @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV12 ) ) ) )
= $false )
| ( ( c_in @ ( c_Union @ SV3 @ ( tc_set @ SV12 ) ) @ ( c_Zorn_OTFin @ SV8 @ SV12 ) @ ( tc_set @ ( tc_set @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( c_in @ SV4 @ ( c_Zorn_OTFin @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) )
= $false )
| ( ( c_in @ SV4 @ ( c_Zorn_Ochain @ SV9 @ SV13 ) @ ( tc_set @ ( tc_set @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SV10 @ SV14 ) @ ( c_Zorn_Omaxchain @ SV10 @ SV14 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV14 ) ) ) ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
= $false )
| ( ( ( c_Zorn_Osucc @ SV10 @ SV5 @ SV14 )
!= SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV6: $i,SV11: $i,SV15: $i,SV1: $i] :
( ( ( ( c_in @ SV1 @ SV15 @ SV11 )
| ( c_in @ SV1 @ ( c_minus @ SV6 @ SV15 @ ( tc_set @ SV11 ) ) @ SV11 ) )
= $true )
| ( ( c_in @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV14: $i,SV5: $i,SV10: $i] :
( ( ( ( c_Zorn_Osucc @ SV10 @ SV5 @ SV14 )
= SV5 )
= $false )
| ( ( c_in @ SV5 @ ( c_minus @ ( c_Zorn_Ochain @ SV10 @ SV14 ) @ ( c_Zorn_Omaxchain @ SV10 @ SV14 ) @ ( tc_set @ ( tc_set @ ( tc_set @ SV14 ) ) ) ) @ ( tc_set @ ( tc_set @ SV14 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: $i,SV11: $i,SV15: $i,SV1: $i] :
( ( ( c_in @ SV1 @ SV15 @ SV11 )
= $true )
| ( ( c_in @ SV1 @ ( c_minus @ SV6 @ SV15 @ ( tc_set @ SV11 ) ) @ SV11 )
= $true )
| ( ( c_in @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,55,54,51,50,37,35,29]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET848-2 : 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
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 14:54:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 7
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21 .
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 57 ****
% 0.08/0.22 %**** clause counter: 56 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------