%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET822-2 : 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 : 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 10:41:26 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.20s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 59 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 338 ( 34 ~; 35 |; 0 &; 269 @)
% ( 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 : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_tc_IntDef_Oint,type,
tc_IntDef_Oint: $i ).
thf(tp_v_P,type,
v_P: $i > $o ).
thf(tp_v_b,type,
v_b: $i ).
thf(tp_v_f,type,
v_f: $i > $i ).
thf(tp_v_x,type,
v_x: $i > $i > $i ).
thf(1,axiom,
! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
| ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(2,axiom,
! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(3,axiom,
! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
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,
! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ V_U @ V_V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(7,negated_conjecture,
! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ V_U @ V_V ) @ V_V @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,negated_conjecture,
v_P @ ( v_f @ v_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
| ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ V_U @ V_V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ V_U @ V_V ) @ V_V @ tc_IntDef_Oint ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( v_P @ ( v_f @ v_b ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( v_P @ ( v_f @ v_b ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ V_U @ V_V ) @ V_V @ tc_IntDef_Oint ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [V_U: $i,V_V: $i] :
( ~ ( c_in @ ( v_f @ V_U ) @ V_V @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ V_U @ V_V ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
| ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( c_in @ ( v_f @ SV1 ) @ SY13 @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ SV1 @ SY13 ) @ SY13 @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ~ ( c_in @ ( v_f @ SV2 ) @ SY14 @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ SV2 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
~ ( c_in @ SV3 @ c_emptyset @ SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV4: $i] :
( ( ! [SY16: $i,SY17: $i] : ( c_in @ SV4 @ ( c_insert @ SV4 @ SY16 @ SY17 ) @ SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ~ ( c_in @ SV5 @ ( c_insert @ SY18 @ SY19 @ SY20 ) @ SY20 )
| ( c_in @ SV5 @ SY19 @ SY20 )
| ( SV5 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( c_in @ ( v_f @ SV1 ) @ SV6 @ tc_IntDef_Oint )
| ( c_in @ ( v_x @ SV1 @ SV6 ) @ SV6 @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( c_in @ ( v_f @ SV2 ) @ SV7 @ tc_IntDef_Oint )
| ~ ( v_P @ ( v_x @ SV2 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ c_emptyset @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY21: $i] : ( c_in @ SV4 @ ( c_insert @ SV4 @ SV9 @ SY21 ) @ SY21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( c_in @ SV5 @ ( c_insert @ SV10 @ SY22 @ SY23 ) @ SY23 )
| ( c_in @ SV5 @ SY22 @ SY23 )
| ( SV5 = SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( v_f @ SV1 ) @ SV6 @ tc_IntDef_Oint ) )
= $true )
| ( ( c_in @ ( v_x @ SV1 @ SV6 ) @ SV6 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( c_in @ ( v_f @ SV2 ) @ SV7 @ tc_IntDef_Oint ) )
= $true )
| ( ( ~ ( v_P @ ( v_x @ SV2 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV8: $i,SV3: $i] :
( ( c_in @ SV3 @ c_emptyset @ SV8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( c_in @ SV4 @ ( c_insert @ SV4 @ SV9 @ SV11 ) @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ! [SY24: $i] :
( ~ ( c_in @ SV5 @ ( c_insert @ SV10 @ SV12 @ SY24 ) @ SY24 )
| ( c_in @ SV5 @ SV12 @ SY24 )
| ( SV5 = SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV6: $i,SV1: $i] :
( ( ( c_in @ ( v_f @ SV1 ) @ SV6 @ tc_IntDef_Oint )
= $false )
| ( ( c_in @ ( v_x @ SV1 @ SV6 ) @ SV6 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV7: $i,SV2: $i] :
( ( ( c_in @ ( v_f @ SV2 ) @ SV7 @ tc_IntDef_Oint )
= $false )
| ( ( ~ ( v_P @ ( v_x @ SV2 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ ( c_insert @ SV10 @ SV12 @ SV13 ) @ SV13 )
| ( c_in @ SV5 @ SV12 @ SV13 )
| ( SV5 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV7: $i,SV2: $i] :
( ( ( v_P @ ( v_x @ SV2 @ SV7 ) )
= $false )
| ( ( c_in @ ( v_f @ SV2 ) @ SV7 @ tc_IntDef_Oint )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ ( c_insert @ SV10 @ SV12 @ SV13 ) @ SV13 ) )
= $true )
| ( ( ( c_in @ SV5 @ SV12 @ SV13 )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV5: $i] :
( ( ( c_in @ SV5 @ ( c_insert @ SV10 @ SV12 @ SV13 ) @ SV13 )
= $false )
| ( ( ( c_in @ SV5 @ SV12 @ SV13 )
| ( SV5 = SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV12 @ SV13 )
= $true )
| ( ( SV5 = SV10 )
= $true )
| ( ( c_in @ SV5 @ ( c_insert @ SV10 @ SV12 @ SV13 ) @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,46,43,40,38,37,29]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET822-2 : 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
% 0.10/0.16 % Computer : n020.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 14:53:51 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.20
% 0.10/0.20 No.of.Axioms: 6
% 0.10/0.20
% 0.10/0.20 Length.of.Defs: 0
% 0.10/0.20
% 0.10/0.20 Contains.Choice.Funs: false
% 0.10/0.20
% 0.10/0.20 ********************************
% 0.10/0.20 * All subproblems solved! *
% 0.10/0.20 ********************************
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.20
% 0.10/0.20 %**** Beginning of derivation protocol ****
% 0.10/0.20 % SZS output start CNFRefutation
% See solution above
% 0.10/0.20
% 0.10/0.20 %**** End of derivation protocol ****
% 0.10/0.20 %**** no. of clauses in derivation: 48 ****
% 0.10/0.20 %**** clause counter: 47 ****
% 0.10/0.20
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------