%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT277-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:27:11 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 47 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 399 ( 29 ~; 29 |; 0 &; 341 @)
% ( 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 : 17 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Orefl,type,
c_Relation_Orefl: $i > $i > $i > $o ).
thf(tp_c_Tarski_OPartialOrder,type,
c_Tarski_OPartialOrder: $i ).
thf(tp_c_Tarski_Opotype_Oorder,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(tp_c_Tarski_Opotype_Opset,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_Tarski_Opotype_Opotype__ext__type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_A,type,
v_A: $i ).
thf(tp_v_cl,type,
v_cl: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(2,axiom,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(3,axiom,
! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ V_P @ T_a @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
thf(4,axiom,
( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(5,axiom,
! [V_A: $i,V_r: $i,T_a: $i,V_a: $i] :
( ~ ( c_Relation_Orefl @ V_A @ V_r @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OreflD_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_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,negated_conjecture,
c_in @ v_x @ v_A @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ V_P @ T_a @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i,V_a: $i] :
( ~ ( c_Relation_Orefl @ V_A @ V_r @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ~ ( c_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_in @ v_x @ v_A @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( c_in @ v_x @ v_A @ t_a )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( c_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i,V_a: $i] :
( ~ ( c_Relation_Orefl @ V_A @ V_r @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( v_A
= ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
( ( ! [V_P: $i,T_a: $i] :
( ~ ( c_in @ V_P @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ T_a @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ V_P @ T_a @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ V_P @ T_a @ tc_Product__Type_Ounit ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,plain,
( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(25,plain,
( ( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(26,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( c_in @ ( c_Pair @ v_x @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i,SY8: $i] :
( ~ ( c_Relation_Orefl @ SV1 @ SY6 @ SY7 )
| ~ ( c_in @ SY8 @ SV1 @ SY7 )
| ( c_in @ ( c_Pair @ SY8 @ SY8 @ SY7 @ SY7 ) @ SY6 @ ( tc_prod @ SY7 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SY9 @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ SV2 @ SY9 @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ SV2 @ SY9 @ tc_Product__Type_Ounit ) @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ( c_Relation_Orefl @ SV1 @ SV3 @ SY10 )
| ~ ( c_in @ SY11 @ SV1 @ SY10 )
| ( c_in @ ( c_Pair @ SY11 @ SY11 @ SY10 @ SY10 ) @ SV3 @ ( tc_prod @ SY10 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) )
| ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ! [SY12: $i] :
( ~ ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 )
| ~ ( c_in @ SY12 @ SV1 @ SV5 )
| ( c_in @ ( c_Pair @ SY12 @ SY12 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) ) )
= $true )
| ( ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV6: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ~ ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 )
| ~ ( c_in @ SV6 @ SV1 @ SV5 )
| ( c_in @ ( c_Pair @ SV6 @ SV6 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ SV4 @ tc_Product__Type_Ounit ) )
= $false )
| ( ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ SV2 @ SV4 @ tc_Product__Type_Ounit ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV6: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( c_in @ SV6 @ SV1 @ SV5 )
| ( c_in @ ( c_Pair @ SV6 @ SV6 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 )
= $false )
| ( ( ~ ( c_in @ SV6 @ SV1 @ SV5 )
| ( c_in @ ( c_Pair @ SV6 @ SV6 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV3: $i,SV5: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ SV1 @ SV5 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV6 @ SV6 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) )
= $true )
| ( ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: $i,SV5: $i,SV1: $i,SV6: $i] :
( ( ( c_in @ SV6 @ SV1 @ SV5 )
= $false )
| ( ( c_in @ ( c_Pair @ SV6 @ SV6 @ SV5 @ SV5 ) @ SV3 @ ( tc_prod @ SV5 @ SV5 ) )
= $true )
| ( ( c_Relation_Orefl @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,40,36,30,27,25,24,22]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT277-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 11:56:12 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 7
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 42 ****
% 0.07/0.25 %**** clause counter: 41 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------