%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL120-2 : 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 : n010.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 10:11:53 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 273 ( 13 ~; 7 |; 0 &; 253 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $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_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_y,type,
v_y: $i ).
thf(1,axiom,
! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_x @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(5,negated_conjecture,
c_in @ ( c_Pair @ v_y @ v_x @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(6,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_x @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(9,plain,
( ( c_in @ ( c_Pair @ v_y @ v_x @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( c_in @ ( c_Pair @ v_y @ v_x @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ v_x @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ V_U @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
! [SV1: $i] :
( ( ~ ( c_in @ ( c_Pair @ v_x @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY4: $i,SY5: $i] : ( c_in @ ( c_Pair @ SV2 @ SV2 @ SY4 @ SY4 ) @ ( c_Transitive__Closure_Ortrancl @ SY5 @ SY4 ) @ ( tc_prod @ SY4 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ v_x @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY6: $i] : ( c_in @ ( c_Pair @ SV2 @ SV2 @ SV3 @ SV3 ) @ ( c_Transitive__Closure_Ortrancl @ SY6 @ SV3 ) @ ( tc_prod @ SV3 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_x @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( c_in @ ( c_Pair @ SV2 @ SV2 @ SV3 @ SV3 ) @ ( c_Transitive__Closure_Ortrancl @ SV4 @ SV3 ) @ ( tc_prod @ SV3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ v_y @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_x @ SV1 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ v_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,22,21,17]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL120-2 : 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
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 18:36:10 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 3
% 0.08/0.22
% 0.08/0.22 Length.of.Defs: 0
% 0.08/0.22
% 0.08/0.22 Contains.Choice.Funs: false
% 0.08/0.22
% 0.08/0.22 ********************************
% 0.08/0.22 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.22
% 0.08/0.22 %**** Beginning of derivation protocol ****
% 0.08/0.22 % 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: 24 ****
% 0.08/0.22 %**** clause counter: 23 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------