%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU549^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n016.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 10:44:59 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 32 unt; 0 typ; 1 def)
% Number of atoms : 143 ( 64 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 150 ( 48 ~; 18 |; 10 &; 54 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 3 ^; 28 !; 4 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY15,type,
sK3_SY15: $i ).
thf(tp_sK4_SY11,type,
sK4_SY11: $i ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(1,conjecture,
! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(2,negated_conjecture,
( ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY0 @ Xx )
=> ( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,exu]) ).
thf(4,plain,
( ( ? [SY11: $i] :
( ( sK1_SY0 @ SY11 )
& ! [SY12: $i] :
( ( sK1_SY0 @ SY12 )
=> ( SY11 = SY12 ) ) )
=> ! [SY13: $i,SY14: $i] :
( ( sK1_SY0 @ SY13 )
=> ( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY11: $i] :
( ( sK1_SY0 @ SY11 )
& ! [SY12: $i] :
( ( sK1_SY0 @ SY12 )
=> ( SY11 = SY12 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY13: $i,SY14: $i] :
( ( sK1_SY0 @ SY13 )
=> ( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY13: $i,SY14: $i] :
( ( sK1_SY0 @ SY13 )
=> ( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sK1_SY0 @ sK2_SY13 )
& ( sK1_SY0 @ sK3_SY15 )
& ( sK2_SY13 != sK3_SY15 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( sK4_SY11 = SY16 ) )
& ( sK1_SY0 @ sK4_SY11 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( sK4_SY11 = SY16 ) )
& ( sK1_SY0 @ sK4_SY11 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ( sK1_SY0 @ sK2_SY13 )
& ( sK1_SY0 @ sK3_SY15 )
& ( sK2_SY13 != sK3_SY15 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK2_SY13 )
| ~ ~ ( ~ ( sK1_SY0 @ sK3_SY15 )
| ~ ( ( sK2_SY13 != sK3_SY15 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,exu]) ).
thf(13,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY11 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,exu]) ).
thf(14,plain,
( ( ~ ( sK1_SY0 @ sK2_SY13 )
| ~ ~ ( ~ ( sK1_SY0 @ sK3_SY15 )
| ~ ( ( sK2_SY13 != sK3_SY15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY11 = SX0 ) )
| ~ ( sK1_SY0 @ sK4_SY11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK1_SY0 @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK3_SY15 )
| ~ ( ( sK2_SY13 != sK3_SY15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY11 = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( sK1_SY0 @ sK4_SY11 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( sK1_SY0 @ sK2_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK3_SY15 )
| ~ ( ( sK2_SY13 != sK3_SY15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK4_SY11 = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( sK1_SY0 @ sK4_SY11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( sK1_SY0 @ sK3_SY15 )
| ~ ( ( sK2_SY13 != sK3_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( sK1_SY0 @ SV1 )
| ( sK4_SY11 = SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK1_SY0 @ sK3_SY15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( ( sK2_SY13 != sK3_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 ) )
= $true )
| ( ( sK4_SY11 = SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( sK1_SY0 @ sK3_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( sK2_SY13 != sK3_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( sK1_SY0 @ SV1 )
= $false )
| ( ( sK4_SY11 = SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( sK2_SY13 = sK3_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,32,31,29,23]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU549^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.08/0.18 % Computer : n016.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 15:32:59 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: 0
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 174
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 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 Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 34 ****
% 0.08/0.21 %**** clause counter: 33 ****
% 0.08/0.21
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------