%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU932^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n003.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 10:49:15 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 104 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 177 ( 38 ~; 19 |; 14 &; 97 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 24 ^; 26 !; 16 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xf,type,
sK1_Xf: $i > $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i > $i ).
thf(tp_sK3_SY15,type,
sK3_SY15: $i ).
thf(1,conjecture,
! [Xf: $i > $i] :
( ? [Xg: $i > $i] :
( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
& ? [Xx: $i] :
( ( ( Xg @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: $i] :
( ( Xf @ Xy )
= Xy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM141_pme) ).
thf(2,negated_conjecture,
( ( ! [Xf: $i > $i] :
( ? [Xg: $i > $i] :
( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
& ? [Xx: $i] :
( ( ( Xg @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: $i] :
( ( Xf @ Xy )
= Xy ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xf: $i > $i] :
( ? [Xg: $i > $i] :
( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
& ? [Xx: $i] :
( ( ( Xg @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: $i] :
( ( Xf @ Xy )
= Xy ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [SY7: $i > $i] :
( ( ( ^ [SY8: $i] : ( sK1_Xf @ ( SY7 @ SY8 ) ) )
= ( ^ [SY9: $i] : ( SY7 @ ( sK1_Xf @ SY9 ) ) ) )
& ? [Xx: $i] :
( ( ( SY7 @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( SY7 @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [SY12: $i] :
( ( sK1_Xf @ SY12 )
= SY12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY7: $i > $i] :
( ( ( ^ [SY8: $i] : ( sK1_Xf @ ( SY7 @ SY8 ) ) )
= ( ^ [SY9: $i] : ( SY7 @ ( sK1_Xf @ SY9 ) ) ) )
& ? [Xx: $i] :
( ( ( SY7 @ Xx )
= Xx )
& ! [Xz: $i] :
( ( ( SY7 @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ? [SY12: $i] :
( ( sK1_Xf @ SY12 )
= SY12 ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ? [SY12: $i] :
( ( sK1_Xf @ SY12 )
= SY12 ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY12: $i] :
( ( sK1_Xf @ SY12 )
!= SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ( ( ^ [SY13: $i] : ( sK1_Xf @ ( sK2_SY7 @ SY13 ) ) )
= ( ^ [SY14: $i] : ( sK2_SY7 @ ( sK1_Xf @ SY14 ) ) ) )
& ! [SY17: $i] :
( ( ( sK2_SY7 @ SY17 )
!= SY17 )
| ( SY17 = sK3_SY15 ) )
& ( ( sK2_SY7 @ sK3_SY15 )
= sK3_SY15 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ( ( ^ [SY13: $i] : ( sK1_Xf @ ( sK2_SY7 @ SY13 ) ) )
= ( ^ [SY14: $i] : ( sK2_SY7 @ ( sK1_Xf @ SY14 ) ) ) )
& ! [SY17: $i] :
( ( ( sK2_SY7 @ SY17 )
!= SY17 )
| ( SY17 = sK3_SY15 ) )
& ( ( sK2_SY7 @ sK3_SY15 )
= sK3_SY15 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY12: $i] :
( ( sK1_Xf @ SY12 )
!= SY12 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
!= ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) )
| ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ( sK1_Xf @ SV1 )
!= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
!= ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) )
| ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ( sK1_Xf @ SV1 )
= SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
!= ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) )
| ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
= ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) )
| ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [SV2: $i] :
( ( sK1_Xf @ ( sK2_SY7 @ SV2 ) )
= ( sK2_SY7 @ ( sK1_Xf @ SV2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
= ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) )
| ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: $i] :
( ( ( sK1_Xf @ ( sK2_SY7 @ SV3 ) )
= ( sK2_SY7 @ ( sK1_Xf @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( sK2_SY7 @ sK3_SY15 )
!= sK3_SY15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SX0: $i] :
( ( ( sK2_SY7 @ SX0 )
!= SX0 )
| ( SX0 = sK3_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ( sK2_SY7 @ sK3_SY15 )
= sK3_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
!= SV4 )
| ( SV4 = sK3_SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
!= SV4 )
= $true )
| ( ( SV4 = sK3_SY15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= SV4 )
= $false )
| ( ( SV4 = sK3_SY15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,30,27,23,21]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU932^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.19 % Computer : n003.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 15:40:09 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.24
% 0.12/0.24 No.of.Axioms: 0
% 0.12/0.24
% 0.12/0.24 Length.of.Defs: 0
% 0.12/0.24
% 0.12/0.24 Contains.Choice.Funs: false
% 0.12/0.24
% 0.12/0.24 ********************************
% 0.12/0.24 * All subproblems solved! *
% 0.12/0.24 ********************************
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/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:31,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.12/0.24
% 0.12/0.24 %**** Beginning of derivation protocol ****
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24
% 0.12/0.24 %**** End of derivation protocol ****
% 0.12/0.24 %**** no. of clauses in derivation: 32 ****
% 0.12/0.24 %**** clause counter: 31 ****
% 0.12/0.24
% 0.12/0.24 % SZS status Theorem for /export/starexec/sandbox2/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:31,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------