%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG281^5 : 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 : 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 10:08:46 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 47 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 129 ( 2 ~; 0 |; 6 &; 118 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cE,type,
cE: $i ).
thf(tp_cJ,type,
cJ: $i > $i ).
thf(tp_cP,type,
cP: $i > $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(1,conjecture,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: $i] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM16_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: $i] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: $i] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: $i] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xy: $i] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xy: $i] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
! [SV1: $i] :
( ( ( cP @ ( cJ @ SV1 ) @ SV1 )
= cE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(14,plain,
! [SV2: $i] :
( ( ( cP @ cE @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(15,plain,
! [SV3: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ( cP @ ( cP @ SV3 @ SY6 ) @ SY7 )
= ( cP @ SV3 @ ( cP @ SY6 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( cP @ X @ ( cJ @ X ) )
= cE ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV4: $i,SV3: $i] :
( ( ! [SY8: $i] :
( ( cP @ ( cP @ SV3 @ SV4 ) @ SY8 )
= ( cP @ SV3 @ ( cP @ SV4 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( cP @ sK1_X @ ( cJ @ sK1_X ) )
= cE )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
! [SV5: $i,SV4: $i,SV3: $i] :
( ( ( cP @ ( cP @ SV3 @ SV4 ) @ SV5 )
= ( cP @ SV3 @ ( cP @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,19,18,14]) ).
thf(21,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG281^5 : 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
% 0.08/0.18 % Computer : n020.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
% 0.08/0.19 % DateTime : Tue Oct 6 18:11:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 21 ****
% 0.08/0.23 %**** clause counter: 20 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------