%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV163^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:49:40 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 90 ( 2 ~; 0 |; 0 &; 84 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 96 ^; 6 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xp,type,
sK1_Xp: ( a > a > a ) > a ).
thf(tp_sK2_SV3,type,
sK2_SV3: a > a > a ).
thf(1,conjecture,
! [Xp: ( a > a > a ) > a] :
( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
=> ( ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= Xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM187_pme) ).
thf(2,negated_conjecture,
( ( ! [Xp: ( a > a > a ) > a] :
( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
=> ( ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= Xp ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: ( a > a > a ) > a] :
( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
=> ( ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= Xp ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( sK1_Xp
= ( ^ [SY11: a > a > a] :
( SY11
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
=> ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= sK1_Xp ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( sK1_Xp
= ( ^ [SY11: a > a > a] :
( SY11
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= sK1_Xp )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
!= sK1_Xp )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( sK1_Xp
= ( ^ [SY11: a > a > a] :
( SY11
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
!= sK1_Xp )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SV1: a > a > a] :
( ( sK1_Xp @ SV1 )
= ( SV1
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( sK1_Xp
= ( ^ [SY11: a > a > a] :
( SY11
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[8]) ).
thf(12,plain,
( ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= sK1_Xp )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(13,plain,
! [SV2: a > a > a] :
( ( ( sK1_Xp @ SV2 )
= ( SV2
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SV3: a > a > a] :
( ( SV3
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) )
= ( sK1_Xp @ SV3 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ^ [SY16: a > a > a] :
( SY16
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= sK1_Xp )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ( sK2_SV3
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) )
= ( sK1_Xp @ sK2_SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,16,15,13]) ).
thf(18,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV163^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:42:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 18 ****
% 0.07/0.21 %**** clause counter: 17 ****
% 0.07/0.21
% 0.07/0.21 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------