%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV169^5 : 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 : n018.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 10:49:41 AM UTC 2026
% Result : Theorem 0.08s 0.18s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 72 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 138 ( 2 ~; 0 |; 15 &; 116 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 164 ( 152 ^; 12 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xp,type,
sK1_Xp: ( a > a > a ) > a ).
thf(tp_sK2_SY20,type,
sK2_SY20: ( a > a > a ) > a ).
thf(tp_sK3_SV5,type,
sK3_SV5: a > a > a ).
thf(1,conjecture,
! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( Xq
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( Xp = Xq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM188_pme) ).
thf(2,negated_conjecture,
( ( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( Xq
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( Xp = Xq ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( ( Xp
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( Xq
= ( ^ [Xg: a > a > a] :
( Xg
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( Xp = Xq ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY20: ( a > a > a ) > a] :
( ( ( sK1_Xp
= ( ^ [SY21: a > a > a] :
( SY21
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( SY20
= ( ^ [Xg: a > a > a] :
( Xg
@ ( SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( SY20
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( sK1_Xp = SY20 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ( sK1_Xp
= ( ^ [SY21: a > a > a] :
( SY21
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( sK2_SY20
= ( ^ [SY44: a > a > a] :
( SY44
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
& ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx ) )
& ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) )
=> ( sK1_Xp = sK2_SY20 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( sK1_Xp
= ( ^ [SY21: a > a > a] :
( SY21
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( sK2_SY20
= ( ^ [SY44: a > a > a] :
( SY44
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(10,plain,
( ( sK1_Xp = sK2_SY20 )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(11,plain,
( ( sK1_Xp != sK2_SY20 )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
= ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( sK2_SY20
= ( ^ [SY44: a > a > a] :
( SY44
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( sK1_Xp
= ( ^ [SY21: a > a > a] :
( SY21
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(16,plain,
( ( sK1_Xp != sK2_SY20 )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SV1: a > a > a] :
( ( sK2_SY20 @ SV1 )
= ( SV1
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( sK2_SY20
= ( ^ [SY44: a > a > a] :
( SY44
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[14]) ).
thf(19,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_equal_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( sK1_Xp
= ( ^ [SY21: a > a > a] :
( SY21
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(21,plain,
( ( sK1_Xp = sK2_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV3: a > a > a] :
( ( ( sK2_SY20 @ SV3 )
= ( SV3
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK2_SY20
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV4: a > a > a] :
( ( ( sK1_Xp @ SV4 )
= ( SV4
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( sK1_Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SV5: a > a > a] :
( ( sK1_Xp @ SV5 )
= ( sK2_SY20 @ SV5 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( sK1_Xp = sK2_SY20 )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ( sK1_Xp @ sK3_SV5 )
= ( sK2_SY20 @ sK3_SV5 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,26,25,23,22,20,18,13]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n018.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 15:43:52 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18
% 0.08/0.18 No.of.Axioms: 0
% 0.08/0.18
% 0.08/0.18 Length.of.Defs: 0
% 0.08/0.18
% 0.08/0.18 Contains.Choice.Funs: false
% 0.08/0.18
% 0.08/0.18 ********************************
% 0.08/0.18 * All subproblems solved! *
% 0.08/0.18 ********************************
% 0.08/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.18
% 0.08/0.18 %**** Beginning of derivation protocol ****
% 0.08/0.18 % SZS output start CNFRefutation
% See solution above
% 0.08/0.18
% 0.08/0.18 %**** End of derivation protocol ****
% 0.08/0.18 %**** no. of clauses in derivation: 28 ****
% 0.08/0.18 %**** clause counter: 27 ****
% 0.08/0.18
% 0.08/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------