%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n004.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 11:07:15 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 67 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 663 ( 204 ~; 94 |; 10 &; 345 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 122 ( 0 ^; 107 !; 15 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $i > $i > $o ).
thf(tp_sK1_SY4,type,
sK1_SY4: $i > $i ).
thf(1,conjecture,
? [Z: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( p @ Y @ X )
=> ? [W: $i] : ( p @ W @ Y ) )
& ( ( ( p @ Z @ Y )
& ( p @ Y @ Z ) )
=> ( p @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
( ( ? [Z: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( p @ Y @ X )
=> ? [W: $i] : ( p @ W @ Y ) )
& ( ( ( p @ Z @ Y )
& ( p @ Y @ Z ) )
=> ( p @ Y @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Z: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( p @ Y @ X )
=> ? [W: $i] : ( p @ W @ Y ) )
& ( ( ( p @ Z @ Y )
& ( p @ Y @ Z ) )
=> ( p @ Y @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Z: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( p @ Y @ X )
=> ? [W: $i] : ( p @ W @ Y ) )
& ( ( ( p @ Z @ Y )
& ( p @ Y @ Z ) )
=> ( p @ Y @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [Z: $i] :
! [X: $i] :
? [Y: $i] :
( ( ( p @ Y @ X )
=> ? [W: $i] : ( p @ W @ Y ) )
& ( ( ( p @ Z @ Y )
& ( p @ Y @ Z ) )
=> ( p @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( ~ ( p @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SX2 ) )
| ~ ( ~ ~ ( ~ ( p @ SX0 @ SX2 )
| ~ ( p @ SX2 @ SX0 ) )
| ( p @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( ~ ( p @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SX2 ) )
| ~ ( ~ ~ ( ~ ( p @ SX0 @ SX2 )
| ~ ( p @ SX2 @ SX0 ) )
| ( p @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( ~ ( p @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SX2 ) )
| ~ ( ~ ~ ( ~ ( p @ SX0 @ SX2 )
| ~ ( p @ SX2 @ SX0 ) )
| ( p @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ! [SY4: $i] :
~ ! [SY5: $i] :
~ ~ ( ~ ( ~ ( p @ SY5 @ SY4 )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SY5 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SY5 )
| ~ ( p @ SY5 @ SV1 ) )
| ( p @ SY5 @ SY4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ! [SY4: $i] :
~ ! [SY5: $i] :
~ ~ ( ~ ( ~ ( p @ SY5 @ SY4 )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SY5 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SY5 )
| ~ ( p @ SY5 @ SV1 ) )
| ( p @ SY5 @ SY4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ~ ! [SY7: $i] :
~ ~ ( ~ ( ~ ( p @ SY7 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SY7 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SY7 )
| ~ ( p @ SY7 @ SV1 ) )
| ( p @ SY7 @ ( sK1_SY4 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
~ ~ ( ~ ( ~ ( p @ SY7 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SX3: $i] :
~ ( p @ SX3 @ SY7 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SY7 )
| ~ ( p @ SY7 @ SV1 ) )
| ( p @ SY7 @ ( sK1_SY4 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(13,plain,
! [SV1: $i,SV2: $i] :
( ( ~ ~ ( ~ ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: $i,SV2: $i] :
( ( ~ ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
| ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
| ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i,SV2: $i] :
( ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i,SV2: $i] :
( ( ( ! [SY9: $i] :
~ ( p @ SY9 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( p @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i,SV2: $i] :
( ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( p @ SV3 @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) ) )
= $true )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
| ( p @ SV2 @ ( sK1_SY4 @ SV1 ) ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV1: $i,SV2: $i] :
( ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( p @ SV1 @ SV2 ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 @ SV1 ) )
= $false )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) ) )
= $true )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 )
= $true )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: $i,SV2: $i] :
( ( ( p @ SV2 @ SV1 )
= $true )
| ( ( p @ SV2 @ ( sK1_SY4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( p @ SV1 @ SV2 )
| ~ ( p @ SV2 @ SV1 ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( p @ SV1 @ SV2 ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(39,plain,
! [SV3: $i,SV1: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 @ SV1 ) )
= $false )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( p @ SV1 @ SV2 )
= $true )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i,SV1: $i,SV2: $i] :
( ( ( p @ SV2 @ SV1 )
= $true )
| ( ( p @ SV3 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,41,40,36,35,31]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% 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
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:30:24 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 43 ****
% 0.09/0.21 %**** clause counter: 42 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------