%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN940+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 : n006.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 11:07:12 AM UTC 2026
% Result : Theorem 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 41 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 336 ( 74 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 553 ( 190 ~; 102 |; 24 &; 216 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 ^; 65 !; 16 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_r,type,
r: $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: $i ).
thf(1,conjecture,
! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
( ( ! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [B: $i,C: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [X: $i,Y: $i] :
( ( ( p @ ( f @ Y ) )
=> ( ( p @ X )
& ( ( r @ Y )
=> ( ( r @ B )
& ( r @ C ) ) ) ) )
& ( q @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: $i] :
( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [SY7: $i,SY8: $i] :
( ( ( p @ ( f @ SY8 ) )
=> ( ( p @ SY7 )
& ( ( r @ SY8 )
=> ( ( r @ sK1_B )
& ( r @ SY5 ) ) ) ) )
& ( q @ SY7 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) )
=> ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ? [SY10: $i,SY11: $i] :
( ( ( p @ ( f @ SY11 ) )
=> ( ( p @ SY10 )
& ( ( r @ SY11 )
=> ( ( r @ sK1_B )
& ( r @ sK2_SY5 ) ) ) ) )
& ( q @ SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SX1 ) )
| ~ ( ~ ( p @ SX0 )
| ~ ( ~ ( r @ SX1 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: $i] :
( ( q @ ( f @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SX1 ) )
| ~ ( ~ ( p @ SX0 )
| ~ ( ~ ( r @ SX1 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SX1 ) )
| ~ ( ~ ( p @ SX0 )
| ~ ( ~ ( r @ SX1 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(15,plain,
! [SV2: $i] :
( ( ~ ~ ! [SY12: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SY12 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SY12 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV2: $i] :
( ( ~ ! [SY12: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SY12 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SY12 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
~ ~ ( ~ ( ~ ( p @ ( f @ SY12 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SY12 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(18,plain,
! [SV2: $i,SV3: $i] :
( ( ~ ~ ( ~ ( ~ ( p @ ( f @ SV3 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV2: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( p @ ( f @ SV3 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV2: $i,SV3: $i] :
( ( ~ ( ~ ( p @ ( f @ SV3 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
| ~ ( q @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(21,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( p @ ( f @ SV3 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) ) )
= $true )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( p @ ( f @ SV3 ) )
| ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( p @ ( f @ SV3 ) ) )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(24,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) ) )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV3: $i] :
( ( ( p @ ( f @ SV3 ) )
= $true )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 )
| ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) )
= $true )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV3: $i,SV2: $i] :
( ( ( q @ SV2 )
= $false )
| ( ( p @ ( f @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) )
= $true )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: $i,SV2: $i] :
( ( ( p @ SV2 )
= $false )
| ( ( ~ ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) ) )
= $true )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( r @ SV3 )
| ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( r @ SV3 ) )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) ) )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i,SV3: $i] :
( ( ( r @ SV3 )
= $true )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( ~ ( r @ sK1_B )
| ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: $i,SV2: $i] :
( ( ( q @ SV2 )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( r @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( ~ ( r @ sK1_B ) )
= $true )
| ( ( ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( r @ sK1_B )
= $false )
| ( ( ~ ( r @ sK2_SY5 ) )
= $true )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( r @ sK2_SY5 )
= $false )
| ( ( r @ sK1_B )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( q @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( q @ SV2 )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( r @ sK1_B )
= $false )
| ( ( r @ sK2_SY5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,39,35,27]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN940+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
% 0.11/0.16 % Computer : n006.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 17:29:22 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 0
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 41 ****
% 0.11/0.19 %**** clause counter: 40 ****
% 0.11/0.19
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------