%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU887^5 : 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 : n002.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 10:49:10 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 86 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 178 ( 27 ~; 20 |; 28 &; 96 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 36 !; 26 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_sK1_F,type,
sK1_F: b > a ).
thf(tp_sK2_SY7,type,
sK2_SY7: c > b ).
thf(tp_sK3_SY13,type,
sK3_SY13: c > $o ).
thf(tp_sK4_SY18,type,
sK4_SY18: a ).
thf(tp_sK5_SY22,type,
sK5_SY22: c ).
thf(1,conjecture,
! [F: b > a,G: c > b,S: c > $o,Xx: a] :
( ? [Xt: c] :
( ( S @ Xt )
& ( Xx
= ( F @ ( G @ Xt ) ) ) )
=> ? [Xt: b] :
( ? [Xt0: c] :
( ( S @ Xt0 )
& ( Xt
= ( G @ Xt0 ) ) )
& ( Xx
= ( F @ Xt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM28_pme) ).
thf(2,negated_conjecture,
( ( ! [F: b > a,G: c > b,S: c > $o,Xx: a] :
( ? [Xt: c] :
( ( S @ Xt )
& ( Xx
= ( F @ ( G @ Xt ) ) ) )
=> ? [Xt: b] :
( ? [Xt0: c] :
( ( S @ Xt0 )
& ( Xt
= ( G @ Xt0 ) ) )
& ( Xx
= ( F @ Xt ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [F: b > a,G: c > b,S: c > $o,Xx: a] :
( ? [Xt: c] :
( ( S @ Xt )
& ( Xx
= ( F @ ( G @ Xt ) ) ) )
=> ? [Xt: b] :
( ? [Xt0: c] :
( ( S @ Xt0 )
& ( Xt
= ( G @ Xt0 ) ) )
& ( Xx
= ( F @ Xt ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY7: c > b,SY8: c > $o,SY9: a] :
( ? [SY10: c] :
( ( SY8 @ SY10 )
& ( SY9
= ( sK1_F @ ( SY7 @ SY10 ) ) ) )
=> ? [SY11: b] :
( ? [Xt0: c] :
( ( SY8 @ Xt0 )
& ( SY11
= ( SY7 @ Xt0 ) ) )
& ( SY9
= ( sK1_F @ SY11 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: c > $o,SY14: a] :
( ? [SY15: c] :
( ( SY13 @ SY15 )
& ( SY14
= ( sK1_F @ ( sK2_SY7 @ SY15 ) ) ) )
=> ? [SY16: b] :
( ? [SY17: c] :
( ( SY13 @ SY17 )
& ( SY16
= ( sK2_SY7 @ SY17 ) ) )
& ( SY14
= ( sK1_F @ SY16 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY18: a] :
( ? [SY19: c] :
( ( sK3_SY13 @ SY19 )
& ( SY18
= ( sK1_F @ ( sK2_SY7 @ SY19 ) ) ) )
=> ? [SY20: b] :
( ? [SY21: c] :
( ( sK3_SY13 @ SY21 )
& ( SY20
= ( sK2_SY7 @ SY21 ) ) )
& ( SY18
= ( sK1_F @ SY20 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ? [SY22: c] :
( ( sK3_SY13 @ SY22 )
& ( sK4_SY18
= ( sK1_F @ ( sK2_SY7 @ SY22 ) ) ) )
=> ? [SY23: b] :
( ? [SY21: c] :
( ( sK3_SY13 @ SY21 )
& ( SY23
= ( sK2_SY7 @ SY21 ) ) )
& ( sK4_SY18
= ( sK1_F @ SY23 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ? [SY22: c] :
( ( sK3_SY13 @ SY22 )
& ( sK4_SY18
= ( sK1_F @ ( sK2_SY7 @ SY22 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ? [SY23: b] :
( ? [SY21: c] :
( ( sK3_SY13 @ SY21 )
& ( SY23
= ( sK2_SY7 @ SY21 ) ) )
& ( sK4_SY18
= ( sK1_F @ SY23 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ? [SY23: b] :
( ? [SY21: c] :
( ( sK3_SY13 @ SY21 )
& ( SY23
= ( sK2_SY7 @ SY21 ) ) )
& ( sK4_SY18
= ( sK1_F @ SY23 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY23: b] :
( ( sK4_SY18
!= ( sK1_F @ SY23 ) )
| ! [SY21: c] :
( ( SY23
!= ( sK2_SY7 @ SY21 ) )
| ~ ( sK3_SY13 @ SY21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ( sK4_SY18
= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
& ( sK3_SY13 @ sK5_SY22 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( ( sK4_SY18
= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
& ( sK3_SY13 @ sK5_SY22 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SY23: b] :
( ( sK4_SY18
!= ( sK1_F @ SY23 ) )
| ! [SY21: c] :
( ( SY23
!= ( sK2_SY7 @ SY21 ) )
| ~ ( sK3_SY13 @ SY21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( ( sK4_SY18
!= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
| ~ ( sK3_SY13 @ sK5_SY22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: b] :
( ( ( sK4_SY18
!= ( sK1_F @ SV1 ) )
| ! [SY25: c] :
( ( SV1
!= ( sK2_SY7 @ SY25 ) )
| ~ ( sK3_SY13 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ( sK4_SY18
!= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
| ~ ( sK3_SY13 @ sK5_SY22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: b] :
( ( ( sK4_SY18
!= ( sK1_F @ SV1 ) )
= $true )
| ( ( ! [SY25: c] :
( ( SV1
!= ( sK2_SY7 @ SY25 ) )
| ~ ( sK3_SY13 @ SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( sK4_SY18
!= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( sK3_SY13 @ sK5_SY22 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: b] :
( ( ( sK4_SY18
= ( sK1_F @ SV1 ) )
= $false )
| ( ( ! [SY25: c] :
( ( SV1
!= ( sK2_SY7 @ SY25 ) )
| ~ ( sK3_SY13 @ SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( sK4_SY18
= ( sK1_F @ ( sK2_SY7 @ sK5_SY22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( sK3_SY13 @ sK5_SY22 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: c,SV1: b] :
( ( ( ( SV1
!= ( sK2_SY7 @ SV2 ) )
| ~ ( sK3_SY13 @ SV2 ) )
= $true )
| ( ( sK4_SY18
= ( sK1_F @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: c,SV1: b] :
( ( ( SV1
!= ( sK2_SY7 @ SV2 ) )
= $true )
| ( ( ~ ( sK3_SY13 @ SV2 ) )
= $true )
| ( ( sK4_SY18
= ( sK1_F @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV2: c,SV1: b] :
( ( ( SV1
= ( sK2_SY7 @ SV2 ) )
= $false )
| ( ( ~ ( sK3_SY13 @ SV2 ) )
= $true )
| ( ( sK4_SY18
= ( sK1_F @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV1: b,SV2: c] :
( ( ( sK3_SY13 @ SV2 )
= $false )
| ( ( SV1
= ( sK2_SY7 @ SV2 ) )
= $false )
| ( ( sK4_SY18
= ( sK1_F @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,27,23]) ).
thf(29,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU887^5 : 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
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:40:42 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/sandbox/solver/bin/eprover /export/starexec/sandbox/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/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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:28,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: 29 ****
% 0.08/0.23 %**** clause counter: 28 ****
% 0.08/0.23
% 0.08/0.23 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------