%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU898^5 : 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 : n015.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 10:49:12 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 76 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 386 ( 30 ~; 22 |; 20 &; 272 @)
% ( 0 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xh,type,
sK1_Xh: a > a ).
thf(tp_sK2_SY8,type,
sK2_SY8: a > $o ).
thf(tp_sK3_SY15,type,
sK3_SY15: a > a ).
thf(tp_sK4_SY25,type,
sK4_SY25: a ).
thf(1,conjecture,
! [Xh: a > a,Xs: a > $o,Xf: a > a] :
( ( ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xh @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xf @ Xx ) )
= ( Xf @ ( Xh @ Xx ) ) ) ) )
=> ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xh @ ( Xf @ Xx ) ) )
= ( Xf @ ( Xh @ ( Xh @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM132_pme) ).
thf(2,negated_conjecture,
( ( ! [Xh: a > a,Xs: a > $o,Xf: a > a] :
( ( ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xh @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xf @ Xx ) )
= ( Xf @ ( Xh @ Xx ) ) ) ) )
=> ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xh @ ( Xf @ Xx ) ) )
= ( Xf @ ( Xh @ ( Xh @ Xx ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xh: a > a,Xs: a > $o,Xf: a > a] :
( ( ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xf @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xs @ ( Xh @ Xx ) ) )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xf @ Xx ) )
= ( Xf @ ( Xh @ Xx ) ) ) ) )
=> ! [Xx: a] :
( ( Xs @ Xx )
=> ( ( Xh @ ( Xh @ ( Xf @ Xx ) ) )
= ( Xf @ ( Xh @ ( Xh @ Xx ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY8: a > $o,SY9: a > a] :
( ( ! [Xx: a] :
( ( SY8 @ Xx )
=> ( SY8 @ ( SY9 @ Xx ) ) )
& ! [Xx: a] :
( ( SY8 @ Xx )
=> ( SY8 @ ( SY9 @ Xx ) ) )
& ! [SY12: a] :
( ( SY8 @ SY12 )
=> ( SY8 @ ( sK1_Xh @ SY12 ) ) )
& ! [SY13: a] :
( ( SY8 @ SY13 )
=> ( ( sK1_Xh @ ( SY9 @ SY13 ) )
= ( SY9 @ ( sK1_Xh @ SY13 ) ) ) ) )
=> ! [SY14: a] :
( ( SY8 @ SY14 )
=> ( ( sK1_Xh @ ( sK1_Xh @ ( SY9 @ SY14 ) ) )
= ( SY9 @ ( sK1_Xh @ ( sK1_Xh @ SY14 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY15: a > a] :
( ( ! [SY16: a] :
( ( sK2_SY8 @ SY16 )
=> ( sK2_SY8 @ ( SY15 @ SY16 ) ) )
& ! [SY17: a] :
( ( sK2_SY8 @ SY17 )
=> ( sK2_SY8 @ ( SY15 @ SY17 ) ) )
& ! [SY18: a] :
( ( sK2_SY8 @ SY18 )
=> ( sK2_SY8 @ ( sK1_Xh @ SY18 ) ) )
& ! [SY19: a] :
( ( sK2_SY8 @ SY19 )
=> ( ( sK1_Xh @ ( SY15 @ SY19 ) )
= ( SY15 @ ( sK1_Xh @ SY19 ) ) ) ) )
=> ! [SY20: a] :
( ( sK2_SY8 @ SY20 )
=> ( ( sK1_Xh @ ( sK1_Xh @ ( SY15 @ SY20 ) ) )
= ( SY15 @ ( sK1_Xh @ ( sK1_Xh @ SY20 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY21: a] :
( ( sK2_SY8 @ SY21 )
=> ( sK2_SY8 @ ( sK3_SY15 @ SY21 ) ) )
& ! [SY22: a] :
( ( sK2_SY8 @ SY22 )
=> ( sK2_SY8 @ ( sK3_SY15 @ SY22 ) ) )
& ! [SY18: a] :
( ( sK2_SY8 @ SY18 )
=> ( sK2_SY8 @ ( sK1_Xh @ SY18 ) ) )
& ! [SY24: a] :
( ( sK2_SY8 @ SY24 )
=> ( ( sK1_Xh @ ( sK3_SY15 @ SY24 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SY24 ) ) ) ) )
=> ! [SY25: a] :
( ( sK2_SY8 @ SY25 )
=> ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ SY25 ) ) )
= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ SY25 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY21: a] :
( ( sK2_SY8 @ SY21 )
=> ( sK2_SY8 @ ( sK3_SY15 @ SY21 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY22: a] :
( ( sK2_SY8 @ SY22 )
=> ( sK2_SY8 @ ( sK3_SY15 @ SY22 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY18: a] :
( ( sK2_SY8 @ SY18 )
=> ( sK2_SY8 @ ( sK1_Xh @ SY18 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SY24: a] :
( ( sK2_SY8 @ SY24 )
=> ( ( sK1_Xh @ ( sK3_SY15 @ SY24 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SY24 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [SY25: a] :
( ( sK2_SY8 @ SY25 )
=> ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ SY25 ) ) )
= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ SY25 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ ! [SY25: a] :
( ( sK2_SY8 @ SY25 )
=> ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ SY25 ) ) )
= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ SY25 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ( sK2_SY8 @ sK4_SY25 )
& ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(14,plain,
( ( ! [SY21: a] :
( ~ ( sK2_SY8 @ SY21 )
| ( sK2_SY8 @ ( sK3_SY15 @ SY21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [SY22: a] :
( ~ ( sK2_SY8 @ SY22 )
| ( sK2_SY8 @ ( sK3_SY15 @ SY22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(16,plain,
( ( ! [SY18: a] :
( ~ ( sK2_SY8 @ SY18 )
| ( sK2_SY8 @ ( sK1_Xh @ SY18 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [SY24: a] :
( ~ ( sK2_SY8 @ SY24 )
| ( ( sK1_Xh @ ( sK3_SY15 @ SY24 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( ! [SY24: a] :
( ~ ( sK2_SY8 @ SY24 )
| ( ( sK1_Xh @ ( sK3_SY15 @ SY24 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SY24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [SY18: a] :
( ~ ( sK2_SY8 @ SY18 )
| ( sK2_SY8 @ ( sK1_Xh @ SY18 ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SY22: a] :
( ~ ( sK2_SY8 @ SY22 )
| ( sK2_SY8 @ ( sK3_SY15 @ SY22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [SY21: a] :
( ~ ( sK2_SY8 @ SY21 )
| ( sK2_SY8 @ ( sK3_SY15 @ SY21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( ( sK2_SY8 @ sK4_SY25 )
& ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(23,plain,
( ( ~ ( ~ ( sK2_SY8 @ sK4_SY25 )
| ~ ( ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
! [SV1: a] :
( ( ~ ( sK2_SY8 @ SV1 )
| ( ( sK1_Xh @ ( sK3_SY15 @ SV1 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV2: a] :
( ( ~ ( sK2_SY8 @ SV2 )
| ( sK2_SY8 @ ( sK1_Xh @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV3: a] :
( ( ~ ( sK2_SY8 @ SV3 )
| ( sK2_SY8 @ ( sK3_SY15 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV4: a] :
( ( ~ ( sK2_SY8 @ SV4 )
| ( sK2_SY8 @ ( sK3_SY15 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ( sK2_SY8 @ sK4_SY25 )
| ~ ( ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV1: a] :
( ( ( ~ ( sK2_SY8 @ SV1 ) )
= $true )
| ( ( ( sK1_Xh @ ( sK3_SY15 @ SV1 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV2: a] :
( ( ( ~ ( sK2_SY8 @ SV2 ) )
= $true )
| ( ( sK2_SY8 @ ( sK1_Xh @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY8 @ SV3 ) )
= $true )
| ( ( sK2_SY8 @ ( sK3_SY15 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY8 @ SV4 ) )
= $true )
| ( ( sK2_SY8 @ ( sK3_SY15 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ( sK2_SY8 @ sK4_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ( ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
! [SV1: a] :
( ( ( sK2_SY8 @ SV1 )
= $false )
| ( ( ( sK1_Xh @ ( sK3_SY15 @ SV1 ) )
= ( sK3_SY15 @ ( sK1_Xh @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV2: a] :
( ( ( sK2_SY8 @ SV2 )
= $false )
| ( ( sK2_SY8 @ ( sK1_Xh @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV3: a] :
( ( ( sK2_SY8 @ SV3 )
= $false )
| ( ( sK2_SY8 @ ( sK3_SY15 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV4: a] :
( ( ( sK2_SY8 @ SV4 )
= $false )
| ( ( sK2_SY8 @ ( sK3_SY15 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( sK2_SY8 @ sK4_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(40,plain,
( ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
!= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ( sK1_Xh @ ( sK1_Xh @ ( sK3_SY15 @ sK4_SY25 ) ) )
= ( sK3_SY15 @ ( sK1_Xh @ ( sK1_Xh @ sK4_SY25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,41,39,38,37,36]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU898^5 : 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 : n015.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 15:41:13 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 ********************************
% 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:4,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:42,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: 43 ****
% 0.08/0.23 %**** clause counter: 42 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------