%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU839^5 : 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 : 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 10:49:05 AM UTC 2026
% Result : Theorem 0.13s 0.22s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 204 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 199 ( 17 ~; 70 |; 0 &; 112 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 18 ^; 8 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_S,type,
sK1_S: a > $o ).
thf(tp_sK2_SY4,type,
sK2_SY4: a > $o ).
thf(tp_sK3_SV1,type,
sK3_SV1: a ).
thf(1,conjecture,
! [S: a > $o,T: a > $o] :
( ( ^ [Xz: a] :
( ( S @ Xz )
| ( T @ Xz ) ) )
= ( ^ [Xz: a] :
( ( T @ Xz )
| ( S @ Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM26_pme) ).
thf(2,negated_conjecture,
( ( ! [S: a > $o,T: a > $o] :
( ( ^ [Xz: a] :
( ( S @ Xz )
| ( T @ Xz ) ) )
= ( ^ [Xz: a] :
( ( T @ Xz )
| ( S @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [S: a > $o,T: a > $o] :
( ( ^ [Xz: a] :
( ( S @ Xz )
| ( T @ Xz ) ) )
= ( ^ [Xz: a] :
( ( T @ Xz )
| ( S @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: a > $o] :
( ( ^ [SY5: a] :
( ( sK1_S @ SY5 )
| ( SY4 @ SY5 ) ) )
= ( ^ [SY6: a] :
( ( SY4 @ SY6 )
| ( sK1_S @ SY6 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [SY7: a] :
( ( sK1_S @ SY7 )
| ( sK2_SY4 @ SY7 ) ) )
= ( ^ [SY8: a] :
( ( sK2_SY4 @ SY8 )
| ( sK1_S @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ^ [SY7: a] :
( ( sK1_S @ SY7 )
| ( sK2_SY4 @ SY7 ) ) )
!= ( ^ [SY8: a] :
( ( sK2_SY4 @ SY8 )
| ( sK1_S @ SY8 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ^ [SY7: a] :
( ( sK1_S @ SY7 )
| ( sK2_SY4 @ SY7 ) ) )
!= ( ^ [SY8: a] :
( ( sK2_SY4 @ SY8 )
| ( sK1_S @ SY8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ^ [SY7: a] :
( ( sK1_S @ SY7 )
| ( sK2_SY4 @ SY7 ) ) )
= ( ^ [SY8: a] :
( ( sK2_SY4 @ SY8 )
| ( sK1_S @ SY8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SV1: a] :
( ( ( sK1_S @ SV1 )
| ( sK2_SY4 @ SV1 ) )
= ( ( sK2_SY4 @ SV1 )
| ( sK1_S @ SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ^ [SY7: a] :
( ( sK1_S @ SY7 )
| ( sK2_SY4 @ SY7 ) ) )
= ( ^ [SY8: a] :
( ( sK2_SY4 @ SY8 )
| ( sK1_S @ SY8 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(12,plain,
( ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
| ~ ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
| ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
| ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
| ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $true )
| ( ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ~ ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) ) )
= $true )
| ( ( ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( sK1_S @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ( sK1_S @ sK3_SV1 )
| ( sK2_SY4 @ sK3_SV1 ) )
= $false )
| ( ( ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( sK1_S @ sK3_SV1 )
= $true )
| ( ( sK2_SY4 @ sK3_SV1 )
= $true )
| ( ( sK1_S @ sK3_SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( sK1_S @ sK3_SV1 )
= $false )
| ( ( ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( ~ ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
= $false )
| ( ( sK1_S @ sK3_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ( ( sK2_SY4 @ sK3_SV1 )
| ( sK1_S @ sK3_SV1 ) )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK1_S @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ( sK1_S @ sK3_SV1 )
= $false )
| ( ( sK1_S @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ( sK2_SY4 @ sK3_SV1 )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( sK1_S @ sK3_SV1 )
= $false )
| ( ( sK2_SY4 @ sK3_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,30,29,28,27,22,13]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU839^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.19 % Computer : n015.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Oct 6 15:40:28 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.22
% 0.13/0.22 No.of.Axioms: 0
% 0.13/0.22
% 0.13/0.22 Length.of.Defs: 0
% 0.13/0.22
% 0.13/0.22 Contains.Choice.Funs: false
% 0.13/0.22
% 0.13/0.22 ********************************
% 0.13/0.22 * All subproblems solved! *
% 0.13/0.22 ********************************
% 0.13/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.22
% 0.13/0.22 %**** Beginning of derivation protocol ****
% 0.13/0.22 % SZS output start CNFRefutation
% See solution above
% 0.13/0.22
% 0.13/0.22 %**** End of derivation protocol ****
% 0.13/0.22 %**** no. of clauses in derivation: 32 ****
% 0.13/0.22 %**** clause counter: 31 ****
% 0.13/0.22
% 0.13/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------