%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO218^5 : 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 : n012.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 11:07:51 AM UTC 2026
% Result : Theorem 0.10s 0.18s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 84 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 50 ( 6 ~; 7 |; 0 &; 26 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 26 ^; 20 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: $i ).
thf(tp_sK3_Eigen,type,
sK3_Eigen: ( $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(1,conjecture,
! [Xx: $i,Xy: $i] :
( ! [Xq: ( $i > $o ) > $i] :
( ( Xx
= ( Xq
@ ^ [Xz: $i] : ( Xx = Xz ) ) )
=> ( Xy
= ( Xq
@ ^ [Xz: $i] : ( Xy = Xz ) ) ) )
=> ( Xx = Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM7B_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i,Xy: $i] :
( ! [Xq: ( $i > $o ) > $i] :
( ( Xx
= ( Xq
@ ^ [Xz: $i] : ( Xx = Xz ) ) )
=> ( Xy
= ( Xq
@ ^ [Xz: $i] : ( Xy = Xz ) ) ) )
=> ( Xx = Xy ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ! [Xq: ( $i > $o ) > $i] :
( ( Xx
= ( Xq
@ ^ [Xz: $i] : ( Xx = Xz ) ) )
=> ( Xy
= ( Xq
@ ^ [Xz: $i] : ( Xy = Xz ) ) ) )
=> ( Xx = Xy ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: $i] :
( ! [SY6: ( $i > $o ) > $i] :
( ( sK1_Xx
= ( SY6
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
=> ( SY5
= ( SY6
@ ^ [Xz: $i] : ( SY5 = Xz ) ) ) )
=> ( sK1_Xx = SY5 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY9: ( $i > $o ) > $i] :
( ( sK1_Xx
= ( SY9
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
=> ( sK2_SY5
= ( SY9
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) ) )
=> ( sK1_Xx = sK2_SY5 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY9: ( $i > $o ) > $i] :
( ( sK1_Xx
= ( SY9
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
=> ( sK2_SY5
= ( SY9
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( sK1_Xx = sK2_SY5 )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( sK1_Xx != sK2_SY5 )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY9: ( $i > $o ) > $i] :
( ( sK1_Xx
!= ( SY9
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
| ( sK2_SY5
= ( SY9
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(10,plain,
( ( ! [SY9: ( $i > $o ) > $i] :
( ( sK1_Xx
!= ( SY9
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
| ( sK2_SY5
= ( SY9
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( sK1_Xx != sK2_SY5 )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ( sK1_Xx
!= ( SV1
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
| ( sK2_SY5
= ( SV1
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( sK1_Xx = sK2_SY5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ( sK1_Xx
!= ( SV1
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
= $true )
| ( ( sK2_SY5
= ( SV1
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ( sK1_Xx
= ( SV1
@ ^ [SY7: $i] : ( sK1_Xx = SY7 ) ) )
= $false )
| ( ( sK2_SY5
= ( SV1
@ ^ [SY11: $i] : ( sK2_SY5 = SY11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(69,plain,
! [SV12: ( $i > $o ) > $i] :
( ( ( sK1_Xx
= ( SV12
@ ^ [SX0: $i] : ( sK1_Xx = SX0 ) ) )
= $false )
| ( ( sK2_SY5
= ( SV12
@ ^ [SX0: $i] : ( sK2_SY5 = SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[15]) ).
thf(75,plain,
! [SV12: ( $i > $o ) > $i] :
( ( ( ( sK2_SY5
= ( SV12
@ ^ [SX0: $i] : ( sK2_SY5 = SX0 ) ) )
= ( sK1_Xx = sK2_SY5 ) )
= $false )
| ( ( sK1_Xx
= ( SV12
@ ^ [SX0: $i] : ( sK1_Xx = SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[69,13]) ).
thf(90,plain,
$false = $true,
inference(extuni,[status(esa)],[75:[bind(SV12,$thf( ^ [SX0: $i > $o] : sK1_Xx ))]]) ).
thf(91,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO218^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 17:33:01 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18
% 0.10/0.18 No.of.Axioms: 0
% 0.10/0.18
% 0.10/0.18 Length.of.Defs: 0
% 0.10/0.18
% 0.10/0.18 Contains.Choice.Funs: false
% 0.10/0.18
% 0.10/0.18 *** Modified list of choice operators: sK3_Eigen ***
% 0.10/0.18 .
% 0.10/0.18
% 0.10/0.18 ********************************
% 0.10/0.18 * All subproblems solved! *
% 0.10/0.18 ********************************
% 0.10/0.18 % 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:90,loop_count:5,foatp_calls:3,translation:fof_experiment)
% 0.10/0.18
% 0.10/0.18 %**** Beginning of derivation protocol ****
% 0.10/0.18 % SZS output start CNFRefutation
% See solution above
% 0.10/0.18
% 0.10/0.18 %**** End of derivation protocol ****
% 0.10/0.18 %**** no. of clauses in derivation: 19 ****
% 0.10/0.18 %**** clause counter: 90 ****
% 0.10/0.18
% 0.10/0.18 % 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:90,loop_count:5,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------