%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO271^5 : 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 : n008.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 11:07:58 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 : 35 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 156 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 392 ( 112 ~; 18 |; 2 &; 252 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 52 ^; 27 !; 2 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_cJ,type,
cJ: ( b > $o ) > b ).
thf(tp_sK1_Xf,type,
sK1_Xf: b > a ).
thf(tp_sK2_SY0,type,
sK2_SY0: b > a ).
thf(tp_sK3_SV3,type,
sK3_SV3: b ).
thf(tp_sK4_E,type,
sK4_E: b ).
thf(1,conjecture,
( ! [P: b > $o] :
( ? [Xx: b] : ( P @ Xx )
=> ( P @ ( cJ @ P ) ) )
=> ! [Xf: b > a,Xg: b > a] :
( ( ( Xf
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) )
= ( Xg
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) ) )
=> ( Xf = Xg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5500) ).
thf(2,negated_conjecture,
( ( ! [P: b > $o] :
( ? [Xx: b] : ( P @ Xx )
=> ( P @ ( cJ @ P ) ) )
=> ! [Xf: b > a,Xg: b > a] :
( ( ( Xf
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) )
= ( Xg
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) ) )
=> ( Xf = Xg ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(4,plain,
( ( ! [Xf: b > a,Xg: b > a] :
( ( ( Xf
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) )
= ( Xg
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) ) )
=> ( Xf = Xg ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ~ ! [Xf: b > a,Xg: b > a] :
( ( ( Xf
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) )
= ( Xg
@ ( cJ
@ ^ [Xx: b] :
( ( Xf @ Xx )
!= ( Xg @ Xx ) ) ) ) )
=> ( Xf = Xg ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sK1_Xf
@ ( cJ
@ ^ [SY3: b] :
( ( sK1_Xf @ SY3 )
!= ( sK2_SY0 @ SY3 ) ) ) )
= ( sK2_SY0
@ ( cJ
@ ^ [SY4: b] :
( ( sK1_Xf @ SY4 )
!= ( sK2_SY0 @ SY4 ) ) ) ) )
& ( sK1_Xf != sK2_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(9,plain,
( ( ( ( sK1_Xf
@ ( cJ
@ ^ [SY3: b] :
( ( sK1_Xf @ SY3 )
!= ( sK2_SY0 @ SY3 ) ) ) )
= ( sK2_SY0
@ ( cJ
@ ^ [SY4: b] :
( ( sK1_Xf @ SY4 )
!= ( sK2_SY0 @ SY4 ) ) ) ) )
& ( sK1_Xf != sK2_SY0 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
| ~ ( ( sK1_Xf != sK2_SY0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
| ~ ( ( sK1_Xf != sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ( sK1_Xf != sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(17,plain,
( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( sK1_Xf != sK2_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( sK1_Xf = sK2_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [SV3: b] :
( ( sK1_Xf @ SV3 )
= ( sK2_SY0 @ SV3 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[20]) ).
thf(22,plain,
( ( sK1_Xf = sK2_SY0 )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ( sK1_Xf @ sK3_SV3 )
= ( sK2_SY0 @ sK3_SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
( ( ~ ~ ! [SY6: b] :
~ ( ( ( sK1_Xf @ SY6 )
!= ( sK2_SY0 @ SY6 ) ) )
| ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) ) )
= $true ),
inference(choice,[status(thm)],[17]) ).
thf(25,plain,
( ( ~ ~ ! [SY8: b] :
~ ( ( ( sK1_Xf @ SY8 )
!= ( sK2_SY0 @ SY8 ) ) )
| ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) ) )
= $true ),
inference(choice,[status(thm)],[17]) ).
thf(26,plain,
( ( ( ~ ~ ! [SY6: b] :
~ ( ( ( sK1_Xf @ SY6 )
!= ( sK2_SY0 @ SY6 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ( ~ ~ ! [SY8: b] :
~ ( ( ( sK1_Xf @ SY8 )
!= ( sK2_SY0 @ SY8 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ( ~ ! [SY6: b] :
~ ( ( ( sK1_Xf @ SY6 )
!= ( sK2_SY0 @ SY6 ) ) ) )
= $false )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
( ( ( ~ ! [SY8: b] :
~ ( ( ( sK1_Xf @ SY8 )
!= ( sK2_SY0 @ SY8 ) ) ) )
= $false )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ( ! [SY6: b] :
~ ( ( ( sK1_Xf @ SY6 )
!= ( sK2_SY0 @ SY6 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ( ! [SY8: b] :
~ ( ( ( sK1_Xf @ SY8 )
!= ( sK2_SY0 @ SY8 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
! [SV6: b] :
( ( ( ~ ( ( ( sK1_Xf @ SV6 )
!= ( sK2_SY0 @ SV6 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV7: b] :
( ( ( ~ ( ( ( sK1_Xf @ SV7 )
!= ( sK2_SY0 @ SV7 ) ) ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV6: b] :
( ( ( ( sK1_Xf @ SV6 )
!= ( sK2_SY0 @ SV6 ) )
= $false )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV7: b] :
( ( ( ( sK1_Xf @ SV7 )
!= ( sK2_SY0 @ SV7 ) )
= $false )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: b] :
( ( ( ( sK1_Xf @ SV6 )
= ( sK2_SY0 @ SV6 ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV7: b] :
( ( ( ( sK1_Xf @ SV7 )
= ( sK2_SY0 @ SV7 ) )
= $true )
| ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
!= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: b] :
( ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK1_Xf @ SV6 )
= ( sK2_SY0 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV7: b] :
( ( ( ( sK1_Xf
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) )
= ( sK2_SY0
@ ( cJ
@ ^ [SX0: b] :
( ( sK1_Xf @ SX0 )
!= ( sK2_SY0 @ SX0 ) ) ) ) )
= $false )
| ( ( ( sK1_Xf @ SV7 )
= ( sK2_SY0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( sK1_Xf @ sK4_E )
= ( sK2_SY0 @ sK4_E ) )
= $false ),
inference(extuni,[status(esa)],[22]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,40,39,38,23,22]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO271^5 : 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
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 17:34:59 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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: true
% 0.08/0.23
% 0.08/0.23 *** Modified list of choice operators: cJ ***
% 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/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:1,ude:false,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:41,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 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: 35 ****
% 0.08/0.23 %**** clause counter: 41 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:1,ude:false,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:41,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------