%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO501^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n018.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 11:08:37 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 114 ( 41 ~; 18 |; 0 &; 55 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $o > $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $o ).
thf(1,conjecture,
( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
( ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( p
@ ( f @ x
@ ~ ~ y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6]) ).
thf(8,plain,
( ( p @ ( f @ x @ y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6]) ).
thf(9,plain,
( ( p
@ ( f @ x
@ ~ ~ y ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ( p
@ ( f @ x
@ ~ ~ y ) )
= ( p @ ( f @ x @ y ) ) )
= $false ),
inference(res,[status(thm)],[9,8]) ).
thf(11,plain,
( ( ( ~ ~ y )
= $true )
| ( y = $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ~ ~ y )
= $false )
| ( y = $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(13,plain,
( ( ( f @ x
@ ~ ~ y )
= ( f @ x @ y ) )
= $false ),
inference(extuni,[status(esa)],[10]) ).
thf(14,plain,
( ( ( ~ y ) = $true )
| ( y = $false ) ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ~ y ) = $false )
| ( y = $true ) ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( y = $false )
| ( y = $false ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( y = $true )
| ( y = $true ) ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
y = $false,
inference(sim,[status(thm)],[16]) ).
thf(19,plain,
y = $true,
inference(sim,[status(thm)],[17]) ).
thf(21,plain,
( ( ( ~ ~ y )
= $true )
| ( y = $true ) ),
inference(extuni,[status(esa)],[13]) ).
thf(22,plain,
( ( ( ~ ~ y )
= $false )
| ( y = $false ) ),
inference(extuni,[status(esa)],[13]) ).
thf(23,plain,
( ( ( ~ y ) = $true )
| ( y = $false ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(24,plain,
( ( ( ~ y ) = $false )
| ( y = $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( y = $false )
| ( y = $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( y = $true )
| ( y = $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
y = $false,
inference(sim,[status(thm)],[25]) ).
thf(28,plain,
y = $true,
inference(sim,[status(thm)],[26]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,28,27,19,18,13,9]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO501^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.11/0.18 % Computer : n018.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 17:44:07 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.24
% 0.11/0.24 No.of.Axioms: 0
% 0.11/0.24
% 0.11/0.24 Length.of.Defs: 0
% 0.11/0.24
% 0.11/0.24 Contains.Choice.Funs: false
% 0.11/0.24
% 0.11/0.24 ********************************
% 0.11/0.24 * All subproblems solved! *
% 0.11/0.24 ********************************
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox/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:30,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.11/0.24
% 0.11/0.24 %**** Beginning of derivation protocol ****
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24
% 0.11/0.24 %**** End of derivation protocol ****
% 0.11/0.24 %**** no. of clauses in derivation: 29 ****
% 0.11/0.24 %**** clause counter: 30 ****
% 0.11/0.24
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox/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:30,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------