%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n020.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 11:07:23 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 13 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 115 ( 18 ~; 5 |; 11 &; 78 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 14 ^; 0 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: ( $i > $i ) > $o ).
thf(tp_b,type,
b: $o ).
thf(tp_f,type,
f: $o > $i > $i ).
thf(tp_p,type,
p: ( $i > $i ) > $o ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(tp_sK2_E,type,
sK2_E: $i ).
thf(1,conjecture,
( ( p
@ ^ [X: $i] :
( f
@ ( ( a
@ ^ [X: $i] : ( f @ b @ X ) )
& b )
@ X ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ( p
@ ^ [X: $i] :
( f
@ ( ( a
@ ^ [X: $i] : ( f @ b @ X ) )
& b )
@ X ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( p
@ ^ [X: $i] :
( f
@ ( ( a
@ ^ [X: $i] : ( f @ b @ X ) )
& b )
@ X ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( p
@ ^ [X: $i] :
( f
@ ( ( a
@ ^ [X: $i] : ( f @ b @ X ) )
& b )
@ X ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( p
@ ^ [X: $i] :
( f
@ ( ( a
@ ^ [X: $i] : ( f @ b @ X ) )
& b )
@ X ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( p
@ ( f
@ ~ ( ~ b
| ~ ( a @ ( f @ b ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( p
@ ^ [SX0: $i] :
( f
@ ~ ( ~ ( a
@ ^ [SX1: $i] : ( f @ b @ SX1 ) )
| ~ b )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( p
@ ( f
@ ~ ( ~ b
| ~ ( a @ ( f @ b ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
( ( ( p
@ ( f
@ ~ ( ~ b
| ~ ( a @ ( f @ b ) ) ) ) )
= ( p
@ ^ [SX0: $i] :
( f
@ ~ ( ~ ( a
@ ^ [SX1: $i] : ( f @ b @ SX1 ) )
| ~ b )
@ SX0 ) ) )
= $false ),
inference(res,[status(thm)],[11,10]) ).
thf(13,plain,
$false = $true,
inference(extuni,[status(esa)],[12]) ).
thf(14,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.08/0.18 % Computer : n020.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 17:31:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 0
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % 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:13,loop_count:2,foatp_calls:1,translation:fof_experiment)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 14 ****
% 0.08/0.21 %**** clause counter: 13 ****
% 0.08/0.21
% 0.08/0.21 % 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:13,loop_count:2,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------