%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO026^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:07:24 AM UTC 2026
% Result : Theorem 0.06s 0.29s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 111 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 119 ( 10 ~; 44 |; 6 &; 57 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 18 con; 0-2 aty)
% Number of variables : 24 ( 20 ^; 4 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: ( $o > $o ) > $o ).
thf(tp_sK10_E,type,
sK10_E: $o ).
thf(tp_sK11_E,type,
sK11_E: $o ).
thf(tp_sK12_E,type,
sK12_E: $o ).
thf(tp_sK13_E,type,
sK13_E: $o ).
thf(tp_sK14_E,type,
sK14_E: $o ).
thf(tp_sK15_E,type,
sK15_E: $o ).
thf(tp_sK16_E,type,
sK16_E: $o ).
thf(tp_sK17_E,type,
sK17_E: $o ).
thf(tp_sK1_Y,type,
sK1_Y: $o > $o ).
thf(tp_sK2_E,type,
sK2_E: $o ).
thf(tp_sK3_E,type,
sK3_E: $o ).
thf(tp_sK4_E,type,
sK4_E: $o ).
thf(tp_sK5_E,type,
sK5_E: $o ).
thf(tp_sK6_E,type,
sK6_E: $o ).
thf(tp_sK7_E,type,
sK7_E: $o ).
thf(tp_sK8_E,type,
sK8_E: $o ).
thf(tp_sK9_E,type,
sK9_E: $o ).
thf(1,conjecture,
( ( ( p
@ ^ [X: $o] : X )
& ( p
@ ^ [X: $o] : ~ X )
& ( p
@ ^ [X: $o] : $false )
& ( p
@ ^ [X: $o] : $true ) )
=> ! [Y: $o > $o] : ( p @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ( ( p
@ ^ [X: $o] : X )
& ( p
@ ^ [X: $o] : ~ X )
& ( p
@ ^ [X: $o] : $false )
& ( p
@ ^ [X: $o] : $true ) )
=> ! [Y: $o > $o] : ( p @ Y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( p
@ ^ [X: $o] : X )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
( ( p
@ ^ [X: $o] : ~ X )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( p
@ ^ [X: $o] : $false )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
( ( p
@ ^ [X: $o] : $true )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
( ( ! [Y: $o > $o] : ( p @ Y ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ! [Y: $o > $o] : ( p @ Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ( p @ sK1_Y ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( p
@ ^ [X: $o] : $true )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( p
@ ^ [X: $o] : $false )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( p
@ ^ [X: $o] : ~ X )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(13,plain,
( ( p
@ ^ [X: $o] : X )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(14,plain,
( ( ~ ( p @ sK1_Y ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( p @ sK1_Y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(16,plain,
( ( ( p @ sK1_Y )
= ( p
@ ^ [X: $o] : X ) )
= $false ),
inference(res,[status(thm)],[15,13]) ).
thf(17,plain,
( ( ( p @ sK1_Y )
= ( p
@ ^ [X: $o] : ~ X ) )
= $false ),
inference(res,[status(thm)],[15,12]) ).
thf(18,plain,
( ( ( p @ sK1_Y )
= ( p
@ ^ [X: $o] : $false ) )
= $false ),
inference(res,[status(thm)],[15,11]) ).
thf(19,plain,
( ( ( p @ sK1_Y )
= ( p
@ ^ [X: $o] : $true ) )
= $false ),
inference(res,[status(thm)],[15,10]) ).
thf(21,plain,
( ( ( sK1_Y @ sK14_E )
= $false )
| ( $true = $false ) ),
inference(extuni,[status(esa)],[19]) ).
thf(22,plain,
( ( ( sK1_Y @ sK15_E )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[18]) ).
thf(24,plain,
( ( ( sK1_Y @ sK16_E )
= $true )
| ( ( ~ sK16_E ) = $true ) ),
inference(extuni,[status(esa)],[17]) ).
thf(25,plain,
( ( ( sK1_Y @ sK16_E )
= $false )
| ( ( ~ sK16_E ) = $false ) ),
inference(extuni,[status(esa)],[17]) ).
thf(26,plain,
( ( ( sK1_Y @ sK17_E )
= $true )
| ( sK17_E = $true ) ),
inference(extuni,[status(esa)],[16]) ).
thf(27,plain,
( ( ( sK1_Y @ sK17_E )
= $false )
| ( sK17_E = $false ) ),
inference(extuni,[status(esa)],[16]) ).
thf(28,plain,
( ( sK16_E = $true )
| ( ( sK1_Y @ sK16_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( sK16_E = $false )
| ( ( sK1_Y @ sK16_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( sK1_Y @ sK14_E )
= $false ),
inference(sim,[status(thm)],[21]) ).
thf(31,plain,
( ( sK1_Y @ sK15_E )
= $true ),
inference(sim,[status(thm)],[22]) ).
thf(36,plain,
( ( ( sK1_Y @ sK15_E )
= ( sK1_Y @ sK14_E ) )
= $false ),
inference(res,[status(thm)],[31,30]) ).
thf(38,plain,
( ( sK15_E = $true )
| ( sK14_E = $true ) ),
inference(extuni,[status(esa)],[36]) ).
thf(39,plain,
( ( sK15_E = $false )
| ( sK14_E = $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(41,plain,
( ( ( ( sK1_Y @ sK17_E )
= ( sK1_Y @ sK14_E ) )
= $false )
| ( sK17_E = $true ) ),
inference(res,[status(thm)],[26,30]) ).
thf(45,plain,
( ( sK17_E = $true )
| ( sK17_E = $true )
| ( sK14_E = $true ) ),
inference(extuni,[status(esa)],[41]) ).
thf(47,plain,
( ( sK17_E = $true )
| ( sK14_E = $true ) ),
inference(sim,[status(thm)],[45]) ).
thf(49,plain,
( ( ( ( sK1_Y @ sK17_E )
= ( sK1_Y @ sK15_E ) )
= $false )
| ( sK17_E = $false ) ),
inference(res,[status(thm)],[27,31]) ).
thf(66,plain,
( ( sK17_E = $false )
| ( sK17_E = $false )
| ( sK15_E = $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(67,plain,
( ( sK17_E = $false )
| ( sK15_E = $false ) ),
inference(sim,[status(thm)],[66]) ).
thf(68,plain,
( ( ( ( sK1_Y @ sK16_E )
= ( sK1_Y @ sK15_E ) )
= $false )
| ( sK16_E = $true ) ),
inference(res,[status(thm)],[28,31]) ).
thf(75,plain,
( ( ( ( sK1_Y @ sK16_E )
= ( sK1_Y @ sK17_E ) )
= $false )
| ( sK16_E = $true )
| ( sK17_E = $true ) ),
inference(res,[status(thm)],[28,26]) ).
thf(81,plain,
( ( sK17_E = $true )
| ( sK16_E = $true )
| ( sK16_E = $true )
| ( sK17_E = $true ) ),
inference(extuni,[status(esa)],[75]) ).
thf(83,plain,
( ( sK16_E = $true )
| ( sK16_E = $true )
| ( sK15_E = $true ) ),
inference(extuni,[status(esa)],[68]) ).
thf(85,plain,
( ( sK17_E = $true )
| ( sK16_E = $true ) ),
inference(sim,[status(thm)],[81]) ).
thf(86,plain,
( ( sK16_E = $true )
| ( sK15_E = $true ) ),
inference(sim,[status(thm)],[83]) ).
thf(88,plain,
( ( ( ( sK1_Y @ sK16_E )
= ( sK1_Y @ sK14_E ) )
= $false )
| ( sK16_E = $false ) ),
inference(res,[status(thm)],[29,30]) ).
thf(94,plain,
( ( ( ( sK1_Y @ sK16_E )
= ( sK1_Y @ sK17_E ) )
= $false )
| ( sK16_E = $false )
| ( sK17_E = $false ) ),
inference(res,[status(thm)],[29,27]) ).
thf(103,plain,
( ( sK17_E = $false )
| ( sK16_E = $false )
| ( sK16_E = $false )
| ( sK17_E = $false ) ),
inference(extuni,[status(esa)],[94]) ).
thf(107,plain,
( ( sK16_E = $false )
| ( sK16_E = $false )
| ( sK14_E = $false ) ),
inference(extuni,[status(esa)],[88]) ).
thf(108,plain,
( ( sK17_E = $false )
| ( sK16_E = $false ) ),
inference(sim,[status(thm)],[103]) ).
thf(109,plain,
( ( sK16_E = $false )
| ( sK14_E = $false ) ),
inference(sim,[status(thm)],[107]) ).
thf(148,plain,
( ( ( sK14_E = sK14_E )
= $false )
| ( sK17_E = $true )
| ( sK15_E = $false ) ),
inference(res,[status(thm)],[47,39]) ).
thf(159,plain,
( ( ( sK17_E = sK17_E )
= $false )
| ( sK14_E = $true )
| ( ( sK1_Y @ sK17_E )
= $false ) ),
inference(res,[status(thm)],[47,27]) ).
thf(165,plain,
( ( ( sK1_Y @ sK17_E )
= $false )
| ( sK14_E = $true ) ),
inference(extuni,[status(esa)],[159]) ).
thf(166,plain,
( ( sK15_E = $false )
| ( sK17_E = $true ) ),
inference(extuni,[status(esa)],[148]) ).
thf(167,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,166,165,109,108,86,85,67,47,39,38,31,30,29,28,27,26,15,13,12,11]) ).
thf(168,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO026^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.20 % Computer : n003.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Oct 6 17:32:54 UTC 2026
% 0.06/0.21 % CPUTime :
% 0.06/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.29
% 0.06/0.29 No.of.Axioms: 0
% 0.06/0.29
% 0.06/0.29 Length.of.Defs: 0
% 0.06/0.29
% 0.06/0.29 Contains.Choice.Funs: true
% 0.06/0.29 ...
% 0.06/0.29
% 0.06/0.29 ********************************
% 0.06/0.29 * All subproblems solved! *
% 0.06/0.29 ********************************
% 0.06/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:167,loop_count:15,foatp_calls:3,translation:fof_full)
% 0.06/0.29
% 0.06/0.29 %**** Beginning of derivation protocol ****
% 0.06/0.29 % SZS output start CNFRefutation
% See solution above
% 0.06/0.29
% 0.06/0.29 %**** End of derivation protocol ****
% 0.06/0.29 %**** no. of clauses in derivation: 56 ****
% 0.06/0.29 %**** clause counter: 167 ****
% 0.06/0.29
% 0.06/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:167,loop_count:15,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------