%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO042^2 : 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/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 11:07:27 AM UTC 2026
% Result : Theorem 0.32s 0.36s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 107 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 949 ( 271 equ; 11 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 483 ( 183 ~; 151 |; 20 &; 129 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $o > $o ).
thf(tp_p,type,
p: ( $o > $o ) > $o ).
thf(tp_sK1_E,type,
sK1_E: $o ).
thf(tp_x,type,
x: $o ).
thf(tp_y,type,
y: $o ).
thf(1,conjecture,
~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',4) ).
thf(2,negated_conjecture,
( ( ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) )
= $true ),
inference(polarity_switch,[status(thm)],[2]) ).
thf(4,plain,
( ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[3]) ).
thf(5,plain,
( ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
| ~ ( p @ g ) )
| ~ ~ ( p @ (~) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
| ~ ( p @ g ) )
| ~ ~ ( p @ (~) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
| ~ ( p @ g ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ~ ( p @ (~) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
| ~ ( p @ g ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( p @ (~) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
| ~ ( p @ g ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( p @ (~) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( p @ g ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( p @ g )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
| ( ( g @ y )
!= x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(20,plain,
( ( ( g @ y )
!= x )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ( g @ y )
= x )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( ( x != y ) )
| ( ( g @ x )
!= y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( ( g @ y )
| x )
| ~ ( ~ ( g @ y )
| ~ x ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ( g @ y )
= x )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( ( x != y ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ( g @ x )
!= y )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ~ ( ( g @ y )
| x ) )
= $true )
| ( ( ~ ( ~ ( g @ y )
| ~ x ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( x != y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( g @ x )
= y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ( g @ y )
| x )
= $false )
| ( ( ~ ( ~ ( g @ y )
| ~ x ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( x = y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ( ( g @ x )
| y )
| ~ ( ~ ( g @ x )
| ~ y ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( g @ x )
= y )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ( g @ y )
= $false )
| ( ( ~ ( ~ ( g @ y )
| ~ x ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( x = $false )
| ( ( ~ ( ~ ( g @ y )
| ~ x ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ ( x
| y )
| ~ ( ~ x
| ~ y ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(38,plain,
( ( x = y )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[32]) ).
thf(39,plain,
( ( ( ~ ( ( g @ x )
| y ) )
= $true )
| ( ( ~ ( ~ ( g @ x )
| ~ y ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ( ~ ( g @ y )
| ~ x )
= $false )
| ( ( g @ y )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ( ~ ( g @ y )
| ~ x )
= $false )
| ( x = $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( x
| y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ( ~ x
| ~ y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
( ( ( ( g @ x )
| y )
= $false )
| ( ( ~ ( ~ ( g @ x )
| ~ y ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ( ~ x ) = $false )
| ( ( g @ y )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(47,plain,
( ( ( ~ ( g @ y ) )
= $false )
| ( x = $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( x
| y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
( ( ~ x
| ~ y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(51,plain,
( ( ( g @ x )
= $false )
| ( ( ~ ( ~ ( g @ x )
| ~ y ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(52,plain,
( ( y = $false )
| ( ( ~ ( ~ ( g @ x )
| ~ y ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(54,plain,
( ( x = $true )
| ( ( g @ y )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(55,plain,
( ( ( g @ y )
= $true )
| ( x = $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(57,plain,
( ( x = $true )
| ( y = $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(58,plain,
( ( ( ~ x ) = $true )
| ( ( ~ y ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(59,plain,
( ( ( ~ ( g @ x )
| ~ y )
= $false )
| ( ( g @ x )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(60,plain,
( ( ( ~ ( g @ x )
| ~ y )
= $false )
| ( y = $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
( ( x = $false )
| ( ( ~ y ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
( ( ( ~ y ) = $false )
| ( ( g @ x )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(64,plain,
( ( ( ~ ( g @ x ) )
= $false )
| ( y = $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(66,plain,
( ( y = $false )
| ( x = $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(68,plain,
( ( y = $true )
| ( ( g @ x )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(69,plain,
( ( ( g @ x )
= $true )
| ( y = $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(99,plain,
( ( ( p @ g )
= ( p @ (~) ) )
= $false ),
inference(res,[status(thm)],[17,13]) ).
thf(100,plain,
( ( ( g @ sK1_E )
= $true )
| ( ( ~ sK1_E ) = $true ) ),
inference(extuni,[status(esa)],[99]) ).
thf(101,plain,
( ( ( g @ sK1_E )
= $false )
| ( ( ~ sK1_E ) = $false ) ),
inference(extuni,[status(esa)],[99]) ).
thf(102,plain,
( ( sK1_E = $true )
| ( ( g @ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(103,plain,
( ( sK1_E = $false )
| ( ( g @ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
( ( ( g @ y )
= $true )
| ( x = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[25]) ).
thf(106,plain,
( ( ( g @ y )
= $false )
| ( x = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[25]) ).
thf(108,plain,
( ( ( g @ x )
= $true )
| ( y = $false ) ),
inference(extcnf_equal_pos,[status(thm)],[34]) ).
thf(109,plain,
( ( ( g @ x )
= $false )
| ( y = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[34]) ).
thf(110,plain,
( ( ( x = y )
= ( ( g @ x )
= y ) )
= $false ),
inference(res,[status(thm)],[38,34]) ).
thf(111,plain,
( ( ( x = y )
= ( ( g @ y )
= x ) )
= $false ),
inference(res,[status(thm)],[38,25]) ).
thf(113,plain,
( ( y = $true )
| ( ( g @ y )
= $true ) ),
inference(extuni,[status(esa)],[111]) ).
thf(114,plain,
( ( y = $false )
| ( ( g @ y )
= $false ) ),
inference(extuni,[status(esa)],[111]) ).
thf(115,plain,
( ( y = $true )
| ( x = $true )
| ( x = $true )
| ( ( g @ y )
= $true ) ),
inference(extuni,[status(esa)],[111]) ).
thf(118,plain,
( ( y = $false )
| ( x = $false )
| ( x = $false )
| ( ( g @ y )
= $false ) ),
inference(extuni,[status(esa)],[111]) ).
thf(119,plain,
( ( x = $true )
| ( y = $true )
| ( y = $true )
| ( ( g @ x )
= $true ) ),
inference(extuni,[status(esa)],[110]) ).
thf(122,plain,
( ( x = $false )
| ( y = $false )
| ( y = $false )
| ( ( g @ x )
= $false ) ),
inference(extuni,[status(esa)],[110]) ).
thf(123,plain,
( ( x = $true )
| ( ( g @ x )
= $true ) ),
inference(extuni,[status(esa)],[110]) ).
thf(124,plain,
( ( x = $false )
| ( ( g @ x )
= $false ) ),
inference(extuni,[status(esa)],[110]) ).
thf(125,plain,
( ( y = $false )
| ( x = $false )
| ( ( g @ y )
= $false ) ),
inference(sim,[status(thm)],[118]) ).
thf(126,plain,
( ( y = $true )
| ( x = $true )
| ( ( g @ y )
= $true ) ),
inference(sim,[status(thm)],[115]) ).
thf(127,plain,
( ( x = $false )
| ( y = $false )
| ( ( g @ x )
= $false ) ),
inference(sim,[status(thm)],[122]) ).
thf(128,plain,
( ( x = $true )
| ( y = $true )
| ( ( g @ x )
= $true ) ),
inference(sim,[status(thm)],[119]) ).
thf(148,plain,
( ( ( x = x )
= $false )
| ( y = $true )
| ( ( g @ y )
= $true ) ),
inference(res,[status(thm)],[57,55]) ).
thf(156,plain,
( ( ( g @ y )
= $true )
| ( y = $true ) ),
inference(extuni,[status(esa)],[148]) ).
thf(163,plain,
( ( ( x = x )
= $false )
| ( y = $false )
| ( ( g @ y )
= $false ) ),
inference(res,[status(thm)],[66,54]) ).
thf(172,plain,
( ( ( g @ y )
= $false )
| ( y = $false ) ),
inference(extuni,[status(esa)],[163]) ).
thf(178,plain,
( ( ( y = y )
= $false )
| ( ( g @ x )
= $false )
| ( x = $false ) ),
inference(res,[status(thm)],[68,66]) ).
thf(192,plain,
( ( x = $false )
| ( ( g @ x )
= $false ) ),
inference(extuni,[status(esa)],[178]) ).
thf(199,plain,
( ( ( y = y )
= $false )
| ( ( g @ x )
= $true )
| ( x = $true ) ),
inference(res,[status(thm)],[69,57]) ).
thf(212,plain,
( ( x = $true )
| ( ( g @ x )
= $true ) ),
inference(extuni,[status(esa)],[199]) ).
thf(218,plain,
( ( ( ( g @ sK1_E )
= ( g @ x ) )
= $false )
| ( sK1_E = $true )
| ( y = $false ) ),
inference(res,[status(thm)],[102,69]) ).
thf(226,plain,
( ( ( ( g @ sK1_E )
= ( g @ y ) )
= $false )
| ( sK1_E = $true )
| ( x = $false ) ),
inference(res,[status(thm)],[102,55]) ).
thf(234,plain,
( ( x = $false )
| ( sK1_E = $true )
| ( sK1_E = $true )
| ( y = $true ) ),
inference(extuni,[status(esa)],[226]) ).
thf(236,plain,
( ( y = $false )
| ( sK1_E = $true )
| ( sK1_E = $true )
| ( x = $true ) ),
inference(extuni,[status(esa)],[218]) ).
thf(238,plain,
( ( x = $false )
| ( sK1_E = $true )
| ( y = $true ) ),
inference(sim,[status(thm)],[234]) ).
thf(239,plain,
( ( y = $false )
| ( sK1_E = $true )
| ( x = $true ) ),
inference(sim,[status(thm)],[236]) ).
thf(246,plain,
( ( ( ( g @ sK1_E )
= ( g @ x ) )
= $false )
| ( sK1_E = $false )
| ( y = $true ) ),
inference(res,[status(thm)],[103,68]) ).
thf(254,plain,
( ( ( ( g @ sK1_E )
= ( g @ y ) )
= $false )
| ( sK1_E = $false )
| ( x = $true ) ),
inference(res,[status(thm)],[103,54]) ).
thf(262,plain,
( ( x = $true )
| ( sK1_E = $false )
| ( sK1_E = $false )
| ( y = $false ) ),
inference(extuni,[status(esa)],[254]) ).
thf(264,plain,
( ( y = $true )
| ( sK1_E = $false )
| ( sK1_E = $false )
| ( x = $false ) ),
inference(extuni,[status(esa)],[246]) ).
thf(267,plain,
( ( x = $true )
| ( sK1_E = $false )
| ( y = $false ) ),
inference(sim,[status(thm)],[262]) ).
thf(268,plain,
( ( y = $true )
| ( sK1_E = $false )
| ( x = $false ) ),
inference(sim,[status(thm)],[264]) ).
thf(269,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,268,267,239,238,212,192,172,156,128,127,126,125,124,123,114,113,109,108,106,105,103,102,69,68,66,57,55,54,38,34,25,17]) ).
thf(270,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO042^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n003.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 17:33:09 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.36
% 0.32/0.36 No.of.Axioms: 0
% 0.32/0.36
% 0.32/0.36 Length.of.Defs: 0
% 0.32/0.36
% 0.32/0.36 Contains.Choice.Funs: true
% 0.32/0.36 ....
% 0.32/0.36
% 0.32/0.36 ********************************
% 0.32/0.36 * All subproblems solved! *
% 0.32/0.36 ********************************
% 0.32/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:269,loop_count:20,foatp_calls:6,translation:fof_full)
% 0.32/0.36
% 0.32/0.36 %**** Beginning of derivation protocol ****
% 0.32/0.36 % SZS output start CNFRefutation
% See solution above
% 0.32/0.36
% 0.32/0.36 %**** End of derivation protocol ****
% 0.32/0.36 %**** no. of clauses in derivation: 107 ****
% 0.32/0.36 %**** clause counter: 269 ****
% 0.32/0.36
% 0.32/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:269,loop_count:20,foatp_calls:6,translation:fof_full)
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