%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO376^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 11:08:09 AM UTC 2026
% Result : Theorem 0.52s 0.30s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 90 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 750 ( 189 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 371 ( 37 ~; 120 |; 4 &; 208 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 26 ( 26 ^; 0 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cF,type,
cF: $o > $o ).
thf(tp_cG,type,
cG: $o > $o ).
thf(tp_cP,type,
cP: ( $o > $o ) > $o ).
thf(tp_sK1_E,type,
sK1_E: $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(1,conjecture,
( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
| ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM627) ).
thf(2,negated_conjecture,
( ( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
| ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( cP @ cF )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
( ( cP @ cG )
= $true ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
| ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
( ( ~ ( ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
| ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
& ~ ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( cP @ cG )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
( ( cP @ cF )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( cP
@ ^ [Xx: $o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
& ~ ( cP
@ ^ [Xx: $o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) )
| ~ ~ ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) )
| ~ ~ ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= ( cP @ cF ) )
= $false ),
inference(res,[status(thm)],[17,9]) ).
thf(20,plain,
( ( ( cP
@ ^ [SX0: $o] :
( ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= ( cP @ cG ) )
= $false ),
inference(res,[status(thm)],[17,8]) ).
thf(21,plain,
( ( ( ( cF @ sK1_E )
| ( cG @ sK1_E ) )
= $true )
| ( ( cG @ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[20]) ).
thf(22,plain,
( ( ( ( cF @ sK1_E )
| ( cG @ sK1_E ) )
= $false )
| ( ( cG @ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[20]) ).
thf(23,plain,
( ( ( ( cF @ sK2_E )
| ( cG @ sK2_E ) )
= $true )
| ( ( cF @ sK2_E )
= $true ) ),
inference(extuni,[status(esa)],[19]) ).
thf(24,plain,
( ( ( ( cF @ sK2_E )
| ( cG @ sK2_E ) )
= $false )
| ( ( cF @ sK2_E )
= $false ) ),
inference(extuni,[status(esa)],[19]) ).
thf(26,plain,
( ( ( cG @ sK1_E )
= $false )
| ( ( cG @ sK1_E )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ( cF @ sK1_E )
= $true )
| ( ( cG @ sK1_E )
= $true )
| ( ( cG @ sK1_E )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( ( cF @ sK2_E )
= $false )
| ( ( cF @ sK2_E )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ( cF @ sK2_E )
= $true )
| ( ( cG @ sK2_E )
= $true )
| ( ( cF @ sK2_E )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(31,plain,
( ( cG @ sK1_E )
= $false ),
inference(sim,[status(thm)],[26]) ).
thf(32,plain,
( ( ( cF @ sK1_E )
= $true )
| ( ( cG @ sK1_E )
= $true ) ),
inference(sim,[status(thm)],[27]) ).
thf(33,plain,
( ( cF @ sK2_E )
= $false ),
inference(sim,[status(thm)],[28]) ).
thf(34,plain,
( ( ( cF @ sK2_E )
= $true )
| ( ( cG @ sK2_E )
= $true ) ),
inference(sim,[status(thm)],[30]) ).
thf(35,plain,
( ( ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= ( cP @ cF ) )
= $false ),
inference(res,[status(thm)],[18,9]) ).
thf(36,plain,
( ( ( cP
@ ^ [SX0: $o] :
( ~ ( cF @ SX0 )
| ( cG @ SX0 ) ) )
= ( cP @ cG ) )
= $false ),
inference(res,[status(thm)],[18,8]) ).
thf(37,plain,
( ( ( ~ ( cF @ sK5_E )
| ( cG @ sK5_E ) )
= $true )
| ( ( cG @ sK5_E )
= $true ) ),
inference(extuni,[status(esa)],[36]) ).
thf(38,plain,
( ( ( ~ ( cF @ sK5_E )
| ( cG @ sK5_E ) )
= $false )
| ( ( cG @ sK5_E )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(40,plain,
( ( ( ~ ( cF @ sK6_E )
| ( cG @ sK6_E ) )
= $false )
| ( ( cF @ sK6_E )
= $false ) ),
inference(extuni,[status(esa)],[35]) ).
thf(42,plain,
( ( ( cG @ sK5_E )
= $false )
| ( ( cG @ sK5_E )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ( ~ ( cF @ sK5_E ) )
= $true )
| ( ( cG @ sK5_E )
= $true )
| ( ( cG @ sK5_E )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ( cG @ sK6_E )
= $false )
| ( ( cF @ sK6_E )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ( cF @ sK5_E )
= $false )
| ( ( cG @ sK5_E )
= $true )
| ( ( cG @ sK5_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
( ( cG @ sK5_E )
= $false ),
inference(sim,[status(thm)],[42]) ).
thf(52,plain,
( ( ( cF @ sK5_E )
= $false )
| ( ( cG @ sK5_E )
= $true ) ),
inference(sim,[status(thm)],[48]) ).
thf(64,plain,
( ( ( ( cG @ sK1_E )
= ( cG @ sK5_E ) )
= $false )
| ( ( cF @ sK1_E )
= $true ) ),
inference(res,[status(thm)],[32,51]) ).
thf(67,plain,
( ( ( ( cF @ sK1_E )
= ( cF @ sK2_E ) )
= $false )
| ( ( cG @ sK1_E )
= $true ) ),
inference(res,[status(thm)],[32,33]) ).
thf(68,plain,
( ( ( ( cG @ sK1_E )
= ( cG @ sK1_E ) )
= $false )
| ( ( cF @ sK1_E )
= $true ) ),
inference(res,[status(thm)],[32,31]) ).
thf(75,plain,
( ( cF @ sK1_E )
= $true ),
inference(extuni,[status(esa)],[68]) ).
thf(76,plain,
( ( ( cG @ sK1_E )
= $true )
| ( sK1_E = $true )
| ( sK2_E = $true ) ),
inference(extuni,[status(esa)],[67]) ).
thf(77,plain,
( ( ( cG @ sK1_E )
= $true )
| ( sK1_E = $false )
| ( sK2_E = $false ) ),
inference(extuni,[status(esa)],[67]) ).
thf(78,plain,
( ( ( cF @ sK1_E )
= $true )
| ( sK1_E = $true )
| ( sK5_E = $true ) ),
inference(extuni,[status(esa)],[64]) ).
thf(79,plain,
( ( ( cF @ sK1_E )
= $true )
| ( sK1_E = $false )
| ( sK5_E = $false ) ),
inference(extuni,[status(esa)],[64]) ).
thf(81,plain,
( ( ( cF @ sK1_E )
= ( cF @ sK2_E ) )
= $false ),
inference(res,[status(thm)],[75,33]) ).
thf(85,plain,
( ( sK1_E = $true )
| ( sK2_E = $true ) ),
inference(extuni,[status(esa)],[81]) ).
thf(86,plain,
( ( sK1_E = $false )
| ( sK2_E = $false ) ),
inference(extuni,[status(esa)],[81]) ).
thf(87,plain,
( ( ( ( cG @ sK2_E )
= ( cG @ sK5_E ) )
= $false )
| ( ( cF @ sK2_E )
= $true ) ),
inference(res,[status(thm)],[34,51]) ).
thf(90,plain,
( ( ( ( cF @ sK2_E )
= ( cF @ sK2_E ) )
= $false )
| ( ( cG @ sK2_E )
= $true ) ),
inference(res,[status(thm)],[34,33]) ).
thf(91,plain,
( ( ( ( cG @ sK2_E )
= ( cG @ sK1_E ) )
= $false )
| ( ( cF @ sK2_E )
= $true ) ),
inference(res,[status(thm)],[34,31]) ).
thf(98,plain,
( ( ( cF @ sK2_E )
= $true )
| ( sK2_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[91]) ).
thf(99,plain,
( ( ( cF @ sK2_E )
= $true )
| ( sK2_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[91]) ).
thf(100,plain,
( ( cG @ sK2_E )
= $true ),
inference(extuni,[status(esa)],[90]) ).
thf(101,plain,
( ( ( cF @ sK2_E )
= $true )
| ( sK2_E = $true )
| ( sK5_E = $true ) ),
inference(extuni,[status(esa)],[87]) ).
thf(102,plain,
( ( ( cF @ sK2_E )
= $true )
| ( sK2_E = $false )
| ( sK5_E = $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(103,plain,
( ( ( cG @ sK2_E )
= ( cG @ sK5_E ) )
= $false ),
inference(res,[status(thm)],[100,51]) ).
thf(105,plain,
( ( ( cG @ sK2_E )
= ( cG @ sK1_E ) )
= $false ),
inference(res,[status(thm)],[100,31]) ).
thf(108,plain,
( ( sK2_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[105]) ).
thf(109,plain,
( ( sK2_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[105]) ).
thf(110,plain,
( ( sK2_E = $true )
| ( sK5_E = $true ) ),
inference(extuni,[status(esa)],[103]) ).
thf(111,plain,
( ( sK2_E = $false )
| ( sK5_E = $false ) ),
inference(extuni,[status(esa)],[103]) ).
thf(113,plain,
( ( ( ( cG @ sK6_E )
= ( cG @ sK2_E ) )
= $false )
| ( ( cF @ sK6_E )
= $false ) ),
inference(res,[status(thm)],[45,100]) ).
thf(114,plain,
( ( ( ( cF @ sK6_E )
= ( cF @ sK1_E ) )
= $false )
| ( ( cG @ sK6_E )
= $false ) ),
inference(res,[status(thm)],[45,75]) ).
thf(121,plain,
( ( ( cG @ sK6_E )
= $false )
| ( sK6_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[114]) ).
thf(122,plain,
( ( ( cG @ sK6_E )
= $false )
| ( sK6_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[114]) ).
thf(123,plain,
( ( ( cF @ sK6_E )
= $false )
| ( sK6_E = $true )
| ( sK2_E = $true ) ),
inference(extuni,[status(esa)],[113]) ).
thf(124,plain,
( ( ( cF @ sK6_E )
= $false )
| ( sK6_E = $false )
| ( sK2_E = $false ) ),
inference(extuni,[status(esa)],[113]) ).
thf(126,plain,
( ( ( ( cF @ sK5_E )
= ( cF @ sK1_E ) )
= $false )
| ( ( cG @ sK5_E )
= $true ) ),
inference(res,[status(thm)],[52,75]) ).
thf(129,plain,
( ( ( ( cG @ sK5_E )
= ( cG @ sK5_E ) )
= $false )
| ( ( cF @ sK5_E )
= $false ) ),
inference(res,[status(thm)],[52,51]) ).
thf(131,plain,
( ( ( ( cG @ sK5_E )
= ( cG @ sK6_E ) )
= $false )
| ( ( cF @ sK5_E )
= $false )
| ( ( cF @ sK6_E )
= $false ) ),
inference(res,[status(thm)],[52,45]) ).
thf(133,plain,
( ( ( ( cG @ sK5_E )
= ( cG @ sK1_E ) )
= $false )
| ( ( cF @ sK5_E )
= $false ) ),
inference(res,[status(thm)],[52,31]) ).
thf(138,plain,
( ( ( cF @ sK5_E )
= $false )
| ( sK5_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[133]) ).
thf(139,plain,
( ( ( cF @ sK5_E )
= $false )
| ( sK5_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[133]) ).
thf(140,plain,
( ( ( cF @ sK6_E )
= $false )
| ( ( cF @ sK5_E )
= $false )
| ( sK5_E = $true )
| ( sK6_E = $true ) ),
inference(extuni,[status(esa)],[131]) ).
thf(141,plain,
( ( ( cF @ sK6_E )
= $false )
| ( ( cF @ sK5_E )
= $false )
| ( sK5_E = $false )
| ( sK6_E = $false ) ),
inference(extuni,[status(esa)],[131]) ).
thf(142,plain,
( ( cF @ sK5_E )
= $false ),
inference(extuni,[status(esa)],[129]) ).
thf(143,plain,
( ( ( cG @ sK5_E )
= $true )
| ( sK5_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[126]) ).
thf(144,plain,
( ( ( cG @ sK5_E )
= $true )
| ( sK5_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[126]) ).
thf(146,plain,
( ( ( cF @ sK5_E )
= ( cF @ sK1_E ) )
= $false ),
inference(res,[status(thm)],[142,75]) ).
thf(149,plain,
( ( sK5_E = $true )
| ( sK1_E = $true ) ),
inference(extuni,[status(esa)],[146]) ).
thf(150,plain,
( ( sK5_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[146]) ).
thf(183,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,150,149,144,143,142,141,140,139,138,124,123,122,121,111,110,109,108,102,101,100,99,98,86,85,79,78,77,76,75,51,45,33,31,18,17,9]) ).
thf(184,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO376^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 17:39:36 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.30
% 0.52/0.30 No.of.Axioms: 0
% 0.52/0.30
% 0.52/0.30 Length.of.Defs: 0
% 0.52/0.30
% 0.52/0.30 Contains.Choice.Funs: true
% 0.52/0.30 ...
% 0.52/0.30
% 0.52/0.30 ********************************
% 0.52/0.30 * All subproblems solved! *
% 0.52/0.30 ********************************
% 0.52/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:183,loop_count:20,foatp_calls:5,translation:fof_full)
% 0.52/0.30
% 0.52/0.30 %**** Beginning of derivation protocol ****
% 0.52/0.30 % SZS output start CNFRefutation
% See solution above
% 0.52/0.31
% 0.52/0.31 %**** End of derivation protocol ****
% 0.52/0.31 %**** no. of clauses in derivation: 90 ****
% 0.52/0.31 %**** clause counter: 183 ****
% 0.52/0.31
% 0.52/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:183,loop_count:20,foatp_calls:5,translation:fof_full)
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