%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO549^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n015.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 11:08:42 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 75 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 826 ( 241 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 448 ( 168 ~; 167 |; 0 &; 113 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 11 ( 11 ^; 0 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $o > $o ).
thf(tp_g,type,
g: $o > $o ).
thf(tp_p,type,
p: ( $o > $o ) > ( $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(1,axiom,
( p
@ ^ [X: $o] :
( f
@ ~ ~ X )
@ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pfg) ).
thf(2,conjecture,
( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pfgc) ).
thf(3,negated_conjecture,
( ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( p
@ ^ [X: $o] :
( f
@ ~ ~ X )
@ g )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( p
@ ^ [X: $o] :
( f
@ ~ ~ X )
@ g )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
( ( ( p @ f
@ ^ [X: $o] :
( g
@ ~ ~ X ) )
= ( p
@ ^ [X: $o] :
( f
@ ~ ~ X )
@ g ) )
= $false ),
inference(res,[status(thm)],[9,7]) ).
thf(11,plain,
( ( ( ~ ~ sK2_E )
= $true )
| ( sK2_E = $true )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ~ ~ sK2_E )
= $false )
| ( sK2_E = $false )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(13,plain,
( ( ( g
@ ~ ~ sK2_E )
= $true )
| ( ( g @ sK2_E )
= $true )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(14,plain,
( ( ( g
@ ~ ~ sK2_E )
= $false )
| ( ( g @ sK2_E )
= $false )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(15,plain,
( ( ( ~ ~ sK3_E )
= $true )
| ( sK3_E = $true )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(16,plain,
( ( ( ~ ~ sK3_E )
= $false )
| ( sK3_E = $false )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(17,plain,
( ( ( g
@ ~ ~ sK3_E )
= $true )
| ( ( g @ sK3_E )
= $true )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(18,plain,
( ( ( g
@ ~ ~ sK3_E )
= $false )
| ( ( g @ sK3_E )
= $false )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(19,plain,
( ( ( ~ ~ sK4_E )
= $true )
| ( sK4_E = $true )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(20,plain,
( ( ( ~ ~ sK4_E )
= $false )
| ( sK4_E = $false )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(21,plain,
( ( ( g
@ ~ ~ sK4_E )
= $true )
| ( ( g @ sK4_E )
= $true )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(22,plain,
( ( ( g
@ ~ ~ sK4_E )
= $false )
| ( ( g @ sK4_E )
= $false )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extuni,[status(esa)],[10]) ).
thf(23,plain,
( ( ( ~ ~ sK5_E )
= $true )
| ( sK5_E = $true )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(24,plain,
( ( ( ~ ~ sK5_E )
= $false )
| ( sK5_E = $false )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(25,plain,
( ( ( g
@ ~ ~ sK5_E )
= $true )
| ( ( g @ sK5_E )
= $true )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(26,plain,
( ( ( g
@ ~ ~ sK5_E )
= $false )
| ( ( g @ sK5_E )
= $false )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extuni,[status(esa)],[10]) ).
thf(27,plain,
( ( ( ~ sK5_E ) = $true )
| ( sK5_E = $false )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ~ sK5_E ) = $false )
| ( sK5_E = $true )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ( ~ sK4_E ) = $true )
| ( sK4_E = $false )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(30,plain,
( ( ( ~ sK4_E ) = $false )
| ( sK4_E = $true )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(31,plain,
( ( ( ~ sK1_E ) = $true )
| ( sK1_E = $false )
| ( ( g @ sK3_E )
= $false )
| ( ( g
@ ~ ~ sK3_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(32,plain,
( ( ( ~ sK1_E ) = $true )
| ( sK1_E = $false )
| ( ( g @ sK3_E )
= $true )
| ( ( g
@ ~ ~ sK3_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(33,plain,
( ( ( ~ sK3_E ) = $true )
| ( sK3_E = $false )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(34,plain,
( ( ( ~ sK3_E ) = $false )
| ( sK3_E = $true )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(35,plain,
( ( ( ~ sK1_E ) = $false )
| ( sK1_E = $true )
| ( ( g @ sK2_E )
= $false )
| ( ( g
@ ~ ~ sK2_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(36,plain,
( ( ( ~ sK1_E ) = $false )
| ( sK1_E = $true )
| ( ( g @ sK2_E )
= $true )
| ( ( g
@ ~ ~ sK2_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(37,plain,
( ( ( ~ sK2_E ) = $true )
| ( sK2_E = $false )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(38,plain,
( ( ( ~ sK2_E ) = $false )
| ( sK2_E = $true )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(39,plain,
( ( sK5_E = $false )
| ( sK5_E = $false )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(40,plain,
( ( sK5_E = $true )
| ( sK5_E = $true )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(41,plain,
( ( sK4_E = $false )
| ( sK4_E = $false )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(42,plain,
( ( sK4_E = $true )
| ( sK4_E = $true )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(43,plain,
( ( sK1_E = $false )
| ( sK1_E = $false )
| ( ( g @ sK3_E )
= $false )
| ( ( g
@ ~ ~ sK3_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(44,plain,
( ( sK1_E = $false )
| ( sK1_E = $false )
| ( ( g @ sK3_E )
= $true )
| ( ( g
@ ~ ~ sK3_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(45,plain,
( ( sK3_E = $false )
| ( sK3_E = $false )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(46,plain,
( ( sK3_E = $true )
| ( sK3_E = $true )
| ( sK1_E = $false )
| ( ( ~ ~ sK1_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(47,plain,
( ( sK1_E = $true )
| ( sK1_E = $true )
| ( ( g @ sK2_E )
= $false )
| ( ( g
@ ~ ~ sK2_E )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(48,plain,
( ( sK1_E = $true )
| ( sK1_E = $true )
| ( ( g @ sK2_E )
= $true )
| ( ( g
@ ~ ~ sK2_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(49,plain,
( ( sK2_E = $false )
| ( sK2_E = $false )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(50,plain,
( ( sK2_E = $true )
| ( sK2_E = $true )
| ( sK1_E = $true )
| ( ( ~ ~ sK1_E )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(51,plain,
( ( ( ~ sK1_E ) = $true )
| ( sK1_E = $false )
| ( sK3_E = $false )
| ( sK3_E = $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
( ( ( ~ sK1_E ) = $true )
| ( sK1_E = $false )
| ( sK3_E = $true )
| ( sK3_E = $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
( ( ( ~ sK1_E ) = $false )
| ( sK1_E = $true )
| ( sK2_E = $false )
| ( sK2_E = $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
( ( ( ~ sK1_E ) = $false )
| ( sK1_E = $true )
| ( sK2_E = $true )
| ( sK2_E = $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
( ( sK1_E = $false )
| ( sK1_E = $false )
| ( sK3_E = $false )
| ( sK3_E = $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( sK1_E = $false )
| ( sK1_E = $false )
| ( sK3_E = $true )
| ( sK3_E = $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
( ( sK1_E = $true )
| ( sK1_E = $true )
| ( sK2_E = $false )
| ( sK2_E = $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
( ( sK1_E = $true )
| ( sK1_E = $true )
| ( sK2_E = $true )
| ( sK2_E = $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
( ( sK5_E = $false )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(sim,[status(thm)],[39]) ).
thf(60,plain,
( ( sK5_E = $true )
| ( ( f @ sK1_E )
= $false )
| ( ( f
@ ~ ~ sK1_E )
= $false ) ),
inference(sim,[status(thm)],[40]) ).
thf(61,plain,
( ( sK4_E = $false )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(sim,[status(thm)],[41]) ).
thf(62,plain,
( ( sK4_E = $true )
| ( ( f @ sK1_E )
= $true )
| ( ( f
@ ~ ~ sK1_E )
= $true ) ),
inference(sim,[status(thm)],[42]) ).
thf(63,plain,
( ( sK1_E = $false )
| ( ( g @ sK3_E )
= $false )
| ( ( g
@ ~ ~ sK3_E )
= $false ) ),
inference(sim,[status(thm)],[43]) ).
thf(64,plain,
( ( sK1_E = $false )
| ( ( g @ sK3_E )
= $true )
| ( ( g
@ ~ ~ sK3_E )
= $true ) ),
inference(sim,[status(thm)],[44]) ).
thf(65,plain,
( ( sK1_E = $false )
| ( sK3_E = $false ) ),
inference(sim,[status(thm)],[55]) ).
thf(66,plain,
( ( sK1_E = $false )
| ( sK3_E = $true ) ),
inference(sim,[status(thm)],[56]) ).
thf(67,plain,
( ( sK1_E = $true )
| ( ( g @ sK2_E )
= $false )
| ( ( g
@ ~ ~ sK2_E )
= $false ) ),
inference(sim,[status(thm)],[47]) ).
thf(68,plain,
( ( sK1_E = $true )
| ( ( g @ sK2_E )
= $true )
| ( ( g
@ ~ ~ sK2_E )
= $true ) ),
inference(sim,[status(thm)],[48]) ).
thf(69,plain,
( ( sK1_E = $true )
| ( sK2_E = $false ) ),
inference(sim,[status(thm)],[57]) ).
thf(70,plain,
( ( sK1_E = $true )
| ( sK2_E = $true ) ),
inference(sim,[status(thm)],[58]) ).
thf(76,plain,
( ( ( sK3_E = sK3_E )
= $false )
| ( sK1_E = $false )
| ( sK1_E = $false ) ),
inference(res,[status(thm)],[66,65]) ).
thf(80,plain,
( ( sK1_E = $false )
| ( sK1_E = $false ) ),
inference(extuni,[status(esa)],[76]) ).
thf(81,plain,
sK1_E = $false,
inference(sim,[status(thm)],[80]) ).
thf(82,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[7,81,70,69,68,67,66,65,64,63,62,61,60,59,26,25,22,21,9]) ).
thf(83,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO549^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 17:45:28 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 1
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 .
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % 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:82,loop_count:5,foatp_calls:2,translation:fof_experiment)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 75 ****
% 0.07/0.22 %**** clause counter: 82 ****
% 0.07/0.22
% 0.07/0.22 % 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:82,loop_count:5,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------