%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM739^1 : 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 : n016.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 10:35:04 AM UTC 2026
% Result : Theorem 0.12s 0.23s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 330 ( 91 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 424 ( 63 ~; 74 |; 0 &; 268 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 112 ( 0 ^; 112 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_moref,type,
moref: frac > frac > $o ).
thf(tp_u,type,
u: frac ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(tp_z,type,
z: frac ).
thf(1,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( moref @ Xx @ Xy )
=> ( ( eq @ Xx @ Xz )
=> ( ( eq @ Xy @ Xu )
=> ( moref @ Xz @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(2,axiom,
! [Xx: frac,Xy: frac] :
( ( eq @ Xx @ Xy )
=> ( eq @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(3,axiom,
! [Xx: frac,Xy: frac,Xz: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xy @ Xz )
=> ( eq @ Xx @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(4,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).
thf(5,axiom,
eq @ y @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(6,axiom,
eq @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(7,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(8,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz46) ).
thf(9,negated_conjecture,
( ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( moref @ Xx @ Xy )
=> ( ( eq @ Xx @ Xz )
=> ( ( eq @ Xy @ Xu )
=> ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [Xx: frac,Xy: frac] :
( ( eq @ Xx @ Xy )
=> ( eq @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xy @ Xz )
=> ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( eq @ y @ u )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( eq @ x @ z )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ~ ( moref @ z @ u ) )
= $true ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(19,plain,
( ( eq @ z @ u )
= $false ),
inference(standard_cnf,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ ( eq @ z @ u ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xx @ Xz )
| ! [Xu: frac] :
( ~ ( eq @ Xy @ Xu )
| ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(22,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ( eq @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xy @ Xz )
| ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(24,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(25,plain,
( ( ( moref @ x @ y )
| ( eq @ x @ y ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(26,plain,
( ( ( moref @ x @ y )
| ( eq @ x @ y ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( eq @ x @ z )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(28,plain,
( ( eq @ y @ u )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xy @ Xz )
| ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ( eq @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xx @ Xz )
| ! [Xu: frac] :
( ~ ( eq @ Xy @ Xu )
| ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ~ ( moref @ z @ u ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(34,plain,
( ( ~ ( eq @ z @ u ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(35,plain,
( ( ( moref @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV1: $o] :
( ( ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[29]) ).
thf(38,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV2: frac] :
( ( ! [SY10: frac] :
( ~ ( eq @ SV2 @ SY10 )
| ! [SY11: frac] :
( ~ ( eq @ SY10 @ SY11 )
| ( eq @ SV2 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV3: frac] :
( ( ! [SY12: frac] :
( ~ ( eq @ SV3 @ SY12 )
| ( eq @ SY12 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV4: frac] :
( ( ! [SY13: frac] :
( ~ ( moref @ SV4 @ SY13 )
| ! [SY14: frac] :
( ~ ( eq @ SV4 @ SY14 )
| ! [Xu: frac] :
( ~ ( eq @ SY13 @ Xu )
| ( moref @ SY14 @ Xu ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
( ( moref @ z @ u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(43,plain,
( ( eq @ z @ u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(45,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(46,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV5: frac,SV2: frac] :
( ( ~ ( eq @ SV2 @ SV5 )
| ! [SY16: frac] :
( ~ ( eq @ SV5 @ SY16 )
| ( eq @ SV2 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV6: frac,SV3: frac] :
( ( ~ ( eq @ SV3 @ SV6 )
| ( eq @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV7: frac,SV4: frac] :
( ( ~ ( moref @ SV4 @ SV7 )
| ! [SY17: frac] :
( ~ ( eq @ SV4 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV7 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV5: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY16: frac] :
( ~ ( eq @ SV5 @ SY16 )
| ( eq @ SV2 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV6: frac,SV3: frac] :
( ( ( ~ ( eq @ SV3 @ SV6 ) )
= $true )
| ( ( eq @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV7: frac,SV4: frac] :
( ( ( ~ ( moref @ SV4 @ SV7 ) )
= $true )
| ( ( ! [SY17: frac] :
( ~ ( eq @ SV4 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV7 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV5: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV5 )
= $false )
| ( ( ! [SY16: frac] :
( ~ ( eq @ SV5 @ SY16 )
| ( eq @ SV2 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV6: frac,SV3: frac] :
( ( ( eq @ SV3 @ SV6 )
= $false )
| ( ( eq @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV7: frac,SV4: frac] :
( ( ( moref @ SV4 @ SV7 )
= $false )
| ( ( ! [SY17: frac] :
( ~ ( eq @ SV4 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV7 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV2: frac,SV8: frac,SV5: frac] :
( ( ( ~ ( eq @ SV5 @ SV8 )
| ( eq @ SV2 @ SV8 ) )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV7: frac,SV9: frac,SV4: frac] :
( ( ( ~ ( eq @ SV4 @ SV9 )
| ! [SY19: frac] :
( ~ ( eq @ SV7 @ SY19 )
| ( moref @ SV9 @ SY19 ) ) )
= $true )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV2: frac,SV8: frac,SV5: frac] :
( ( ( ~ ( eq @ SV5 @ SV8 ) )
= $true )
| ( ( eq @ SV2 @ SV8 )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV7: frac,SV9: frac,SV4: frac] :
( ( ( ~ ( eq @ SV4 @ SV9 ) )
= $true )
| ( ( ! [SY19: frac] :
( ~ ( eq @ SV7 @ SY19 )
| ( moref @ SV9 @ SY19 ) ) )
= $true )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV2: frac,SV8: frac,SV5: frac] :
( ( ( eq @ SV5 @ SV8 )
= $false )
| ( ( eq @ SV2 @ SV8 )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV7: frac,SV9: frac,SV4: frac] :
( ( ( eq @ SV4 @ SV9 )
= $false )
| ( ( ! [SY19: frac] :
( ~ ( eq @ SV7 @ SY19 )
| ( moref @ SV9 @ SY19 ) ) )
= $true )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV4: frac,SV9: frac,SV10: frac,SV7: frac] :
( ( ( ~ ( eq @ SV7 @ SV10 )
| ( moref @ SV9 @ SV10 ) )
= $true )
| ( ( eq @ SV4 @ SV9 )
= $false )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(66,plain,
! [SV4: frac,SV9: frac,SV10: frac,SV7: frac] :
( ( ( ~ ( eq @ SV7 @ SV10 ) )
= $true )
| ( ( moref @ SV9 @ SV10 )
= $true )
| ( ( eq @ SV4 @ SV9 )
= $false )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(67,plain,
! [SV4: frac,SV9: frac,SV10: frac,SV7: frac] :
( ( ( eq @ SV7 @ SV10 )
= $false )
| ( ( moref @ SV9 @ SV10 )
= $true )
| ( ( eq @ SV4 @ SV9 )
= $false )
| ( ( moref @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,67,63,57,52,51,50,43,42,35,28]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM739^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.12/0.18 % Computer : n016.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 13:41:59 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.23
% 0.12/0.23 No.of.Axioms: 7
% 0.12/0.23
% 0.12/0.23 Length.of.Defs: 0
% 0.12/0.23
% 0.12/0.23 Contains.Choice.Funs: false
% 0.12/0.23 .
% 0.12/0.23
% 0.12/0.23 ********************************
% 0.12/0.23 * All subproblems solved! *
% 0.12/0.23 ********************************
% 0.12/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.23
% 0.12/0.23 %**** Beginning of derivation protocol ****
% 0.12/0.23 % SZS output start CNFRefutation
% See solution above
% 0.12/0.23
% 0.12/0.23 %**** End of derivation protocol ****
% 0.12/0.23 %**** no. of clauses in derivation: 69 ****
% 0.12/0.23 %**** clause counter: 68 ****
% 0.12/0.23
% 0.12/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------