%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG285^5 : 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 : 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 10:08:46 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 52 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 115 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 318 ( 11 ~; 0 |; 14 &; 290 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 122 ( 0 ^; 110 !; 12 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cE,type,
cE: a ).
thf(tp_cJ,type,
cJ: a > a ).
thf(tp_cP,type,
cP: a > a > a ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY12,type,
sK2_SY12: a ).
thf(tp_sK3_SY14,type,
sK3_SY14: a ).
thf(tp_sK4_X,type,
sK4_X: a ).
thf(tp_sK5_SY15,type,
sK5_SY15: a ).
thf(tp_sK6_X,type,
sK6_X: a ).
thf(tp_sK7_SY18,type,
sK7_SY18: a ).
thf(1,conjecture,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [X: a,Y: a] :
( ? [U: a] :
( ( cP @ X @ U )
= Y )
& ? [V: a] :
( ( cP @ V @ X )
= Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM22_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [X: a,Y: a] :
( ? [U: a] :
( ( cP @ X @ U )
= Y )
& ? [V: a] :
( ( cP @ V @ X )
= Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [X: a,Y: a] :
( ? [U: a] :
( ( cP @ X @ U )
= Y )
& ? [V: a] :
( ( cP @ V @ X )
= Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [X: a,Y: a] :
( ? [U: a] :
( ( cP @ X @ U )
= Y )
& ? [V: a] :
( ( cP @ V @ X )
= Y ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [X: a,Y: a] :
? [U: a] :
( ( cP @ X @ U )
= Y ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ! [X: a,Y: a] :
? [V: a] :
( ( cP @ V @ X )
= Y ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(11,plain,
( ( ~ ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [X: a,Y: a] :
? [U: a] :
( ( cP @ X @ U )
= Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [X: a,Y: a] :
? [V: a] :
( ( cP @ V @ X )
= Y ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(14,plain,
( ( ( cP @ ( cP @ sK1_Xx @ sK2_SY12 ) @ sK3_SY14 )
!= ( cP @ sK1_Xx @ ( cP @ sK2_SY12 @ sK3_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(15,plain,
( ( ! [SY17: a] :
( ( cP @ sK4_X @ SY17 )
!= sK5_SY15 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(16,plain,
( ( ! [SY20: a] :
( ( cP @ SY20 @ sK6_X )
!= sK7_SY18 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(17,plain,
( ( ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(20,plain,
( ( ( cP @ ( cP @ sK1_Xx @ sK2_SY12 ) @ sK3_SY14 )
!= ( cP @ sK1_Xx @ ( cP @ sK2_SY12 @ sK3_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
! [SV1: a] :
( ( ( cP @ ( cJ @ SV1 ) @ SV1 )
= cE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: a] :
( ( ( cP @ cE @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: a] :
( ( ! [SY21: a,SY22: a] :
( ( cP @ ( cP @ SV3 @ SY21 ) @ SY22 )
= ( cP @ SV3 @ ( cP @ SY21 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ( cP @ ( cP @ sK1_Xx @ sK2_SY12 ) @ sK3_SY14 )
= ( cP @ sK1_Xx @ ( cP @ sK2_SY12 @ sK3_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: a,SV3: a] :
( ( ! [SY23: a] :
( ( cP @ ( cP @ SV3 @ SV4 ) @ SY23 )
= ( cP @ SV3 @ ( cP @ SV4 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV5: a,SV4: a,SV3: a] :
( ( ( cP @ ( cP @ SV3 @ SV4 ) @ SV5 )
= ( cP @ SV3 @ ( cP @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,26,24,22]) ).
thf(28,plain,
( ( ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [SY17: a] :
( ( cP @ sK4_X @ SY17 )
!= sK5_SY15 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(32,plain,
! [SV6: a] :
( ( ( cP @ ( cJ @ SV6 ) @ SV6 )
= cE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV7: a] :
( ( ( cP @ cE @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV8: a] :
( ( ! [SY24: a,SY25: a] :
( ( cP @ ( cP @ SV8 @ SY24 ) @ SY25 )
= ( cP @ SV8 @ ( cP @ SY24 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV9: a] :
( ( ( cP @ sK4_X @ SV9 )
!= sK5_SY15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV10: a,SV8: a] :
( ( ! [SY26: a] :
( ( cP @ ( cP @ SV8 @ SV10 ) @ SY26 )
= ( cP @ SV8 @ ( cP @ SV10 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV9: a] :
( ( ( cP @ sK4_X @ SV9 )
= sK5_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV11: a,SV10: a,SV8: a] :
( ( ( cP @ ( cP @ SV8 @ SV10 ) @ SV11 )
= ( cP @ SV8 @ ( cP @ SV10 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,38,37,33]) ).
thf(40,plain,
( ( ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(41,plain,
( ( ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(42,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [SY20: a] :
( ( cP @ SY20 @ sK6_X )
!= sK7_SY18 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(44,plain,
! [SV12: a] :
( ( ( cP @ ( cJ @ SV12 ) @ SV12 )
= cE )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV13: a] :
( ( ( cP @ cE @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV14: a] :
( ( ! [SY27: a,SY28: a] :
( ( cP @ ( cP @ SV14 @ SY27 ) @ SY28 )
= ( cP @ SV14 @ ( cP @ SY27 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV15: a] :
( ( ( cP @ SV15 @ sK6_X )
!= sK7_SY18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV16: a,SV14: a] :
( ( ! [SY29: a] :
( ( cP @ ( cP @ SV14 @ SV16 ) @ SY29 )
= ( cP @ SV14 @ ( cP @ SV16 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV15: a] :
( ( ( cP @ SV15 @ sK6_X )
= sK7_SY18 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV17: a,SV16: a,SV14: a] :
( ( ( cP @ ( cP @ SV14 @ SV16 ) @ SV17 )
= ( cP @ SV14 @ ( cP @ SV16 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,50,49,45]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51,27,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG285^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.22 % Computer : n015.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Oct 6 18:13:43 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.32
% 0.25/0.32 No.of.Axioms: 0
% 0.25/0.32
% 0.25/0.32 Length.of.Defs: 0
% 0.25/0.32
% 0.25/0.32 Contains.Choice.Funs: false
% 0.25/0.32 .
% 0.25/0.32
% 0.25/0.32 ********************************
% 0.25/0.32 * All subproblems solved! *
% 0.25/0.32 ********************************
% 0.25/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:51,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.25/0.32
% 0.25/0.32 %**** Beginning of derivation protocol ****
% 0.25/0.32 % SZS output start CNFRefutation
% See solution above
% 0.25/0.32
% 0.25/0.32 %**** End of derivation protocol ****
% 0.25/0.32 %**** no. of clauses in derivation: 52 ****
% 0.25/0.32 %**** clause counter: 51 ****
% 0.25/0.32
% 0.25/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:51,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------