%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG270^5 : 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 : n014.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 10:08:44 AM UTC 2026
% Result : Theorem 0.06s 0.20s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 166 ( 3 ~; 0 |; 0 &; 160 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_c_star,type,
c_star: a > a > a ).
thf(tp_sK1_W,type,
sK1_W: a ).
thf(tp_sK2_SY7,type,
sK2_SY7: a ).
thf(tp_sK3_SY10,type,
sK3_SY10: a ).
thf(tp_sK4_SY12,type,
sK4_SY12: a ).
thf(1,conjecture,
( ! [Xx: a,Xy: a,Xz: a] :
( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
= ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) )
=> ! [W: a,X: a,Y: a,Z: a] :
( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
= ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM23_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
= ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) )
=> ! [W: a,X: a,Y: a,Z: a] :
( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
= ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
= ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) )
=> ! [W: a,X: a,Y: a,Z: a] :
( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
= ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
= ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [W: a,X: a,Y: a,Z: a] :
( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
= ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [W: a,X: a,Y: a,Z: a] :
( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
= ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( c_star @ ( c_star @ ( c_star @ sK1_W @ sK2_SY7 ) @ sK3_SY10 ) @ sK4_SY12 )
!= ( c_star @ sK1_W @ ( c_star @ sK2_SY7 @ ( c_star @ sK3_SY10 @ sK4_SY12 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
= ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
( ( ( c_star @ ( c_star @ ( c_star @ sK1_W @ sK2_SY7 ) @ sK3_SY10 ) @ sK4_SY12 )
!= ( c_star @ sK1_W @ ( c_star @ sK2_SY7 @ ( c_star @ sK3_SY10 @ sK4_SY12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
! [SV1: a] :
( ( ! [SY13: a,SY14: a] :
( ( c_star @ ( c_star @ SV1 @ SY13 ) @ SY14 )
= ( c_star @ SV1 @ ( c_star @ SY13 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( ( c_star @ ( c_star @ ( c_star @ sK1_W @ sK2_SY7 ) @ sK3_SY10 ) @ sK4_SY12 )
= ( c_star @ sK1_W @ ( c_star @ sK2_SY7 @ ( c_star @ sK3_SY10 @ sK4_SY12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV2: a,SV1: a] :
( ( ! [SY15: a] :
( ( c_star @ ( c_star @ SV1 @ SV2 ) @ SY15 )
= ( c_star @ SV1 @ ( c_star @ SV2 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV3: a,SV2: a,SV1: a] :
( ( ( c_star @ ( c_star @ SV1 @ SV2 ) @ SV3 )
= ( c_star @ SV1 @ ( c_star @ SV2 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(14,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,13]) ).
thf(15,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG270^5 : 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
% 0.06/0.17 % Computer : n014.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 18:09:41 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.20
% 0.06/0.20 No.of.Axioms: 0
% 0.06/0.20
% 0.06/0.20 Length.of.Defs: 0
% 0.06/0.20
% 0.06/0.20 Contains.Choice.Funs: false
% 0.06/0.20
% 0.06/0.20 ********************************
% 0.06/0.20 * All subproblems solved! *
% 0.06/0.20 ********************************
% 0.06/0.20 % 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:14,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.06/0.20
% 0.06/0.20 %**** Beginning of derivation protocol ****
% 0.06/0.20 % SZS output start CNFRefutation
% See solution above
% 0.06/0.20
% 0.06/0.20 %**** End of derivation protocol ****
% 0.06/0.20 %**** no. of clauses in derivation: 15 ****
% 0.06/0.20 %**** clause counter: 14 ****
% 0.06/0.20
% 0.06/0.20 % 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:14,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------