%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% 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 : n006.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 10:27:44 AM UTC 2026
% Result : Unsatisfiable 47.72s 8.23s
% Output : CNFRefutation 47.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 186 ( 6 ~; 0 |; 0 &; 180 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i > $i ).
thf(tp_x0,type,
x0: $i ).
thf(tp_x1,type,
x1: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SY4 ) @ ( f @ SY4 @ SY5 ) ) @ SY6 ) @ ( f @ SY4 @ ( f @ ( f @ SY4 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SY5 ) ) )
= SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SV2 ) @ ( f @ SV2 @ SY7 ) ) @ SY8 ) @ ( f @ SV2 @ ( f @ ( f @ SV2 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SY7 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY9: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SV2 ) @ ( f @ SV2 @ SV3 ) ) @ SY9 ) @ ( f @ SV2 @ ( f @ ( f @ SV2 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SV3 ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( f @ ( f @ ( f @ ( f @ SV1 @ SV2 ) @ ( f @ SV2 @ SV3 ) ) @ SV4 ) @ ( f @ SV2 @ ( f @ ( f @ SV2 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SV3 ) ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,18,15]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 12:05:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.72/8.23
% 47.72/8.23 No.of.Axioms: 2
% 47.72/8.23
% 47.72/8.23 Length.of.Defs: 0
% 47.72/8.23
% 47.72/8.23 Contains.Choice.Funs: false
% 47.72/8.23
% 47.72/8.23 ********************************
% 47.72/8.23 * All subproblems solved! *
% 47.72/8.23 ********************************
% 47.72/8.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 47.72/8.23
% 47.72/8.23 %**** Beginning of derivation protocol ****
% 47.72/8.23 % SZS output start CNFRefutation
% See solution above
% 47.72/8.23
% 47.72/8.23 %**** End of derivation protocol ****
% 47.72/8.23 %**** no. of clauses in derivation: 20 ****
% 47.72/8.23 %**** clause counter: 19 ****
% 47.72/8.23
% 47.72/8.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------