%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL012-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n010.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 10:10:55 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.18s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 26 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 69 ( 7 ~; 0 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 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 : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_combinator,type,
combinator: $i ).
thf(tp_u,type,
u: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( apply @ ( apply @ u @ X ) @ Y )
= ( apply @ Y @ ( apply @ ( apply @ X @ X ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_definition) ).
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,
! [Y: $i] :
( Y
!= ( apply @ combinator @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ u @ X ) @ Y )
= ( apply @ Y @ ( apply @ ( apply @ X @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [Y: $i] :
( Y
!= ( apply @ combinator @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Y: $i] :
( Y
!= ( apply @ combinator @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( apply @ u @ X ) @ Y )
= ( apply @ Y @ ( apply @ ( apply @ X @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: $i] :
( SX0
!= ( apply @ combinator @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ( apply @ ( apply @ u @ SV1 ) @ SY3 )
= ( apply @ SY3 @ ( apply @ ( apply @ SV1 @ SV1 ) @ SY3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( SV2
!= ( apply @ combinator @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i,SV1: $i] :
( ( ( apply @ ( apply @ u @ SV1 ) @ SV3 )
= ( apply @ SV3 @ ( apply @ ( apply @ SV1 @ SV1 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i] :
( ( SV2
= ( apply @ combinator @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,17,16]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.15 % Computer : n010.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Oct 6 18:34:06 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18
% 0.08/0.18 No.of.Axioms: 2
% 0.08/0.18
% 0.08/0.18 Length.of.Defs: 0
% 0.08/0.18
% 0.08/0.18 Contains.Choice.Funs: false
% 0.08/0.18
% 0.08/0.18 ********************************
% 0.08/0.18 * All subproblems solved! *
% 0.08/0.18 ********************************
% 0.08/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.18
% 0.08/0.18 %**** Beginning of derivation protocol ****
% 0.08/0.18 % SZS output start CNFRefutation
% See solution above
% 0.08/0.18
% 0.08/0.18 %**** End of derivation protocol ****
% 0.08/0.18 %**** no. of clauses in derivation: 19 ****
% 0.08/0.18 %**** clause counter: 18 ****
% 0.08/0.18
% 0.08/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------