%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL052-1 : 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/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 10:11:01 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 109 ( 7 ~; 0 |; 0 &; 102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_common_bird,type,
common_bird: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_odd_bird,type,
odd_bird: $i ).
thf(tp_response,type,
response: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,W: $i] :
( ( response @ ( compose @ X @ Y ) @ W )
= ( response @ X @ ( response @ Y @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composer_exists) ).
thf(2,axiom,
( c
= ( compose @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_composes_a_with_b) ).
thf(3,axiom,
! [X: $i] :
( ( response @ c @ ( common_bird @ X ) )
= ( response @ X @ ( common_bird @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agreeable1) ).
thf(4,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(5,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,negated_conjecture,
! [V: $i] :
( ( response @ a @ V )
!= ( response @ odd_bird @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_is_agreeable) ).
thf(7,plain,
$false = $false,
inference(unfold_def,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( response @ ( compose @ X @ Y ) @ W )
= ( response @ X @ ( response @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( c
= ( compose @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( response @ c @ ( common_bird @ X ) )
= ( response @ X @ ( common_bird @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [V: $i] :
( ( response @ a @ V )
!= ( response @ odd_bird @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(12,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [V: $i] :
( ( response @ a @ V )
!= ( response @ odd_bird @ V ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( response @ c @ ( common_bird @ X ) )
= ( response @ X @ ( common_bird @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( c
= ( compose @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( response @ ( compose @ X @ Y ) @ W )
= ( response @ X @ ( response @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: $i] :
( ( response @ a @ SX0 )
!= ( response @ odd_bird @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
! [SV1: $i] :
( ( ( response @ c @ ( common_bird @ SV1 ) )
= ( response @ SV1 @ ( common_bird @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY5: $i,SY6: $i] :
( ( response @ ( compose @ SV2 @ SY5 ) @ SY6 )
= ( response @ SV2 @ ( response @ SY5 @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ( response @ a @ SV3 )
!= ( response @ odd_bird @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY7: $i] :
( ( response @ ( compose @ SV2 @ SV4 ) @ SY7 )
= ( response @ SV2 @ ( response @ SV4 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: $i] :
( ( ( response @ a @ SV3 )
= ( response @ odd_bird @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( response @ ( compose @ SV2 @ SV4 ) @ SV5 )
= ( response @ SV2 @ ( response @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,25,24,21,19]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL052-1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n014.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 18:33:11 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 4
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 0
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 27 ****
% 0.11/0.19 %**** clause counter: 26 ****
% 0.11/0.19
% 0.11/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------