%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LDA003-1 : 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 : n013.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 10:31:13 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 56 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 216 ( 22 ~; 22 |; 0 &; 172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i > $i ).
thf(tp_left,type,
left: $i > $i > $o ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_u,type,
u: $i ).
thf(1,axiom,
( u
= ( f @ n2 @ n2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(2,axiom,
( n3
= ( f @ n2 @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(3,axiom,
( n2
= ( f @ n1 @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( left @ X @ Y )
| ~ ( left @ Y @ Z )
| ( left @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(5,axiom,
! [X: $i,Y: $i] : ( left @ X @ ( f @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
~ ( left @ n3 @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( u
= ( f @ n2 @ n2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( n3
= ( f @ n2 @ n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( n2
= ( f @ n1 @ n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( left @ X @ Y )
| ~ ( left @ Y @ Z )
| ( left @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] : ( left @ X @ ( f @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ~ ( left @ n3 @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left @ X @ Y )
| ! [Z: $i] :
( ~ ( left @ Y @ Z )
| ( left @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(20,plain,
( ( ~ ( left @ n3 @ u ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] : ( left @ X @ ( f @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( left @ X @ Y )
| ! [Z: $i] :
( ~ ( left @ Y @ Z )
| ( left @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(24,plain,
( ( n2
= ( f @ n1 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(25,plain,
( ( n3
= ( f @ n2 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(26,plain,
( ( u
= ( f @ n2 @ n2 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(27,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( left @ n3 @ u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( f @ SV1 @ ( f @ SY8 @ SY9 ) )
= ( f @ ( f @ SV1 @ SY8 ) @ ( f @ SV1 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY10: $i] : ( left @ SV2 @ ( f @ SV2 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(31,plain,
! [SV3: $i] :
( ( ! [SY11: $i] :
( ~ ( left @ SV3 @ SY11 )
| ! [SY12: $i] :
( ~ ( left @ SY11 @ SY12 )
| ( left @ SV3 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(32,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY13: $i] :
( ( f @ SV1 @ ( f @ SV4 @ SY13 ) )
= ( f @ ( f @ SV1 @ SV4 ) @ ( f @ SV1 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( left @ SV2 @ ( f @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( left @ SV3 @ SV6 )
| ! [SY14: $i] :
( ~ ( left @ SV6 @ SY14 )
| ( left @ SV3 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( f @ SV1 @ ( f @ SV4 @ SV7 ) )
= ( f @ ( f @ SV1 @ SV4 ) @ ( f @ SV1 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( left @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY14: $i] :
( ~ ( left @ SV6 @ SY14 )
| ( left @ SV3 @ SY14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV6: $i,SV3: $i] :
( ( ( left @ SV3 @ SV6 )
= $false )
| ( ( ! [SY14: $i] :
( ~ ( left @ SV6 @ SY14 )
| ( left @ SV3 @ SY14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( left @ SV6 @ SV8 )
| ( left @ SV3 @ SV8 ) )
= $true )
| ( ( left @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( left @ SV6 @ SV8 ) )
= $true )
| ( ( left @ SV3 @ SV8 )
= $true )
| ( ( left @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( left @ SV6 @ SV8 )
= $false )
| ( ( left @ SV3 @ SV8 )
= $true )
| ( ( left @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,41,36,34,32,28,26,25]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA003-1 : 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
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 12:37:51 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 7
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 .
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 43 ****
% 0.08/0.25 %**** clause counter: 42 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------