%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO611-1 : TPTP v9.3.1. Released v7.1.0.
% 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 : n001.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 11:08:52 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 294 ( 41 ~; 38 |; 0 &; 215 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 78 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a0,type,
a0: $i ).
thf(tp_eq,type,
eq: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_le,type,
le: $i > $i > $o ).
thf(tp_max,type,
max: $i > $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(1,axiom,
! [A0: $i,A1: $i] :
( ~ ( eq @ ( f @ A0 ) @ a0 )
| ~ ( eq @ ( f @ A1 ) @ a0 )
| ~ ( le @ ( s @ A0 ) @ A1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
thf(2,axiom,
! [A: $i] : ( eq @ ( f @ A ) @ a0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
thf(5,axiom,
! [A: $i] : ( le @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A0: $i,A1: $i] :
( ~ ( eq @ ( f @ A0 ) @ a0 )
| ~ ( eq @ ( f @ A1 ) @ a0 )
| ~ ( le @ ( s @ A0 ) @ A1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i] : ( eq @ ( f @ A ) @ a0 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i] : ( le @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [A0: $i] :
( ~ ( eq @ ( f @ A0 ) @ a0 )
| ! [A1: $i] :
( ~ ( eq @ ( f @ A1 ) @ a0 )
| ~ ( le @ ( s @ A0 ) @ A1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(16,plain,
( ( ! [A: $i] : ( le @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( le @ ( max @ A @ B ) @ C )
| ( le @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [A: $i] : ( eq @ ( f @ A ) @ a0 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [A0: $i] :
( ~ ( eq @ ( f @ A0 ) @ a0 )
| ! [A1: $i] :
( ~ ( eq @ ( f @ A1 ) @ a0 )
| ~ ( le @ ( s @ A0 ) @ A1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
! [SV1: $i] :
( ( le @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ( le @ ( max @ SV2 @ SY10 ) @ SY11 )
| ( le @ SV2 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ~ ( le @ ( max @ SV3 @ SY12 ) @ SY13 )
| ( le @ SY12 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( eq @ ( f @ SV4 ) @ a0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV5: $i] :
( ( ~ ( eq @ ( f @ SV5 ) @ a0 )
| ! [SY14: $i] :
( ~ ( eq @ ( f @ SY14 ) @ a0 )
| ~ ( le @ ( s @ SV5 ) @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY15: $i] :
( ~ ( le @ ( max @ SV2 @ SV6 ) @ SY15 )
| ( le @ SV2 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY16: $i] :
( ~ ( le @ ( max @ SV3 @ SV7 ) @ SY16 )
| ( le @ SV7 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV5: $i] :
( ( ( ~ ( eq @ ( f @ SV5 ) @ a0 ) )
= $true )
| ( ( ! [SY14: $i] :
( ~ ( eq @ ( f @ SY14 ) @ a0 )
| ~ ( le @ ( s @ SV5 ) @ SY14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV8: $i,SV6: $i,SV2: $i] :
( ( ~ ( le @ ( max @ SV2 @ SV6 ) @ SV8 )
| ( le @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV9: $i,SV7: $i,SV3: $i] :
( ( ~ ( le @ ( max @ SV3 @ SV7 ) @ SV9 )
| ( le @ SV7 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i] :
( ( ( eq @ ( f @ SV5 ) @ a0 )
= $false )
| ( ( ! [SY14: $i] :
( ~ ( eq @ ( f @ SY14 ) @ a0 )
| ~ ( le @ ( s @ SV5 ) @ SY14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV8: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( le @ ( max @ SV2 @ SV6 ) @ SV8 ) )
= $true )
| ( ( le @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV9: $i,SV7: $i,SV3: $i] :
( ( ( ~ ( le @ ( max @ SV3 @ SV7 ) @ SV9 ) )
= $true )
| ( ( le @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( eq @ ( f @ SV10 ) @ a0 )
| ~ ( le @ ( s @ SV5 ) @ SV10 ) )
= $true )
| ( ( eq @ ( f @ SV5 ) @ a0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV8: $i,SV6: $i,SV2: $i] :
( ( ( le @ ( max @ SV2 @ SV6 ) @ SV8 )
= $false )
| ( ( le @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV9: $i,SV7: $i,SV3: $i] :
( ( ( le @ ( max @ SV3 @ SV7 ) @ SV9 )
= $false )
| ( ( le @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV10: $i] :
( ( ( ~ ( eq @ ( f @ SV10 ) @ a0 ) )
= $true )
| ( ( ~ ( le @ ( s @ SV5 ) @ SV10 ) )
= $true )
| ( ( eq @ ( f @ SV5 ) @ a0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: $i,SV10: $i] :
( ( ( eq @ ( f @ SV10 ) @ a0 )
= $false )
| ( ( ~ ( le @ ( s @ SV5 ) @ SV10 ) )
= $true )
| ( ( eq @ ( f @ SV5 ) @ a0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV10: $i,SV5: $i] :
( ( ( le @ ( s @ SV5 ) @ SV10 )
= $false )
| ( ( eq @ ( f @ SV10 ) @ a0 )
= $false )
| ( ( eq @ ( f @ SV5 ) @ a0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,41,38,37,27,25]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO611-1 : TPTP v9.3.1. Released v7.1.0.
% 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
% 0.08/0.19 % Computer : n001.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 17:50:09 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 5
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 43 ****
% 0.08/0.23 %**** clause counter: 42 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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)
%------------------------------------------------------------------------------