%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM730^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n018.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 10:35:03 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 268 ( 2 ~; 0 |; 0 &; 266 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_c1x,type,
c1x: frac > nat ).
thf(tp_c1y,type,
c1y: frac > nat ).
thf(tp_c2x,type,
c2x: frac > nat ).
thf(tp_c2y,type,
c2y: frac > nat ).
thf(tp_less,type,
less: nat > nat > $o ).
thf(tp_more,type,
more: nat > nat > $o ).
thf(tp_orec3,type,
orec3: $o > $o > $o > $o ).
thf(tp_ts,type,
ts: nat > nat > nat ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(1,axiom,
! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10) ).
thf(2,conjecture,
( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41) ).
thf(3,negated_conjecture,
( ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
! [SV1: nat] :
( ( ! [SY2: nat] : ( orec3 @ ( SV1 = SY2 ) @ ( more @ SV1 @ SY2 ) @ ( less @ SV1 @ SY2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(10,plain,
( ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(11,plain,
! [SV2: nat,SV1: nat] :
( ( orec3 @ ( SV1 = SV2 ) @ ( more @ SV1 @ SV2 ) @ ( less @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV3: nat,SV4: nat] :
( ( orec3 @ ( SV4 = SV3 ) @ ( more @ SV4 @ SV3 ) @ ( less @ SV4 @ SV3 ) )
= $true ),
inference(rename,[status(thm)],[11]) ).
thf(13,plain,
! [SV3: nat,SV4: nat] :
( ( ( orec3 @ ( SV4 = SV3 ) @ ( more @ SV4 @ SV3 ) @ ( less @ SV4 @ SV3 ) )
= ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
= $false ),
inference(res,[status(thm)],[12,10]) ).
thf(50,plain,
$false = $true,
inference(extuni,[status(esa)],[13:[bind(SV3,$thf( ts @ ( c1y @ y ) @ ( c2x @ x ) )),bind(SV4,$thf( ts @ ( c1x @ x ) @ ( c2y @ y ) ))]]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM730^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 13:38:52 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26
% 0.08/0.26 No.of.Axioms: 1
% 0.08/0.26
% 0.08/0.26 Length.of.Defs: 0
% 0.08/0.26
% 0.08/0.26 Contains.Choice.Funs: false
% 0.08/0.26
% 0.08/0.26 ********************************
% 0.08/0.26 * All subproblems solved! *
% 0.08/0.26 ********************************
% 0.08/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:2,foatp_calls:1,translation:fof_full)
% 0.08/0.26
% 0.08/0.26 %**** Beginning of derivation protocol ****
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26
% 0.08/0.26 %**** End of derivation protocol ****
% 0.08/0.26 %**** no. of clauses in derivation: 15 ****
% 0.08/0.26 %**** clause counter: 50 ****
% 0.08/0.26
% 0.08/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:2,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------