%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM748^1 : 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 : n015.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 10:35:06 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 27 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 254 ( 2 ~; 0 |; 0 &; 252 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_den,type,
den: frac > nat ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_fr,type,
fr: nat > nat > frac ).
thf(tp_num,type,
num: frac > nat ).
thf(tp_pl,type,
pl: nat > nat > nat ).
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] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(3,axiom,
! [Xx: frac] : ( eq @ Xx @ Xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(4,conjecture,
eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(5,negated_conjecture,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
! [SV1: frac] :
( ( eq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: nat] :
( ( ! [SY5: nat] :
( ( ts @ SV2 @ SY5 )
= ( ts @ SY5 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV3: nat] :
( ( ! [SY6: nat] :
( ( pl @ SV3 @ SY6 )
= ( pl @ SY6 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV4: nat,SV2: nat] :
( ( ( ts @ SV2 @ SV4 )
= ( ts @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV5: nat,SV3: nat] :
( ( ( pl @ SV3 @ SV5 )
= ( pl @ SV5 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,20,19,18]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM748^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 13:40:58 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27
% 0.07/0.27 No.of.Axioms: 3
% 0.07/0.27
% 0.07/0.27 Length.of.Defs: 0
% 0.07/0.27
% 0.07/0.27 Contains.Choice.Funs: false
% 0.07/0.27
% 0.07/0.27 ********************************
% 0.07/0.27 * All subproblems solved! *
% 0.07/0.27 ********************************
% 0.07/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.27
% 0.07/0.27 %**** Beginning of derivation protocol ****
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.27
% 0.07/0.27 %**** End of derivation protocol ****
% 0.07/0.27 %**** no. of clauses in derivation: 22 ****
% 0.07/0.27 %**** clause counter: 21 ****
% 0.07/0.27
% 0.07/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------