%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM747^1 : 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 : n008.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 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 190 ( 6 ~; 5 |; 0 &; 176 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_fr,type,
fr: nat > nat > frac ).
thf(tp_n,type,
n: nat ).
thf(tp_pf,type,
pf: frac > frac > frac ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_x1,type,
x1: nat ).
thf(tp_x2,type,
x2: nat ).
thf(1,axiom,
! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(2,axiom,
! [Xx: frac,Xy: frac] :
( ( eq @ Xx @ Xy )
=> ( eq @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(3,conjecture,
eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57a) ).
thf(4,negated_conjecture,
( ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [Xx: frac,Xy: frac] :
( ( eq @ Xx @ Xy )
=> ( eq @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Xx: frac,Xy: frac] :
( ( eq @ Xx @ Xy )
=> ( eq @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: frac,SX1: frac] :
( ~ ( eq @ SX0 @ SX1 )
| ( eq @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: nat] :
( ( ! [SY5: nat,SY6: nat] : ( eq @ ( pf @ ( fr @ SV1 @ SY6 ) @ ( fr @ SY5 @ SY6 ) ) @ ( fr @ ( pl @ SV1 @ SY5 ) @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: frac] :
( ( ! [SY7: frac] :
( ~ ( eq @ SV2 @ SY7 )
| ( eq @ SY7 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: nat,SV1: nat] :
( ( ! [SY8: nat] : ( eq @ ( pf @ ( fr @ SV1 @ SY8 ) @ ( fr @ SV3 @ SY8 ) ) @ ( fr @ ( pl @ SV1 @ SV3 ) @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV4: frac,SV2: frac] :
( ( ~ ( eq @ SV2 @ SV4 )
| ( eq @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV3: nat,SV5: nat,SV1: nat] :
( ( eq @ ( pf @ ( fr @ SV1 @ SV5 ) @ ( fr @ SV3 @ SV5 ) ) @ ( fr @ ( pl @ SV1 @ SV3 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV4: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV4 ) )
= $true )
| ( ( eq @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV4 )
= $false )
| ( ( eq @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,20,18]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM747^1 : 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
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 13:38:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 2
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 22 ****
% 0.07/0.22 %**** clause counter: 21 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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)
%------------------------------------------------------------------------------