%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM750^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 210 ( 16 ~; 18 |; 0 &; 170 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_pf,type,
pf: frac > frac > frac ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(tp_z,type,
z: frac ).
thf(1,axiom,
! [Xx: frac] : ( eq @ Xx @ Xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(2,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
thf(3,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(4,conjecture,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62b) ).
thf(5,negated_conjecture,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( eq @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( eq @ x @ y )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [SX0: frac,SX1: frac,SX2: frac,SX3: frac] :
( ~ ( eq @ SX0 @ SX1 )
| ~ ( eq @ SX2 @ SX3 )
| ( eq @ ( pf @ SX0 @ SX2 ) @ ( pf @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: frac] :
( ( eq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: frac] :
( ( ! [SY5: frac,SY6: frac,SY7: frac] :
( ~ ( eq @ SV2 @ SY5 )
| ~ ( eq @ SY6 @ SY7 )
| ( eq @ ( pf @ SV2 @ SY6 ) @ ( pf @ SY5 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: frac,SV2: frac] :
( ( ! [SY8: frac,SY9: frac] :
( ~ ( eq @ SV2 @ SV3 )
| ~ ( eq @ SY8 @ SY9 )
| ( eq @ ( pf @ SV2 @ SY8 ) @ ( pf @ SV3 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV4: frac,SV3: frac,SV2: frac] :
( ( ! [SY10: frac] :
( ~ ( eq @ SV2 @ SV3 )
| ~ ( eq @ SV4 @ SY10 )
| ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV5: frac,SV4: frac,SV3: frac,SV2: frac] :
( ( ~ ( eq @ SV2 @ SV3 )
| ~ ( eq @ SV4 @ SV5 )
| ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV5: frac,SV4: frac,SV3: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( eq @ SV4 @ SV5 )
| ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(23,plain,
! [SV5: frac,SV4: frac,SV3: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV3 )
= $false )
| ( ( ~ ( eq @ SV4 @ SV5 )
| ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
! [SV3: frac,SV2: frac,SV5: frac,SV4: frac] :
( ( ( ~ ( eq @ SV4 @ SV5 ) )
= $true )
| ( ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SV5 ) )
= $true )
| ( ( eq @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV3: frac,SV2: frac,SV5: frac,SV4: frac] :
( ( ( eq @ SV4 @ SV5 )
= $false )
| ( ( eq @ ( pf @ SV2 @ SV4 ) @ ( pf @ SV3 @ SV5 ) )
= $true )
| ( ( eq @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,25,17,16]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM750^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 13:40:12 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 3
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 27 ****
% 0.08/0.20 %**** clause counter: 26 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------