%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU918^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 10:49:14 AM UTC 2026
% Result : Theorem 164.33s 30.34s
% Output : CNFRefutation 164.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 61 ( 10 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 16 ^; 28 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(1,conjecture,
( ( a != b )
=> ~ ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM197_pme) ).
thf(2,negated_conjecture,
( ( ( a != b )
=> ~ ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( a != b )
=> ~ ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( a != b )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( a != b )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(8,plain,
( ( a != b )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xf: $i > $i,Xg: $i > $i] :
( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(11,plain,
! [SV1: $i > $i] :
( ( ! [SY4: $i > $i] :
( ( ^ [SY5: $i] : ( SV1 @ ( SY4 @ SY5 ) ) )
= ( ^ [SY6: $i] : ( SY4 @ ( SV1 @ SY6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV2: $i > $i,SV1: $i > $i] :
( ( ( ^ [SY7: $i] : ( SV1 @ ( SV2 @ SY7 ) ) )
= ( ^ [SY8: $i] : ( SV2 @ ( SV1 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(13,plain,
! [SV2: $i > $i,SV1: $i > $i] :
( ( ! [SV3: $i] :
( ( SV1 @ ( SV2 @ SV3 ) )
= ( SV2 @ ( SV1 @ SV3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV4: $i,SV2: $i > $i,SV1: $i > $i] :
( ( ( SV1 @ ( SV2 @ SV4 ) )
= ( SV2 @ ( SV1 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(22,plain,
! [SV10: $i,SV11: $i > $i,SV12: $i > $i] :
( ( ( SV12 @ ( SV11 @ SV10 ) )
= ( SV11 @ ( SV12 @ SV10 ) ) )
= $true ),
inference(rename,[status(thm)],[15]) ).
thf(23,plain,
! [SV10: $i,SV11: $i > $i,SV12: $i > $i] :
( ( ( ( SV12 @ ( SV11 @ SV10 ) )
= ( SV11 @ ( SV12 @ SV10 ) ) )
= ( a = b ) )
= $false ),
inference(res,[status(thm)],[22,10]) ).
thf(27,plain,
$false = $true,
inference(extuni,[status(esa)],[23:[bind(SV12,$thf( ^ [SX0: $i] : b )),bind(SV11,$thf( ^ [SX0: $i] : a ))]]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU918^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.16 % Computer : n011.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 15:38:21 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 164.33/30.34
% 164.33/30.34 No.of.Axioms: 0
% 164.33/30.34
% 164.33/30.34 Length.of.Defs: 0
% 164.33/30.34
% 164.33/30.34 Contains.Choice.Funs: false
% 164.33/30.34 eprover: CPU time limit exceeded, terminating
% 164.33/30.34 eprover: CPU time limit exceeded, terminating
% 164.33/30.34
% 164.33/30.34 ********************************
% 164.33/30.34 * All subproblems solved! *
% 164.33/30.34 ********************************
% 164.33/30.34 % 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:27,loop_count:3,foatp_calls:2,translation:fof_experiment)
% 164.33/30.34
% 164.33/30.34 %**** Beginning of derivation protocol ****
% 164.33/30.34 % SZS output start CNFRefutation
% See solution above
% 164.33/30.34
% 164.33/30.34 %**** End of derivation protocol ****
% 164.33/30.34 %**** no. of clauses in derivation: 18 ****
% 164.33/30.34 %**** clause counter: 27 ****
% 164.33/30.34
% 164.33/30.34 % 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:27,loop_count:3,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------