%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV051^5 : 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 : n013.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 10:49:26 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 77 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 64 ( 36 ~; 13 |; 9 &; 0 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SX0,type,
sK2_SX0: a ).
thf(tp_sK3_SY4,type,
sK3_SY4: a ).
thf(tp_sK4_SY6,type,
sK4_SY6: a ).
thf(1,conjecture,
( ! [Xx: a] : ( Xx = Xx )
& ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM557_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] : ( Xx = Xx )
& ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a] : ( Xx = Xx )
& ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: a] : ( Xx = Xx ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: a] : ( Xx = Xx ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [Xx: a] : ( Xx = Xx ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [Xx: a] : ( Xx = Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
( ( sK1_Xx = sK1_Xx )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ! [Xu: a,Xv: a,Xw: a] :
( ( ( Xu = Xw )
& ( Xv = Xw ) )
=> ( Xu = Xv ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ( SX0 != SX2 )
| ( SX1 != SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ( SX0 != SX2 )
| ( SX1 != SX2 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SY4: a,SY5: a] :
( ~ ~ ( ( sK2_SX0 != SY5 )
| ( SY4 != SY5 ) )
| ( sK2_SX0 = SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY6: a] :
( ~ ~ ( ( sK2_SX0 != SY6 )
| ( sK3_SY4 != SY6 ) )
| ( sK2_SX0 = sK3_SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ~ ~ ( ( sK2_SX0 != sK4_SY6 )
| ( sK3_SY4 != sK4_SY6 ) )
| ( sK2_SX0 = sK3_SY4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ~ ~ ( ( sK2_SX0 != sK4_SY6 )
| ( sK3_SY4 != sK4_SY6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
( ( sK2_SX0 = sK3_SY4 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ( sK2_SX0 != sK4_SY6 )
| ( sK3_SY4 != sK4_SY6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ( sK2_SX0 != sK4_SY6 )
| ( sK3_SY4 != sK4_SY6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
( ( sK2_SX0 != sK4_SY6 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
( ( sK3_SY4 != sK4_SY6 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( sK2_SX0 = sK4_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( sK3_SY4 = sK4_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,25,24]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV051^5 : 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
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:39:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 0
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,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)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 27 ****
% 0.08/0.21 %**** clause counter: 26 ****
% 0.08/0.21
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,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)
%------------------------------------------------------------------------------