%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% 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 : 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 10:18:59 AM UTC 2026
% Result : Theorem 0.89s 0.40s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 136 ( 87 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 208 ( 36 ~; 31 |; 0 &; 141 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 10 con; 0-8 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_alpha,type,
alpha: $i ).
thf(tp_beta,type,
beta: $i ).
thf(tp_c63,type,
c63: $i > $i > $i > $i ).
thf(tp_crossbar,type,
crossbar: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_ext,type,
ext: $i > $i > $i > $i > $i ).
thf(tp_gamma,type,
gamma: $i ).
thf(tp_ins,type,
ins: $i > $i > $i > $i > $i ).
thf(tp_insert,type,
insert: $i > $i > $i > $i > $i ).
thf(tp_insert5,type,
insert5: $i > $i > $i > $i > $i > $i ).
thf(tp_ip,type,
ip: $i > $i > $i > $i > $i > $i ).
thf(tp_le,type,
le: $i > $i > $i > $i > $o ).
thf(tp_pointOffLine,type,
pointOffLine: $i > $i > $i ).
thf(tp_s,type,
s: $i > $i > $i ).
thf(tp_sK1_Xa,type,
sK1_Xa: $i ).
thf(tp_sK2_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_sK4_SY16,type,
sK4_SY16: $i ).
thf(tp_s_afs,type,
s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_col,type,
s_col: $i > $i > $i > $o ).
thf(tp_s_e,type,
s_e: $i > $i > $i > $i > $o ).
thf(tp_s_e3,type,
s_e3: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_fs,type,
s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_ifs,type,
s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_kf,type,
s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_s_m,type,
s_m: $i > $i > $i > $o ).
thf(tp_s_t,type,
s_t: $i > $i > $i > $o ).
thf(tp_sameside,type,
sameside: $i > $i > $i > $o ).
thf(tp_xb,type,
xb: $i ).
thf(11,axiom,
! [Xa: $i,Xp: $i] :
( ( s @ Xa @ ( s @ Xa @ Xp ) )
= Xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).
thf(12,axiom,
! [Xp: $i,Xa: $i,Xq: $i] :
( ~ ( s_m @ Xp @ Xa @ Xq )
| ( Xq
= ( s @ Xa @ Xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).
thf(14,axiom,
! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(110,conjecture,
! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
( ( ( s @ Xa @ Xp )
!= Xr )
| ( ( s @ Xa @ Xq )
!= Xr )
| ( Xp = Xq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_8) ).
thf(111,negated_conjecture,
( ( ! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
( ( ( s @ Xa @ Xp )
!= Xr )
| ( ( s @ Xa @ Xq )
!= Xr )
| ( Xp = Xq ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[110]) ).
thf(112,plain,
( ( ! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
( ( ( s @ Xa @ Xp )
!= Xr )
| ( ( s @ Xa @ Xq )
!= Xr )
| ( Xp = Xq ) ) )
= $false ),
inference(unfold_def,[status(thm)],[111]) ).
thf(113,plain,
( ( ! [Xa: $i,Xp: $i] :
( ( s @ Xa @ ( s @ Xa @ Xp ) )
= Xp ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(114,plain,
( ( ! [Xp: $i,Xa: $i,Xq: $i] :
( ~ ( s_m @ Xp @ Xa @ Xq )
| ( Xq
= ( s @ Xa @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(115,plain,
( ( ! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(116,plain,
( ( ! [SY11: $i,SY12: $i,SY13: $i] :
( ( ( s @ sK1_Xa @ SY11 )
!= SY12 )
| ( ( s @ sK1_Xa @ SY13 )
!= SY12 )
| ( SY11 = SY13 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(117,plain,
( ( ! [SY14: $i,SY15: $i] :
( ( ( s @ sK1_Xa @ sK2_SY11 )
!= SY14 )
| ( ( s @ sK1_Xa @ SY15 )
!= SY14 )
| ( sK2_SY11 = SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(118,plain,
( ( ! [SY16: $i] :
( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = SY16 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(119,plain,
( ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = sK4_SY16 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(120,plain,
( ( ~ ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = sK4_SY16 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[119]) ).
thf(121,plain,
( ( ! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(122,plain,
( ( ! [Xp: $i,Xa: $i,Xq: $i] :
( ~ ( s_m @ Xp @ Xa @ Xq )
| ( Xq
= ( s @ Xa @ Xp ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(123,plain,
( ( ! [Xa: $i,Xp: $i] :
( ( s @ Xa @ ( s @ Xa @ Xp ) )
= Xp ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(124,plain,
( ( ~ ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = sK4_SY16 ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(125,plain,
( ( ~ ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = sK4_SY16 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(126,plain,
! [SV1: $i] :
( ( ! [SY17: $i] : ( s_m @ SV1 @ SY17 @ ( s @ SY17 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV2: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( s_m @ SV2 @ SY18 @ SY19 )
| ( SY19
= ( s @ SY18 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(128,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ( s @ SV3 @ ( s @ SV3 @ SY20 ) )
= SY20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(129,plain,
( ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
| ( sK2_SY11 = sK4_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV4: $i,SV1: $i] :
( ( s_m @ SV1 @ SV4 @ ( s @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(131,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY21: $i] :
( ~ ( s_m @ SV2 @ SV5 @ SY21 )
| ( SY21
= ( s @ SV5 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(132,plain,
! [SV6: $i,SV3: $i] :
( ( ( s @ SV3 @ ( s @ SV3 @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(133,plain,
( ( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
| ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(134,plain,
( ( sK2_SY11 = sK4_SY16 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(135,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( s_m @ SV2 @ SV5 @ SV7 )
| ( SV7
= ( s @ SV5 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(136,plain,
( ( ( s @ sK1_Xa @ sK2_SY11 )
!= sK3_SY14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(137,plain,
( ( ( s @ sK1_Xa @ sK4_SY16 )
!= sK3_SY14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(138,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( s_m @ SV2 @ SV5 @ SV7 ) )
= $true )
| ( ( SV7
= ( s @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(139,plain,
( ( ( s @ sK1_Xa @ sK2_SY11 )
= sK3_SY14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(140,plain,
( ( ( s @ sK1_Xa @ sK4_SY16 )
= sK3_SY14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(141,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( s_m @ SV2 @ SV5 @ SV7 )
= $false )
| ( ( SV7
= ( s @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(142,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[130,141,140,139,134,132]) ).
thf(143,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n011.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 10:16:51 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.89/0.40
% 0.89/0.40 No.of.Axioms: 3
% 0.89/0.40
% 0.89/0.40 Length.of.Defs: 0
% 0.89/0.40
% 0.89/0.40 Contains.Choice.Funs: false
% 0.89/0.40 ..
% 0.89/0.40
% 0.89/0.40 ********************************
% 0.89/0.40 * All subproblems solved! *
% 0.89/0.40 ********************************
% 0.89/0.40 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:142,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.89/0.40
% 0.89/0.40 %**** Beginning of derivation protocol ****
% 0.89/0.40 % SZS output start CNFRefutation
% See solution above
% 0.89/0.40
% 0.89/0.40 %**** End of derivation protocol ****
% 0.89/0.40 %**** no. of clauses in derivation: 37 ****
% 0.89/0.40 %**** clause counter: 142 ****
% 0.89/0.40
% 0.89/0.40 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:142,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------