TSTP Solution File: SET930+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:22:46 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 12 unt; 0 def)
% Number of atoms : 171 ( 84 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 221 ( 103 ~; 58 |; 51 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 75 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f607,plain,
$false,
inference(avatar_sat_refutation,[],[f173,f228,f536,f605]) ).
fof(f605,plain,
( ~ spl5_3
| spl5_1 ),
inference(avatar_split_clause,[],[f591,f120,f128]) ).
fof(f128,plain,
( spl5_3
<=> in(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f120,plain,
( spl5_1
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f591,plain,
( in(sK1,sK2)
| ~ in(sK0,sK2) ),
inference(trivial_inequality_removal,[],[f550]) ).
fof(f550,plain,
( ~ in(sK0,sK2)
| singleton(sK1) != singleton(sK1)
| in(sK1,sK2) ),
inference(superposition,[],[f56,f143]) ).
fof(f143,plain,
! [X2,X0,X1] :
( singleton(X0) = set_difference(unordered_pair(X1,X0),X2)
| ~ in(X1,X2)
| in(X0,X2) ),
inference(superposition,[],[f35,f51]) ).
fof(f51,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f35,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ~ in(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ( ( in(X1,X2)
| X0 = X1 )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ~ in(X1,X2)
& X0 != X1 )
| in(X0,X2) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( ( ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) )
| singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| ( ~ in(X0,X2)
& X0 != X1 )
| in(X1,X2) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X1,X0,X2] :
( ( ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) )
| singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
& ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
| ( ~ in(X0,X2)
& X0 != X1 )
| in(X1,X2) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X0,X2] :
( ( ( in(X0,X2)
| X0 = X1 )
& ~ in(X1,X2) )
<=> singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ( ~ in(X0,X2)
& ( X0 = X1
| in(X1,X2) ) )
<=> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f56,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
inference(backward_demodulation,[],[f40,f51]) ).
fof(f40,plain,
set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0)
& empty_set != set_difference(unordered_pair(sK1,sK0),sK2)
& set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1)
& set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2] :
( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
& empty_set != set_difference(unordered_pair(X1,X0),X2)
& singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
& unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) )
=> ( set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0)
& empty_set != set_difference(unordered_pair(sK1,sK0),sK2)
& set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1)
& set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2] :
( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
& empty_set != set_difference(unordered_pair(X1,X0),X2)
& singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
& unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
? [X2,X1,X0] :
( singleton(X2) != set_difference(unordered_pair(X1,X2),X0)
& empty_set != set_difference(unordered_pair(X1,X2),X0)
& singleton(X1) != set_difference(unordered_pair(X1,X2),X0)
& set_difference(unordered_pair(X1,X2),X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X2,X0,X1] :
~ ( singleton(X2) != set_difference(unordered_pair(X1,X2),X0)
& empty_set != set_difference(unordered_pair(X1,X2),X0)
& singleton(X1) != set_difference(unordered_pair(X1,X2),X0)
& set_difference(unordered_pair(X1,X2),X0) != unordered_pair(X1,X2) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X2,X0,X1] :
~ ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2)
& unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X2,X0,X1] :
~ ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2)
& unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f536,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f535,f128,f120]) ).
fof(f535,plain,
( ~ in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(trivial_inequality_removal,[],[f492]) ).
fof(f492,plain,
( empty_set != empty_set
| ~ in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(superposition,[],[f57,f96]) ).
fof(f96,plain,
! [X3,X4,X5] :
( empty_set = set_difference(unordered_pair(X4,X3),X5)
| ~ in(X3,X5)
| ~ in(X4,X5) ),
inference(superposition,[],[f45,f51]) ).
fof(f45,plain,
! [X2,X0,X1] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ( empty_set = set_difference(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) )
& ( ( in(X2,X1)
& in(X0,X1) )
| empty_set != set_difference(unordered_pair(X2,X0),X1) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ( empty_set = set_difference(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) )
& ( ( in(X2,X1)
& in(X0,X1) )
| empty_set != set_difference(unordered_pair(X2,X0),X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X2,X0,X1] :
( empty_set = set_difference(unordered_pair(X2,X0),X1)
<=> ( in(X2,X1)
& in(X0,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X0] :
( ( in(X0,X2)
& in(X1,X2) )
<=> empty_set = set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f57,plain,
empty_set != set_difference(unordered_pair(sK0,sK1),sK2),
inference(backward_demodulation,[],[f41,f51]) ).
fof(f41,plain,
empty_set != set_difference(unordered_pair(sK1,sK0),sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f228,plain,
( spl5_3
| spl5_1 ),
inference(avatar_split_clause,[],[f211,f120,f128]) ).
fof(f211,plain,
( in(sK1,sK2)
| in(sK0,sK2) ),
inference(trivial_inequality_removal,[],[f190]) ).
fof(f190,plain,
( in(sK0,sK2)
| in(sK1,sK2)
| unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1) ),
inference(superposition,[],[f54,f47]) ).
fof(f47,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X0) = set_difference(unordered_pair(X1,X0),X2)
| in(X0,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) )
& ( unordered_pair(X1,X0) = set_difference(unordered_pair(X1,X0),X2)
| in(X1,X2)
| in(X0,X2) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0,X2,X1] :
( ( ( ~ in(X2,X1)
& ~ in(X0,X1) )
| unordered_pair(X2,X0) != set_difference(unordered_pair(X2,X0),X1) )
& ( unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X2,X1] :
( ( ( ~ in(X2,X1)
& ~ in(X0,X1) )
| unordered_pair(X2,X0) != set_difference(unordered_pair(X2,X0),X1) )
& ( unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X2,X1] :
( ( ~ in(X2,X1)
& ~ in(X0,X1) )
<=> unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X2,X0] :
( ( ~ in(X0,X2)
& ~ in(X1,X2) )
<=> unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f54,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1),
inference(backward_demodulation,[],[f39,f51]) ).
fof(f39,plain,
set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f173,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f162,f128,f120]) ).
fof(f162,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(trivial_inequality_removal,[],[f148]) ).
fof(f148,plain,
( ~ in(sK1,sK2)
| singleton(sK0) != singleton(sK0)
| in(sK0,sK2) ),
inference(superposition,[],[f55,f35]) ).
fof(f55,plain,
set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
inference(backward_demodulation,[],[f42,f51]) ).
fof(f42,plain,
set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:52:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (12197)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (12205)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50 % (12197)Instruction limit reached!
% 0.19/0.50 % (12197)------------------------------
% 0.19/0.50 % (12197)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (12197)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (12197)Termination reason: Unknown
% 0.19/0.50 % (12197)Termination phase: Saturation
% 0.19/0.50
% 0.19/0.50 % (12197)Memory used [KB]: 5884
% 0.19/0.50 % (12197)Time elapsed: 0.005 s
% 0.19/0.50 % (12197)Instructions burned: 3 (million)
% 0.19/0.50 % (12197)------------------------------
% 0.19/0.50 % (12197)------------------------------
% 0.19/0.50 % (12189)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51 % (12192)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.51 % (12192)Refutation not found, incomplete strategy% (12192)------------------------------
% 0.19/0.51 % (12192)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (12192)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (12192)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51
% 0.19/0.51 % (12192)Memory used [KB]: 5884
% 0.19/0.51 % (12192)Time elapsed: 0.116 s
% 0.19/0.51 % (12192)Instructions burned: 2 (million)
% 0.19/0.51 % (12192)------------------------------
% 0.19/0.51 % (12192)------------------------------
% 0.19/0.51 % (12193)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.51 % (12188)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.51 % (12190)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51 % (12186)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (12186)Refutation not found, incomplete strategy% (12186)------------------------------
% 0.19/0.51 % (12186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (12186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (12186)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51
% 0.19/0.51 % (12186)Memory used [KB]: 5884
% 0.19/0.51 % (12186)Time elapsed: 0.116 s
% 0.19/0.51 % (12186)Instructions burned: 2 (million)
% 0.19/0.51 % (12186)------------------------------
% 0.19/0.51 % (12186)------------------------------
% 0.19/0.51 % (12183)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52 % (12205)First to succeed.
% 0.19/0.52 % (12189)Also succeeded, but the first one will report.
% 0.19/0.52 % (12205)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (12205)------------------------------
% 0.19/0.52 % (12205)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (12205)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (12205)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (12205)Memory used [KB]: 6140
% 0.19/0.52 % (12205)Time elapsed: 0.071 s
% 0.19/0.52 % (12205)Instructions burned: 14 (million)
% 0.19/0.52 % (12205)------------------------------
% 0.19/0.52 % (12205)------------------------------
% 0.19/0.52 % (12182)Success in time 0.168 s
%------------------------------------------------------------------------------