TSTP Solution File: SET346-6 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET346-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n028.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 18:24:30 EDT 2022
% Result : Unsatisfiable 0.14s 0.57s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 18 unt; 0 def)
% Number of atoms : 113 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 70 ~; 65 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f487,plain,
$false,
inference(subsumption_resolution,[],[f486,f113]) ).
fof(f113,axiom,
member(z,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_class_alternate_defn3_1) ).
fof(f486,plain,
~ member(z,y),
inference(resolution,[],[f481,f114]) ).
fof(f114,axiom,
member(y,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_class_alternate_defn3_2) ).
fof(f481,plain,
! [X2] :
( ~ member(X2,x)
| ~ member(z,X2) ),
inference(resolution,[],[f478,f236]) ).
fof(f236,plain,
! [X1] : member(z,unordered_pair(z,X1)),
inference(resolution,[],[f233,f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f233,plain,
member(z,universal_class),
inference(resolution,[],[f195,f113]) ).
fof(f195,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f478,plain,
! [X0,X1] :
( ~ member(X0,unordered_pair(z,z))
| ~ member(X0,X1)
| ~ member(X1,x) ),
inference(subsumption_resolution,[],[f477,f195]) ).
fof(f477,plain,
! [X0,X1] :
( ~ member(X1,x)
| ~ member(X1,universal_class)
| ~ member(X0,X1)
| ~ member(X0,unordered_pair(z,z)) ),
inference(subsumption_resolution,[],[f476,f195]) ).
fof(f476,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| ~ member(X0,X1)
| ~ member(X1,x)
| ~ member(X0,unordered_pair(z,z)) ),
inference(resolution,[],[f472,f139]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| ~ member(X2,X0)
| ~ member(X3,X1) ),
inference(definition_unfolding,[],[f16,f128]) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f472,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,unordered_pair(z,z))
| ~ member(X0,X1)
| ~ member(X1,x) ),
inference(resolution,[],[f176,f422]) ).
fof(f422,plain,
! [X10,X11] :
( ~ member(unordered_pair(unordered_pair(X10,X10),unordered_pair(X10,unordered_pair(X11,X11))),element_relation)
| ~ member(X10,unordered_pair(z,z))
| ~ member(X11,x) ),
inference(subsumption_resolution,[],[f420,f11]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f420,plain,
! [X10,X11] :
( ~ member(X11,x)
| ~ member(unordered_pair(unordered_pair(X10,X10),unordered_pair(X10,unordered_pair(X11,X11))),element_relation)
| ~ member(X10,unordered_pair(z,z))
| ~ member(unordered_pair(unordered_pair(X10,X10),unordered_pair(X10,unordered_pair(X11,X11))),universal_class) ),
inference(resolution,[],[f414,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f414,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),complement(universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,unordered_pair(z,z))
| ~ member(X1,x) ),
inference(subsumption_resolution,[],[f413,f195]) ).
fof(f413,plain,
! [X0,X1] :
( ~ member(X1,x)
| ~ member(X0,unordered_pair(z,z))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),complement(universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X1,universal_class) ),
inference(subsumption_resolution,[],[f411,f195]) ).
fof(f411,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),complement(universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X1,universal_class)
| ~ member(X1,x)
| ~ member(X0,unordered_pair(z,z)) ),
inference(resolution,[],[f409,f139]) ).
fof(f409,plain,
! [X8,X9] :
( ~ member(unordered_pair(unordered_pair(X8,X8),unordered_pair(X8,unordered_pair(X9,X9))),cross_product(unordered_pair(z,z),universal_class))
| ~ member(unordered_pair(unordered_pair(X8,X8),unordered_pair(X8,unordered_pair(X9,X9))),element_relation)
| ~ member(X8,universal_class)
| ~ member(X9,x)
| member(unordered_pair(unordered_pair(X8,X8),unordered_pair(X8,unordered_pair(X9,X9))),complement(universal_class)) ),
inference(resolution,[],[f139,f388]) ).
fof(f388,plain,
! [X1] :
( ~ member(X1,cross_product(universal_class,x))
| ~ member(X1,element_relation)
| ~ member(X1,cross_product(unordered_pair(z,z),universal_class))
| member(X1,complement(universal_class)) ),
inference(resolution,[],[f366,f23]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f366,plain,
! [X0] :
( ~ member(X0,intersection(element_relation,cross_product(universal_class,x)))
| ~ member(X0,cross_product(unordered_pair(z,z),universal_class))
| member(X0,complement(universal_class)) ),
inference(superposition,[],[f23,f362]) ).
fof(f362,plain,
complement(universal_class) = intersection(intersection(element_relation,cross_product(universal_class,x)),cross_product(unordered_pair(z,z),universal_class)),
inference(subsumption_resolution,[],[f361,f233]) ).
fof(f361,plain,
( ~ member(z,universal_class)
| complement(universal_class) = intersection(intersection(element_relation,cross_product(universal_class,x)),cross_product(unordered_pair(z,z),universal_class)) ),
inference(resolution,[],[f345,f156]) ).
fof(f156,plain,
~ member(z,domain_of(intersection(element_relation,cross_product(universal_class,x)))),
inference(definition_unfolding,[],[f115,f116]) ).
fof(f116,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f53,f28]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f115,axiom,
~ member(z,sum_class(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_class_alternate_defn3_3) ).
fof(f345,plain,
! [X0,X4] :
( member(X4,domain_of(X0))
| complement(universal_class) = intersection(X0,cross_product(unordered_pair(X4,X4),universal_class))
| ~ member(X4,universal_class) ),
inference(forward_demodulation,[],[f138,f312]) ).
fof(f312,plain,
null_class = complement(universal_class),
inference(duplicate_literal_removal,[],[f308]) ).
fof(f308,plain,
( null_class = complement(universal_class)
| null_class = complement(universal_class) ),
inference(resolution,[],[f186,f232]) ).
fof(f232,plain,
! [X2] :
( member(regular(X2),universal_class)
| null_class = X2 ),
inference(resolution,[],[f195,f66]) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f186,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f66,f24]) ).
fof(f138,plain,
! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| null_class = intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)) ),
inference(definition_unfolding,[],[f31,f28,f12]) ).
fof(f31,axiom,
! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) = null_class
| ~ member(X4,universal_class)
| member(X4,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f176,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f20,f128,f128]) ).
fof(f20,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET346-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.05/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.33 % Computer : n028.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue Aug 30 13:49:33 EDT 2022
% 0.10/0.33 % CPUTime :
% 0.14/0.49 % (13344)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.49 % (13346)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.50 % (13354)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.14/0.50 % (13346)Instruction limit reached!
% 0.14/0.50 % (13346)------------------------------
% 0.14/0.50 % (13346)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.50 % (13346)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.50 % (13346)Termination reason: Unknown
% 0.14/0.50 % (13346)Termination phase: Property scanning
% 0.14/0.50
% 0.14/0.50 % (13346)Memory used [KB]: 1023
% 0.14/0.50 % (13346)Time elapsed: 0.004 s
% 0.14/0.50 % (13346)Instructions burned: 3 (million)
% 0.14/0.50 % (13346)------------------------------
% 0.14/0.50 % (13346)------------------------------
% 0.14/0.50 % (13362)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.14/0.51 % (13360)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.14/0.52 % (13352)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.14/0.53 % (13338)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.14/0.53 % (13348)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.14/0.53 % (13345)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.53 % (13345)Instruction limit reached!
% 0.14/0.53 % (13345)------------------------------
% 0.14/0.53 % (13345)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.53 % (13345)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.53 % (13345)Termination reason: Unknown
% 0.14/0.53 % (13345)Termination phase: Saturation
% 0.14/0.53
% 0.14/0.53 % (13345)Memory used [KB]: 5500
% 0.14/0.53 % (13345)Time elapsed: 0.139 s
% 0.14/0.53 % (13345)Instructions burned: 7 (million)
% 0.14/0.53 % (13345)------------------------------
% 0.14/0.53 % (13345)------------------------------
% 0.14/0.54 % (13341)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.54 % (13343)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.14/0.54 % (13342)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.55 % (13340)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.55 % (13367)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.14/0.55 % (13366)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.14/0.56 % (13349)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.14/0.56 % (13359)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.14/0.56 % (13347)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.56 % (13365)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.14/0.56 % (13355)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.14/0.56 % (13356)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.14/0.56 % (13350)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.14/0.56 % (13360)First to succeed.
% 0.14/0.56 % (13351)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.14/0.57 % (13361)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.14/0.57 % (13358)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.14/0.57 % (13364)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.14/0.57 % (13360)Refutation found. Thanks to Tanya!
% 0.14/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.57 % (13360)------------------------------
% 0.14/0.57 % (13360)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.57 % (13360)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.57 % (13360)Termination reason: Refutation
% 0.14/0.57
% 0.14/0.57 % (13360)Memory used [KB]: 1407
% 0.14/0.57 % (13360)Time elapsed: 0.160 s
% 0.14/0.57 % (13360)Instructions burned: 28 (million)
% 0.14/0.57 % (13360)------------------------------
% 0.14/0.57 % (13360)------------------------------
% 0.14/0.57 % (13337)Success in time 0.231 s
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