%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM061-1 : 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 : n025.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 18:03:23 EDT 2022

% Result   : Unsatisfiable 1.65s 0.57s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   48 (  25 unt;   0 def)
%            Number of atoms       :   89 (  18 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   82 (  41   ~;  41   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 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   :   57 (  57   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f724,plain,
    $false,
    inference(subsumption_resolution,[],[f722,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(f722,plain,
    ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),universal_class),
    inference(resolution,[],[f717,f24]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,complement(X0))
      | ~ member(X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f717,plain,
    member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class)),
    inference(subsumption_resolution,[],[f716,f334]) ).

fof(f334,plain,
    ! [X1] : member(u,unordered_pair(u,X1)),
    inference(resolution,[],[f329,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(f329,plain,
    member(u,universal_class),
    inference(resolution,[],[f284,f160]) ).

fof(f160,axiom,
    member(u,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property5_2) ).

fof(f284,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(f716,plain,
    ( ~ member(u,unordered_pair(u,u))
    | member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class)) ),
    inference(subsumption_resolution,[],[f714,f161]) ).

fof(f161,axiom,
    member(z,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property5_3) ).

fof(f714,plain,
    ( ~ member(z,universal_class)
    | ~ member(u,unordered_pair(u,u))
    | member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class)) ),
    inference(resolution,[],[f713,f215]) ).

fof(f215,plain,
    ! [X2,X3,X0,X1] :
      ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
      | ~ member(X3,X1)
      | ~ member(X2,X0) ),
    inference(definition_unfolding,[],[f16,f163]) ).

fof(f163,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(X2,X0)
      | member(ordered_pair(X2,X3),cross_product(X0,X1))
      | ~ member(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f713,plain,
    ( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(unordered_pair(u,u),universal_class))
    | member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class)) ),
    inference(subsumption_resolution,[],[f712,f160]) ).

fof(f712,plain,
    ( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class))
    | ~ member(u,y)
    | ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(unordered_pair(u,u),universal_class)) ),
    inference(subsumption_resolution,[],[f710,f273]) ).

fof(f273,plain,
    ! [X5] : member(z,unordered_pair(z,X5)),
    inference(resolution,[],[f9,f161]) ).

fof(f710,plain,
    ( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(unordered_pair(u,u),universal_class))
    | member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),complement(universal_class))
    | ~ member(z,unordered_pair(z,z))
    | ~ member(u,y) ),
    inference(resolution,[],[f708,f249]) ).

fof(f249,plain,
    member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),xr),
    inference(definition_unfolding,[],[f159,f163]) ).

fof(f159,axiom,
    member(ordered_pair(u,z),xr),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property5_1) ).

fof(f708,plain,
    ! [X8,X9] :
      ( ~ member(unordered_pair(unordered_pair(X9,X9),unordered_pair(X9,unordered_pair(X8,X8))),xr)
      | ~ member(X8,unordered_pair(z,z))
      | ~ member(X9,y)
      | member(unordered_pair(unordered_pair(X9,X9),unordered_pair(X9,unordered_pair(X8,X8))),complement(universal_class))
      | ~ member(unordered_pair(unordered_pair(X9,X9),unordered_pair(X9,unordered_pair(X8,X8))),cross_product(unordered_pair(u,u),universal_class)) ),
    inference(resolution,[],[f215,f519]) ).

fof(f519,plain,
    ! [X1] :
      ( ~ member(X1,cross_product(y,unordered_pair(z,z)))
      | ~ member(X1,cross_product(unordered_pair(u,u),universal_class))
      | member(X1,complement(universal_class))
      | ~ member(X1,xr) ),
    inference(backward_demodulation,[],[f452,f487]) ).

fof(f487,plain,
    null_class = complement(universal_class),
    inference(duplicate_literal_removal,[],[f476]) ).

fof(f476,plain,
    ( null_class = complement(universal_class)
    | null_class = complement(universal_class) ),
    inference(resolution,[],[f266,f328]) ).

fof(f328,plain,
    ! [X5] :
      ( member(regular(X5),universal_class)
      | null_class = X5 ),
    inference(resolution,[],[f284,f66]) ).

fof(f66,axiom,
    ! [X0] :
      ( member(regular(X0),X0)
      | null_class = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f266,plain,
    ! [X0] :
      ( ~ member(regular(complement(X0)),X0)
      | complement(X0) = null_class ),
    inference(resolution,[],[f66,f24]) ).

fof(f452,plain,
    ! [X1] :
      ( ~ member(X1,cross_product(y,unordered_pair(z,z)))
      | member(X1,null_class)
      | ~ member(X1,cross_product(unordered_pair(u,u),universal_class))
      | ~ member(X1,xr) ),
    inference(resolution,[],[f442,f23]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( member(X4,intersection(X0,X1))
      | ~ member(X4,X0)
      | ~ member(X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f442,plain,
    ! [X0] :
      ( ~ member(X0,intersection(xr,cross_product(y,unordered_pair(z,z))))
      | ~ member(X0,cross_product(unordered_pair(u,u),universal_class))
      | member(X0,null_class) ),
    inference(superposition,[],[f23,f441]) ).

fof(f441,plain,
    null_class = intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z)))),
    inference(subsumption_resolution,[],[f439,f329]) ).

fof(f439,plain,
    ( null_class = intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z))))
    | ~ member(u,universal_class) ),
    inference(resolution,[],[f188,f388]) ).

fof(f388,plain,
    ~ member(u,domain_of(intersection(xr,cross_product(y,unordered_pair(z,z))))),
    inference(backward_demodulation,[],[f248,f229]) ).

fof(f229,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

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(f248,plain,
    ~ member(u,domain_of(intersection(cross_product(y,unordered_pair(z,z)),xr))),
    inference(definition_unfolding,[],[f162,f177]) ).

fof(f177,plain,
    ! [X1,X4,X5] : segment(X5,X1,X4) = domain_of(intersection(cross_product(X1,unordered_pair(X4,X4)),X5)),
    inference(definition_unfolding,[],[f122,f29,f12]) ).

fof(f122,axiom,
    ! [X1,X4,X5] : segment(X5,X1,X4) = domain_of(restrict(X5,X1,singleton(X4))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment) ).

fof(f162,axiom,
    ~ member(u,segment(xr,y,z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property5_4) ).

fof(f188,plain,
    ! [X0,X4] :
      ( member(X4,domain_of(X0))
      | ~ member(X4,universal_class)
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

fof(f31,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | restrict(X0,singleton(X4),universal_class) = null_class
      | member(X4,domain_of(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : NUM061-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n025.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 06:02:29 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.51  % (4744)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)
% 0.21/0.51  % (4755)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.51  % (4743)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)
% 0.21/0.51  % (4741)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)
% 0.21/0.52  % (4756)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)
% 0.21/0.52  % (4764)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)
% 0.21/0.53  % (4758)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)
% 0.21/0.53  % (4746)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)
% 0.21/0.53  % (4745)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (4747)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)
% 0.21/0.53  % (4749)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.53  % (4768)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)
% 0.21/0.53  % (4749)Instruction limit reached!
% 0.21/0.53  % (4749)------------------------------
% 0.21/0.53  % (4749)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (4749)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (4749)Termination reason: Unknown
% 0.21/0.53  % (4749)Termination phase: Function definition elimination
% 0.21/0.53  
% 0.21/0.53  % (4749)Memory used [KB]: 1023
% 0.21/0.53  % (4749)Time elapsed: 0.002 s
% 0.21/0.53  % (4749)Instructions burned: 3 (million)
% 0.21/0.53  % (4749)------------------------------
% 0.21/0.53  % (4749)------------------------------
% 0.21/0.53  % (4761)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.54  % (4770)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.54  % (4760)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.54  % (4763)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.54  % (4762)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)
% 0.21/0.54  % (4748)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.55  % (4771)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)
% 0.21/0.55  % (4753)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)
% 0.21/0.55  % (4767)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.55  % (4752)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.55  % (4754)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.57/0.55  % (4742)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.57/0.55  % (4769)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)
% 1.57/0.55  % (4757)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.57/0.56  % (4759)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.57/0.56  % (4765)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)
% 1.57/0.57  % (4751)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)
% 1.57/0.57  % (4748)Instruction limit reached!
% 1.57/0.57  % (4748)------------------------------
% 1.57/0.57  % (4748)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.57/0.57  % (4748)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.57/0.57  % (4748)Termination reason: Unknown
% 1.57/0.57  % (4748)Termination phase: Saturation
% 1.57/0.57  
% 1.57/0.57  % (4748)Memory used [KB]: 5628
% 1.57/0.57  % (4748)Time elapsed: 0.006 s
% 1.57/0.57  % (4748)Instructions burned: 8 (million)
% 1.57/0.57  % (4748)------------------------------
% 1.57/0.57  % (4748)------------------------------
% 1.65/0.57  % (4764)First to succeed.
% 1.65/0.57  % (4764)Refutation found. Thanks to Tanya!
% 1.65/0.57  % SZS status Unsatisfiable for theBenchmark
% 1.65/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.57  % (4764)------------------------------
% 1.65/0.57  % (4764)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.57  % (4764)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.57  % (4764)Termination reason: Refutation
% 1.65/0.57  
% 1.65/0.57  % (4764)Memory used [KB]: 1535
% 1.65/0.57  % (4764)Time elapsed: 0.110 s
% 1.65/0.57  % (4764)Instructions burned: 39 (million)
% 1.65/0.57  % (4764)------------------------------
% 1.65/0.57  % (4764)------------------------------
% 1.65/0.57  % (4740)Success in time 0.221 s
%------------------------------------------------------------------------------