TSTP Solution File: SET071-7 by SnakeForV-SAT---1.0

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET071-7 : 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 : n008.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 18:23:31 EDT 2022

% Result   : Unsatisfiable 1.37s 0.55s
% Output   : Refutation 1.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   35 (  23 unt;   0 def)
%            Number of atoms       :   50 (  29 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  15   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   42 (  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f994,plain,
    $false,
    inference(subsumption_resolution,[],[f993,f585]) ).

fof(f585,plain,
    ! [X28,X29,X27] :
      ( ~ member(x,X29)
      | ~ member(X27,X28) ),
    inference(resolution,[],[f16,f486]) ).

fof(f486,plain,
    ! [X10,X8,X9] : ~ member(ordered_pair(x,X8),cross_product(X9,X10)),
    inference(subsumption_resolution,[],[f480,f115]) ).

fof(f115,axiom,
    ~ member(y,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_3) ).

fof(f480,plain,
    ! [X10,X8,X9] :
      ( member(y,universal_class)
      | ~ member(ordered_pair(x,X8),cross_product(X9,X10)) ),
    inference(superposition,[],[f94,f461]) ).

fof(f461,plain,
    ! [X1] : ordered_pair(y,X1) = ordered_pair(x,X1),
    inference(forward_demodulation,[],[f460,f456]) ).

fof(f456,plain,
    ! [X5] : unordered_pair(sF0,singleton(singleton(X5))) = ordered_pair(x,X5),
    inference(forward_demodulation,[],[f444,f278]) ).

fof(f278,plain,
    singleton(x) = sF0,
    inference(superposition,[],[f119,f254]) ).

fof(f254,plain,
    ! [X1] : singleton(X1) = unordered_pair(X1,y),
    inference(resolution,[],[f111,f115]) ).

fof(f111,axiom,
    ! [X0,X1] :
      ( member(X1,universal_class)
      | unordered_pair(X0,X1) = singleton(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).

fof(f119,plain,
    unordered_pair(x,y) = sF0,
    introduced(function_definition,[]) ).

fof(f444,plain,
    ! [X5] : ordered_pair(x,X5) = unordered_pair(singleton(x),singleton(singleton(X5))),
    inference(superposition,[],[f13,f263]) ).

fof(f263,plain,
    ! [X4] : singleton(X4) = unordered_pair(x,X4),
    inference(superposition,[],[f108,f253]) ).

fof(f253,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,x),
    inference(resolution,[],[f111,f114]) ).

fof(f114,axiom,
    ~ member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_2) ).

fof(f108,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f460,plain,
    ! [X1] : ordered_pair(y,X1) = unordered_pair(sF0,singleton(singleton(X1))),
    inference(forward_demodulation,[],[f438,f269]) ).

fof(f269,plain,
    ! [X1] : singleton(X1) = unordered_pair(y,X1),
    inference(superposition,[],[f254,f108]) ).

fof(f438,plain,
    ! [X1] : ordered_pair(y,X1) = unordered_pair(sF0,unordered_pair(y,singleton(X1))),
    inference(superposition,[],[f13,f304]) ).

fof(f304,plain,
    singleton(y) = sF0,
    inference(superposition,[],[f263,f119]) ).

fof(f94,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
      | member(X2,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).

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/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f993,plain,
    member(x,sF0),
    inference(subsumption_resolution,[],[f991,f120]) ).

fof(f120,plain,
    null_class != sF0,
    inference(definition_folding,[],[f113,f119]) ).

fof(f113,axiom,
    null_class != unordered_pair(x,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_1) ).

fof(f991,plain,
    ( member(x,sF0)
    | null_class = sF0 ),
    inference(superposition,[],[f66,f989]) ).

fof(f989,plain,
    x = regular(sF0),
    inference(subsumption_resolution,[],[f980,f120]) ).

fof(f980,plain,
    ( null_class = sF0
    | x = regular(sF0) ),
    inference(resolution,[],[f977,f66]) ).

fof(f977,plain,
    ! [X0] :
      ( ~ member(X0,sF0)
      | x = X0 ),
    inference(superposition,[],[f425,f278]) ).

fof(f425,plain,
    ! [X3,X4] :
      ( ~ member(X4,singleton(X3))
      | X3 = X4 ),
    inference(duplicate_literal_removal,[],[f419]) ).

fof(f419,plain,
    ! [X3,X4] :
      ( X3 = X4
      | ~ member(X4,singleton(X3))
      | X3 = X4 ),
    inference(superposition,[],[f8,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( ~ member(X2,unordered_pair(X0,X1))
      | X0 = X2
      | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % 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 : n008.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 13:11:55 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  % (6002)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.48  % (6010)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)
% 0.19/0.48  % (6002)Instruction limit reached!
% 0.19/0.48  % (6002)------------------------------
% 0.19/0.48  % (6002)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (6002)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (6002)Termination reason: Unknown
% 0.19/0.48  % (6002)Termination phase: Saturation
% 0.19/0.48  
% 0.19/0.48  % (6002)Memory used [KB]: 5500
% 0.19/0.48  % (6002)Time elapsed: 0.076 s
% 0.19/0.48  % (6002)Instructions burned: 7 (million)
% 0.19/0.48  % (6002)------------------------------
% 0.19/0.48  % (6002)------------------------------
% 0.19/0.50  % (6007)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.24/0.51  % (6005)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.24/0.51  % (5999)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.24/0.52  % (6017)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)
% 1.24/0.52  % (6018)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)
% 1.24/0.53  % (5996)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)
% 1.37/0.53  % (6008)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.37/0.53  % (5997)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)
% 1.37/0.53  % (5998)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)
% 1.37/0.53  % (6009)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)
% 1.37/0.53  % (5995)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)
% 1.37/0.53  % (6006)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)
% 1.37/0.53  % (6000)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)
% 1.37/0.54  % (6020)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.37/0.54  % (6019)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.37/0.54  % (6001)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)
% 1.37/0.54  % (6021)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)
% 1.37/0.54  % (6012)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.37/0.54  % (6023)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.37/0.54  % (6022)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)
% 1.37/0.54  % (6011)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)
% 1.37/0.55  % (6013)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.37/0.55  % (6004)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)
% 1.37/0.55  % (6003)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.37/0.55  % (6014)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)
% 1.37/0.55  % (6010)First to succeed.
% 1.37/0.55  % (6003)Instruction limit reached!
% 1.37/0.55  % (6003)------------------------------
% 1.37/0.55  % (6003)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.55  % (6003)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.55  % (6003)Termination reason: Unknown
% 1.37/0.55  % (6003)Termination phase: Property scanning
% 1.37/0.55  
% 1.37/0.55  % (6003)Memory used [KB]: 1023
% 1.37/0.55  % (6003)Time elapsed: 0.003 s
% 1.37/0.55  % (6003)Instructions burned: 4 (million)
% 1.37/0.55  % (6003)------------------------------
% 1.37/0.55  % (6003)------------------------------
% 1.37/0.55  % (6015)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)
% 1.37/0.55  % (6016)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.37/0.55  % (6010)Refutation found. Thanks to Tanya!
% 1.37/0.55  % SZS status Unsatisfiable for theBenchmark
% 1.37/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.37/0.55  % (6010)------------------------------
% 1.37/0.55  % (6010)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.55  % (6010)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.55  % (6010)Termination reason: Refutation
% 1.37/0.55  
% 1.37/0.55  % (6010)Memory used [KB]: 1663
% 1.37/0.55  % (6010)Time elapsed: 0.145 s
% 1.37/0.55  % (6010)Instructions burned: 44 (million)
% 1.37/0.55  % (6010)------------------------------
% 1.37/0.55  % (6010)------------------------------
% 1.37/0.55  % (5994)Success in time 0.202 s
%------------------------------------------------------------------------------