%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : n016.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 16:14:47 EDT 2022

% Result   : Unsatisfiable 1.36s 0.52s
% Output   : Refutation 1.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   38 (  38 unt;   0 def)
%            Number of atoms       :   38 (  37 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   22 (  22   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f154,plain,
    $false,
    inference(trivial_inequality_removal,[],[f151]) ).

fof(f151,plain,
    least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(a)))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(a)))),
    inference(backward_demodulation,[],[f136,f144]) ).

fof(f144,plain,
    ! [X2] : multiply(X2,identity) = X2,
    inference(superposition,[],[f73,f17]) ).

fof(f17,axiom,
    ! [X0] : inverse(inverse(X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_2) ).

fof(f73,plain,
    ! [X0] : inverse(X0) = multiply(inverse(X0),identity),
    inference(forward_demodulation,[],[f56,f1]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f56,plain,
    ! [X0] : multiply(inverse(X0),identity) = inverse(multiply(identity,X0)),
    inference(superposition,[],[f18,f16]) ).

fof(f16,axiom,
    identity = inverse(identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_1) ).

fof(f18,axiom,
    ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_3) ).

fof(f136,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(identity,inverse(a)))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(a)))),
    inference(superposition,[],[f69,f5]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).

fof(f69,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(a)))),
    inference(forward_demodulation,[],[f68,f1]) ).

fof(f68,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(multiply(identity,a))))),
    inference(forward_demodulation,[],[f67,f16]) ).

fof(f67,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(multiply(inverse(identity),a))))),
    inference(forward_demodulation,[],[f66,f17]) ).

fof(f66,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,inverse(multiply(inverse(identity),inverse(inverse(a))))))),
    inference(backward_demodulation,[],[f39,f63]) ).

fof(f63,plain,
    ! [X4,X5] : multiply(X4,X5) = inverse(multiply(inverse(X5),inverse(X4))),
    inference(superposition,[],[f17,f18]) ).

fof(f39,plain,
    least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,multiply(inverse(a),identity)))),
    inference(backward_demodulation,[],[f35,f38]) ).

fof(f38,plain,
    ! [X0] : identity = multiply(X0,inverse(X0)),
    inference(superposition,[],[f2,f17]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f35,plain,
    least_upper_bound(identity,least_upper_bound(a,least_upper_bound(identity,multiply(inverse(a),identity)))) != least_upper_bound(multiply(a,inverse(a)),least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))),
    inference(backward_demodulation,[],[f34,f5]) ).

fof(f34,plain,
    least_upper_bound(multiply(a,inverse(a)),least_upper_bound(multiply(a,identity),least_upper_bound(inverse(a),identity))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))),
    inference(forward_demodulation,[],[f33,f7]) ).

fof(f7,axiom,
    ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).

fof(f33,plain,
    least_upper_bound(least_upper_bound(multiply(a,inverse(a)),multiply(a,identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))),
    inference(forward_demodulation,[],[f32,f12]) ).

fof(f12,axiom,
    ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).

fof(f32,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))),
    inference(forward_demodulation,[],[f31,f2]) ).

fof(f31,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(multiply(inverse(a),a),least_upper_bound(a,least_upper_bound(multiply(inverse(a),identity),identity))),
    inference(forward_demodulation,[],[f30,f1]) ).

fof(f30,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(multiply(inverse(a),a),least_upper_bound(multiply(identity,a),least_upper_bound(multiply(inverse(a),identity),identity))),
    inference(forward_demodulation,[],[f29,f7]) ).

fof(f29,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(least_upper_bound(multiply(inverse(a),a),multiply(identity,a)),least_upper_bound(multiply(inverse(a),identity),identity)),
    inference(forward_demodulation,[],[f28,f14]) ).

fof(f14,axiom,
    ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).

fof(f28,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(multiply(least_upper_bound(inverse(a),identity),a),least_upper_bound(multiply(inverse(a),identity),identity)),
    inference(forward_demodulation,[],[f27,f1]) ).

fof(f27,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(multiply(least_upper_bound(inverse(a),identity),a),least_upper_bound(multiply(inverse(a),identity),multiply(identity,identity))),
    inference(forward_demodulation,[],[f26,f14]) ).

fof(f26,plain,
    least_upper_bound(multiply(a,least_upper_bound(inverse(a),identity)),least_upper_bound(inverse(a),identity)) != least_upper_bound(multiply(least_upper_bound(inverse(a),identity),a),multiply(least_upper_bound(inverse(a),identity),identity)),
    inference(forward_demodulation,[],[f25,f16]) ).

fof(f25,plain,
    least_upper_bound(multiply(least_upper_bound(inverse(a),inverse(identity)),a),multiply(least_upper_bound(inverse(a),inverse(identity)),identity)) != least_upper_bound(multiply(a,least_upper_bound(inverse(a),inverse(identity))),least_upper_bound(inverse(a),inverse(identity))),
    inference(backward_demodulation,[],[f24,f19]) ).

fof(f19,axiom,
    ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21x_4) ).

fof(f24,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) != least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))),
    inference(forward_demodulation,[],[f23,f1]) ).

fof(f23,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) != least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(forward_demodulation,[],[f22,f14]) ).

fof(f22,plain,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
    inference(forward_demodulation,[],[f21,f12]) ).

fof(f21,axiom,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21x) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 22:45:30 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.46  % (22887)dis+2_1:1024_abs=on:alpa=false:anc=all_dependent:avsq=on:bce=on:drc=off:newcnf=on:slsq=on:slsqc=0:slsqr=1,1:sp=reverse_arity:i=353:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/353Mi)
% 0.18/0.47  % (22895)dis+11_1:64_fd=off:nm=0:nwc=5.0:i=481:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/481Mi)
% 0.18/0.49  % (22874)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99788:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99788Mi)
% 0.18/0.49  % (22903)lrs+10_1:1_drc=off:fd=preordered:plsq=on:sp=occurrence:to=lpo:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.18/0.50  % (22899)lrs+10_1:2_bd=preordered:drc=off:fd=preordered:fde=unused:sp=const_min:to=lpo:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.18/0.50  % (22876)lrs+1004_1:734_av=off:awrs=converge:awrsf=70:br=off:ep=RSTC:erd=off:gs=on:nwc=3.0:s2a=on:s2agt=16:sp=occurrence:updr=off:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.51  % (22877)lrs+10_1:1_amm=off:drc=off:sp=reverse_frequency:spb=goal_then_units:to=lpo:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.51  % (22879)lrs+10_1:1_br=off:ep=RSTC:sos=all:urr=on:i=20:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/20Mi)
% 0.18/0.51  % (22896)lrs+10_5:1_br=off:ep=RSTC:sos=all:urr=on:i=267:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/267Mi)
% 0.18/0.51  % (22875)lrs+10_1:16_awrs=converge:awrsf=40:br=off:ep=RSTC:flr=on:gsp=on:nwc=3.0:sos=on:urr=on:i=10:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/10Mi)
% 0.18/0.51  % (22877)Instruction limit reached!
% 0.18/0.51  % (22877)------------------------------
% 0.18/0.51  % (22877)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (22877)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (22877)Termination reason: Unknown
% 0.18/0.51  % (22877)Termination phase: Saturation
% 0.18/0.51  
% 0.18/0.51  % (22877)Memory used [KB]: 5500
% 0.18/0.51  % (22877)Time elapsed: 0.118 s
% 0.18/0.51  % (22877)Instructions burned: 7 (million)
% 0.18/0.51  % (22877)------------------------------
% 0.18/0.51  % (22877)------------------------------
% 1.36/0.52  % (22891)lrs+10_1:1_br=off:flr=on:slsq=on:slsqc=1:sp=frequency:urr=on:i=257:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/257Mi)
% 1.36/0.52  % (22875)Instruction limit reached!
% 1.36/0.52  % (22875)------------------------------
% 1.36/0.52  % (22875)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.52  % (22875)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.52  % (22875)Termination reason: Unknown
% 1.36/0.52  % (22875)Termination phase: Saturation
% 1.36/0.52  
% 1.36/0.52  % (22875)Memory used [KB]: 5756
% 1.36/0.52  % (22875)Time elapsed: 0.130 s
% 1.36/0.52  % (22875)Instructions burned: 12 (million)
% 1.36/0.52  % (22875)------------------------------
% 1.36/0.52  % (22875)------------------------------
% 1.36/0.52  % (22892)lrs+1011_1:1_asg=cautious:bsr=on:cond=on:drc=off:etr=on:fd=preordered:gs=on:plsq=on:plsqr=388,511:slsq=on:slsqc=1:slsqr=21,31:urr=on:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.36/0.52  % (22903)First to succeed.
% 1.36/0.52  % (22901)lrs+10_1:128_awrs=converge:awrsf=8:bd=off:drc=off:slsq=on:slsqc=1:slsql=off:slsqr=40,29:i=495:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/495Mi)
% 1.36/0.52  % (22903)Refutation found. Thanks to Tanya!
% 1.36/0.52  % SZS status Unsatisfiable for theBenchmark
% 1.36/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.36/0.52  % (22903)------------------------------
% 1.36/0.52  % (22903)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.52  % (22903)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.52  % (22903)Termination reason: Refutation
% 1.36/0.52  
% 1.36/0.52  % (22903)Memory used [KB]: 5628
% 1.36/0.52  % (22903)Time elapsed: 0.134 s
% 1.36/0.52  % (22903)Instructions burned: 8 (million)
% 1.36/0.52  % (22903)------------------------------
% 1.36/0.52  % (22903)------------------------------
% 1.36/0.52  % (22873)Success in time 0.179 s
%------------------------------------------------------------------------------