%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:42:05 PM UTC 2026
% Result : Unsatisfiable 2.67s 1.33s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 1 def)
% Number of atoms : 38 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 13 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(v_g(v_x)) = v_x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
v_x = v_f(v_g(v_x)),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
! [X0] :
( X0 = v_x
| v_f(v_g(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,plain,
! [X0] :
( v_f(v_g(X0)) != X0
| v_x = X0 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
! [X0] :
( v_g(v_f(v_xa(X0))) = v_xa(X0)
| v_g(v_f(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,plain,
! [X0] :
( v_g(v_f(X0)) != X0
| v_xa(X0) = v_g(v_f(v_xa(X0))) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] :
( v_xa(X0) != X0
| v_g(v_f(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,plain,
( v_g(v_x) != v_g(v_x)
| v_xa(v_g(v_x)) = v_g(v_f(v_xa(v_g(v_x)))) ),
inference(superposition,[],[f6,f2]) ).
fof(f9,plain,
v_xa(v_g(v_x)) = v_g(v_f(v_xa(v_g(v_x)))),
inference(trivial_inequality_removal,[],[f8]) ).
fof(f11,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_x = v_f(v_xa(v_g(v_x))) ),
inference(superposition,[],[f4,f9]) ).
fof(f12,plain,
v_x = v_f(v_xa(v_g(v_x))),
inference(trivial_inequality_removal,[],[f11]) ).
fof(f14,plain,
v_g(v_x) = v_xa(v_g(v_x)),
inference(superposition,[],[f9,f12]) ).
fof(f21,definition,
( spl0_2
<=> v_g(v_x) = v_xa(v_g(v_x)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f22,plain,
( v_g(v_x) = v_xa(v_g(v_x))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f14,f21]) ).
fof(f28,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_x) != v_g(v_f(v_g(v_x)))
| ~ spl0_2 ),
inference(superposition,[],[f7,f22]) ).
fof(f29,plain,
( v_g(v_x) != v_g(v_f(v_g(v_x)))
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f28]) ).
fof(f30,plain,
( v_g(v_x) != v_g(v_x)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f29,f2]) ).
fof(f31,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f30]) ).
fof(f32,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 02:59:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.67/1.33 % (2953503)Input is clausal, will run a generic CNF schedule.
% 2.67/1.33 % (2953513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2533602878:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.67/1.33 % (2953513)First to succeed.
% 2.67/1.33 % (2953513)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2953503"
% 2.67/1.33 % (2953508)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4079975530:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.67/1.33 % (2953509)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3257857689:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.67/1.33 % (2953511)lrs+10_1_sil=8000:sp=occurrence:random_seed=1676498745:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.67/1.33 % (2953512)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=332553695:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.67/1.33 % (2953510)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2685491880:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.67/1.33 % (2953511)Also succeeded, but the first one will report.
% 2.67/1.33 % (2953512)Also succeeded, but the first one will report.
% 2.67/1.33 % (2953514)dis-21_1_sil=8000:lcm=predicate:random_seed=3476148695:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.67/1.33 % (2953514)Refutation not found, incomplete strategy
% 2.67/1.33 % (2953514)------------------------------
% 2.67/1.33 % (2953514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.33 % (2953514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.33 % (2953514)CaDiCaL version: 2.1.3
% 2.67/1.33 % (2953514)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.33 % (2953514)Time elapsed: 0.001 s
% 2.67/1.33 % (2953514)Peak memory usage: 88 MB
% 2.67/1.33 % (2953513)Refutation found. Thanks to Tanya!
% 2.67/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.33 % (2953513)------------------------------
% 2.67/1.33 % (2953513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.33 % (2953513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.33 % (2953513)CaDiCaL version: 2.1.3
% 2.67/1.33 % (2953513)Termination reason: Refutation
% 2.67/1.33 % (2953513)Time elapsed: 0.002 s
% 2.67/1.33 % (2953513)Peak memory usage: 89 MB
% 2.67/1.33 % (2953513)Instructions burned: 1 (million)
% 2.67/1.33 % (2953513)------------------------------
% 2.67/1.33 % (2953513)------------------------------
% 2.67/1.33 % (2953503)Success in time 0.291 s
% 2.67/1.33 % Vampire exiting
%------------------------------------------------------------------------------