%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV253-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:08:32 PM UTC 2026
% Result : Unsatisfiable 2.13s 0.71s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 5 unt; 2 def)
% Number of atoms : 50 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 1 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
( v_K != v_K_H
| c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
( c_Message_OinvKey(v_K) = c_Message_OinvKey(v_K_H)
| v_K = v_K_H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X0] : c_Message_OinvKey(c_Message_OinvKey(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f5,definition,
( spl0_1
<=> v_K = v_K_H ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f6,plain,
( v_K != v_K_H
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f7,plain,
( v_K = v_K_H
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f9,definition,
( spl0_2
<=> c_Message_OinvKey(v_K) = c_Message_OinvKey(v_K_H) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f10,plain,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K_H)
| spl0_2 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f11,plain,
( c_Message_OinvKey(v_K) = c_Message_OinvKey(v_K_H)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f2,f9,f5]) ).
fof(f13,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1,f5,f9]) ).
fof(f14,plain,
( v_K_H = c_Message_OinvKey(c_Message_OinvKey(v_K))
| ~ spl0_2 ),
inference(superposition,[],[f3,f11]) ).
fof(f15,plain,
( v_K = v_K_H
| ~ spl0_2 ),
inference(forward_demodulation,[],[f14,f3]) ).
fof(f16,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f15,f6]) ).
fof(f17,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f16]) ).
fof(f18,plain,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K)
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[],[f10,f7]) ).
fof(f19,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[],[f18]) ).
fof(f20,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f19]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f13]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl0_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f21,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV253-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 10:18:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.13/0.71 % (3283566)Input is clausal, will run a generic CNF schedule.
% 2.13/0.71 % (3283646)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1628406394:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 2.13/0.71 % (3283641)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=4158284262:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 2.13/0.71 % (3283642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3207250696:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 2.13/0.71 % (3283644)lrs+10_1_sil=8000:sp=occurrence:random_seed=1220940327:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 2.13/0.71 % (3283645)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2120757719:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 2.13/0.71 % (3283647)dis-21_1_sil=8000:lcm=predicate:random_seed=462235210:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 2.13/0.71 % (3283643)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2194335320:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 2.13/0.71 % (3283647)Refutation not found, incomplete strategy
% 2.13/0.71 % (3283647)------------------------------
% 2.13/0.71 % (3283647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/0.71 % (3283647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/0.71 % (3283647)CaDiCaL version: 2.1.3
% 2.13/0.71 % (3283647)Termination reason: Refutation not found, incomplete strategy
% 2.13/0.71 % (3283647)Time elapsed: 0.0000 s
% 2.13/0.71 % (3283647)Peak memory usage: 88 MB
% 2.13/0.71 % (3283646)Also succeeded, but the first one will report.
% 2.13/0.71 % (3283645)Also succeeded, but the first one will report.
% 2.13/0.71 % (3283644)First to succeed.
% 2.13/0.71 % (3283644)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3283566"
% 2.13/0.71 % (3283647)------------------------------
% 2.13/0.71 % (3283647)------------------------------
% 2.13/0.71 % (3283644)Refutation found. Thanks to Tanya!
% 2.13/0.71 % SZS status Unsatisfiable for theBenchmark
% 2.13/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 2.13/0.71 % (3283644)------------------------------
% 2.13/0.71 % (3283644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/0.71 % (3283644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/0.71 % (3283644)CaDiCaL version: 2.1.3
% 2.13/0.71 % (3283644)Termination reason: Refutation
% 2.13/0.71 % (3283644)Time elapsed: 0.001 s
% 2.13/0.71 % (3283644)Peak memory usage: 89 MB
% 2.13/0.71 % (3283644)Instructions burned: 1 (million)
% 2.13/0.71 % (3283644)------------------------------
% 2.13/0.71 % (3283644)------------------------------
% 2.13/0.71 % (3283566)Success in time 0.255 s
% 2.13/0.71 % Vampire exiting
%------------------------------------------------------------------------------