%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 09:38:24 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 12 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f5,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
fof(f15,plain,
! [X0,X1] :
( apply(X1,n(X1,k(X0))) != X0
| k(X0) = X1 ),
inference(superposition,[],[f3,f1]) ).
fof(f288,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f290,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,X1),k(X0)),X2) = apply(apply(X1,k(X2)),X0),
inference(superposition,[],[f2,f1]) ).
fof(f417,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f288,f2]) ).
fof(f1352,plain,
! [X2,X0,X1] : apply(apply(apply(apply(abstraction,abstraction),X1),k(X0)),X2) = X0,
inference(superposition,[],[f417,f1]) ).
fof(f1552,plain,
! [X2,X0,X1] :
( X0 != X2
| k(X2) = apply(apply(apply(abstraction,abstraction),X1),k(X0)) ),
inference(superposition,[],[f15,f1352]) ).
fof(f1723,plain,
! [X0,X1] : k(X0) = apply(apply(apply(abstraction,abstraction),X1),k(X0)),
inference(equality_resolution,[],[f1552]) ).
fof(f1783,plain,
! [X0,X1] : k(X0) = apply(apply(abstraction,k(k(X0))),X1),
inference(superposition,[],[f1723,f290]) ).
fof(f1831,plain,
! [X0,X1] :
( k(X0) != X1
| k(X1) = apply(abstraction,k(k(X0))) ),
inference(superposition,[],[f15,f1783]) ).
fof(f1851,plain,
! [X0] : k(k(X0)) = apply(abstraction,k(k(X0))),
inference(equality_resolution,[],[f1831]) ).
fof(f1927,plain,
k(k(b)) != k(k(b)),
inference(superposition,[],[f5,f1851]) ).
fof(f1943,plain,
$false,
inference(trivial_inequality_removal,[],[f1927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.16 % Computer : n005.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 21:34:32 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 Running first-order model finding
% 0.08/0.18 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.24 % (1213357)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (1213364)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3517443236:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.24 % (1213363)% WARNING: option uhcvi not known.
% 0.08/0.24 % (1213362)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1202697226_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.24 % (1213363)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=507784806:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.24 % (1213365)dis+10_1_sil=32000:sp=arity:random_seed=4254071339:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.24 % (1213366)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2635224854:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.24 % (1213368)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=802822582:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.24 % (1213367)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=31809595:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.24 % TRYING [1]
% 0.08/0.24 % TRYING [2]
% 0.08/0.24 % TRYING [3]
% 0.08/0.24 % TRYING [4]
% 0.08/0.24 % TRYING [5]
% 0.08/0.24 % (1213364) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1213357-1213364"...
% 0.08/0.24 % (1213364)...printing done.
% 0.08/0.24 % (1213364)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24 % (1213364)------------------------------
% 0.08/0.24 % (1213364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (1213364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (1213364)CaDiCaL version: 2.1.3
% 0.08/0.24 % (1213364)Termination reason: Refutation
% 0.08/0.24 % (1213364)Time elapsed: 0.028 s
% 0.08/0.24 % (1213364)Peak memory usage: 12 MB
% 0.08/0.24 % (1213364)Instructions burned: 90 (million)
% 0.08/0.24 % (1213357)Success in time 0.053 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------