%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 09:38:22 AM UTC 2026
% Result : Unsatisfiable 0.31s 0.42s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f4,negated_conjecture,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p_combinator) ).
fof(f22,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z),
inference(superposition,[],[f4,f1]) ).
fof(f30,plain,
! [X0,X1] : apply(X0,apply(X1,X0)) = apply(apply(w,apply(q,X1)),X0),
inference(superposition,[],[f3,f2]) ).
fof(f100,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),y),z),
inference(superposition,[],[f22,f30]) ).
fof(f103,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z),
inference(superposition,[],[f100,f2]) ).
fof(f105,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z),
inference(superposition,[],[f103,f2]) ).
fof(f106,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(q,apply(x,y)),apply(x,y)),z),
inference(superposition,[],[f105,f2]) ).
fof(f108,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(superposition,[],[f106,f2]) ).
fof(f109,plain,
$false,
inference(trivial_inequality_removal,[],[f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.28 % Computer : n017.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Mon Sep 28 21:29:17 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.27/0.34 Running first-order model finding
% 0.27/0.34 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
% 0.31/0.42 % (4058204)Will run a generic schedule for satisfiability detection.
% 0.31/0.42 % (4058209)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=401301968_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.42 % TRYING [1]
% 0.31/0.42 % TRYING [2]
% 0.31/0.42 % TRYING [3]
% 0.31/0.42 % (4058210)% WARNING: option uhcvi not known.
% 0.31/0.42 % (4058211)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2288249507:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.42 % (4058213)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3653180658:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.42 % (4058212)dis+10_1_sil=32000:sp=arity:random_seed=2574446768:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.42 % TRYING [4]
% 0.31/0.42 % (4058210)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1909079165:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.42 % (4058215)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=655315629:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.42 % (4058214)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3083623340:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.42 % (4058215) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4058204-4058215"...
% 0.31/0.42 % (4058215)...printing done.
% 0.31/0.42 % (4058215)Refutation found. Thanks to Tanya!
% 0.31/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.31/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.42 % (4058215)------------------------------
% 0.31/0.42 % (4058215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (4058215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (4058215)CaDiCaL version: 2.1.3
% 0.31/0.42 % (4058215)Termination reason: Refutation
% 0.31/0.42 % (4058215)Time elapsed: 0.012 s
% 0.31/0.42 % (4058215)Peak memory usage: 11 MB
% 0.31/0.42 % (4058215)Instructions burned: 11 (million)
% 0.31/0.42 % (4058204)Success in time 0.066 s
% 0.31/0.42 % Vampire exiting
%------------------------------------------------------------------------------