%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:38:08 AM UTC 2026
% Result : Unsatisfiable 0.43s 0.28s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 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 : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(g(X0),apply(apply(f(X0),f(X0)),g(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_combinator) ).
fof(f5,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(superposition,[],[f1,f2]) ).
fof(f11,plain,
! [X0,X1] : apply(apply(apply(s,k),X1),X0) = X0,
inference(superposition,[],[f1,f2]) ).
fof(f14,plain,
! [X0,X1] : apply(X0,X1) = apply(apply(apply(s,apply(s,k)),X0),X1),
inference(superposition,[],[f11,f1]) ).
fof(f17,plain,
! [X2,X0,X1] : apply(apply(apply(s,X1),apply(apply(s,k),X2)),X0) = apply(apply(X1,X0),X0),
inference(superposition,[],[f1,f11]) ).
fof(f21,plain,
! [X0,X1] : apply(apply(apply(s,apply(s,apply(s,k))),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[],[f14,f1]) ).
fof(f76,plain,
! [X0,X1] : apply(apply(X0,X1),X1) = apply(apply(apply(apply(s,s),apply(s,k)),X0),X1),
inference(superposition,[],[f17,f1]) ).
fof(f300,plain,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(apply(apply(s,apply(s,apply(s,k))),apply(f(X0),f(X0))),g(X0)),
inference(superposition,[],[f3,f21]) ).
fof(f486,plain,
! [X0] : apply(X0,X0) = apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(s,k))),X0),
inference(superposition,[],[f14,f76]) ).
fof(f524,plain,
! [X0] : apply(X0,X0) = apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),X0),
inference(forward_demodulation,[],[f486,f1]) ).
fof(f650,plain,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),f(X0))),g(X0)),
inference(superposition,[],[f300,f524]) ).
fof(f671,plain,
! [X0,X1] : apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),f(apply(apply(s,apply(k,X0)),X1)))),g(apply(apply(s,apply(k,X0)),X1))) != apply(apply(X0,apply(X1,f(apply(apply(s,apply(k,X0)),X1)))),g(apply(apply(s,apply(k,X0)),X1))),
inference(superposition,[],[f650,f5]) ).
fof(f913,plain,
$false,
inference(equality_resolution,[],[f671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.16 % Computer : n012.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 21:28:49 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 Running first-order model finding
% 0.07/0.18 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.28 % (3796621)Will run a generic schedule for satisfiability detection.
% 0.43/0.28 % (3796627)% WARNING: option uhcvi not known.
% 0.43/0.28 % (3796628)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4122518470:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.43/0.28 % (3796632)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1010066720:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.43/0.28 % (3796627)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=482835033:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.43/0.28 % (3796630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4286525351:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.43/0.28 % (3796631)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2572329386:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.43/0.28 % (3796626)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=673285931_3000 on theBenchmark for (3000ds/0Mi)
% 0.43/0.28 % (3796629)dis+10_1_sil=32000:sp=arity:random_seed=1013878072:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.43/0.28 % TRYING [1]
% 0.43/0.28 % TRYING [2]
% 0.43/0.28 % TRYING [3]
% 0.43/0.28 % TRYING [4]
% 0.43/0.28 % TRYING [5]
% 0.43/0.28 % TRYING [6]
% 0.43/0.28 % (3796629)Instruction limit reached!
% 0.43/0.28 % (3796629)------------------------------
% 0.43/0.28 % (3796629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.28 % (3796629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.28 % (3796629)CaDiCaL version: 2.1.3
% 0.43/0.28 % (3796629)Termination reason: Instruction limit
% 0.43/0.28 % (3796629)Termination phase: Saturation
% 0.43/0.28 % (3796629)Time elapsed: 0.050 s
% 0.43/0.28 % (3796629)Peak memory usage: 12 MB
% 0.43/0.28 % (3796629)Instructions burned: 104 (million)
% 0.43/0.28 % (3796628) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3796621-3796628"...
% 0.43/0.28 % (3796628)...printing done.
% 0.43/0.28 % (3796628)Refutation found. Thanks to Tanya!
% 0.43/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.43/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.43/0.28 % (3796628)------------------------------
% 0.43/0.28 % (3796628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.28 % (3796628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.28 % (3796628)CaDiCaL version: 2.1.3
% 0.43/0.28 % (3796628)Termination reason: Refutation
% 0.43/0.28 % (3796628)Time elapsed: 0.056 s
% 0.43/0.28 % (3796628)Peak memory usage: 12 MB
% 0.43/0.28 % (3796628)Instructions burned: 119 (million)
% 0.43/0.28 % (3796621)Success in time 0.087 s
% 0.43/0.28 % Vampire exiting
%------------------------------------------------------------------------------