0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.03	% Command    : run_vampire %s %d THM
0.06/0.34	% Computer   : n008.cluster.edu
0.06/0.34	% Model      : x86_64 x86_64
0.06/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.06/0.34	% Memory     : 8046.5625MB
0.06/0.34	% OS         : Linux 6.8.0-71-generic
0.06/0.34	% CPULimit   : 1440
0.06/0.34	% WCLimit    : 180
0.06/0.34	% DateTime   : Mon Jul 27 10:05:27 UTC 2026
0.06/0.34	% CPUTime    : 
0.14/0.38	This is a FOF_ problem
0.14/0.38	Running first-order theorem proving
0.14/0.38	Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.14/0.43	% (985539)Running in auto input_syntax mode. Trying TPTP
0.14/0.43	% (985541)lrs+1011_1_sp=occurrence:random_seed=264970469:st=6:sd=4:ss=included_1799 on theBenchmark for (1799ds/0Mi)
0.14/0.44	% (985541)First to succeed.
0.14/0.44	% (985541)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-985539"
0.14/0.44	% (985539)Running in auto input_syntax mode. Trying TPTP
0.14/0.44	% (985541)Refutation found. Thanks to Tanya!
0.14/0.44	% SZS status Theorem for theBenchmark
0.14/0.44	% SZS output start Proof for theBenchmark
0.14/0.44	fof(f272,plain,(
0.14/0.44	  $false),
0.14/0.44	  inference(resolution,[],[f178,f257])).
0.14/0.44	fof(f257,plain,(
0.14/0.44	  ( ! [X0] : (~tc(nil,lam(lam(var(X0))),arr(a,arr(b,b)))) )),
0.14/0.44	  inference(resolution,[],[f202,f92])).
0.14/0.44	fof(f92,plain,(
0.14/0.44	  ( ! [X0] : (~nf(X0) | ~tc(nil,X0,arr(a,arr(b,b)))) )),
0.14/0.44	  inference(cnf_transformation,[],[f54])).
0.14/0.44	fof(f54,plain,(
0.14/0.44	  ! [X0] : (~tc(nil,X0,arr(a,arr(b,b))) | ~nf(X0))),
0.14/0.44	  inference(ennf_transformation,[],[f48])).
0.14/0.44	fof(f48,plain,(
0.14/0.44	  ~? [X0] : (tc(nil,X0,arr(a,arr(b,b))) & nf(X0))),
0.14/0.44	  inference(rectify,[],[f26])).
0.14/0.44	fof(f26,negated_conjecture,(
0.14/0.44	  ~? [X8] : (tc(nil,X8,arr(a,arr(b,b))) & nf(X8))),
0.14/0.44	  inference(negated_conjecture,[status(cth)],[f25])).
0.14/0.44	fof(f25,conjecture,(
0.14/0.44	  ? [X8] : (tc(nil,X8,arr(a,arr(b,b))) & nf(X8))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f202,plain,(
0.14/0.44	  ( ! [X0] : (nf(lam(lam(var(X0))))) )),
0.14/0.44	  inference(subsumption_resolution,[],[f192,f88])).
0.14/0.44	fof(f88,plain,(
0.14/0.44	  ( ! [X0,X1] : (var(X1) != lam(X0)) )),
0.14/0.44	  inference(cnf_transformation,[],[f22])).
0.14/0.44	fof(f22,axiom,(
0.14/0.44	  ! [X0,X1] : var(X1) != lam(X0)),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f192,plain,(
0.14/0.44	  ( ! [X0,X1] : (nf(lam(lam(var(X0)))) | var(X1) = lam(proj1Lam(var(X1)))) )),
0.14/0.44	  inference(resolution,[],[f160,f103])).
0.14/0.44	fof(f103,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (~nf(app(X0,X1,X2)) | nf(X1) | lam(proj1Lam(X0)) = X0) )),
0.14/0.44	  inference(cnf_transformation,[],[f62])).
0.14/0.44	fof(f62,plain,(
0.14/0.44	  ! [X0,X1,X2] : (((nf(app(X0,X1,X2)) | ~nf(X1) | ~nf(X0)) & ((nf(X1) & nf(X0)) | ~nf(app(X0,X1,X2)))) | lam(proj1Lam(X0)) = X0)),
0.14/0.44	  inference(flattening,[],[f61])).
0.14/0.44	fof(f61,plain,(
0.14/0.44	  ! [X0,X1,X2] : (((nf(app(X0,X1,X2)) | (~nf(X1) | ~nf(X0))) & ((nf(X1) & nf(X0)) | ~nf(app(X0,X1,X2)))) | lam(proj1Lam(X0)) = X0)),
0.14/0.44	  inference(nnf_transformation,[],[f55])).
0.14/0.44	fof(f55,plain,(
0.14/0.44	  ! [X0,X1,X2] : ((nf(app(X0,X1,X2)) <=> (nf(X1) & nf(X0))) | lam(proj1Lam(X0)) = X0)),
0.14/0.44	  inference(ennf_transformation,[],[f50])).
0.14/0.44	fof(f50,plain,(
0.14/0.44	  ! [X0,X1,X2] : (lam(proj1Lam(X0)) != X0 => (nf(app(X0,X1,X2)) <=> (nf(X1) & nf(X0))))),
0.14/0.44	  inference(rectify,[],[f36])).
0.14/0.44	fof(f36,axiom,(
0.14/0.44	  ! [X11,X4,X1] : (lam(proj1Lam(X11)) != X11 => (nf(app(X11,X4,X1)) <=> (nf(X4) & nf(X11))))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f160,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (nf(app(var(X0),lam(lam(var(X1))),X2))) )),
0.14/0.44	  inference(resolution,[],[f156,f140])).
0.14/0.44	fof(f140,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (~nf(X1) | nf(app(var(X0),lam(X1),X2))) )),
0.14/0.44	  inference(subsumption_resolution,[],[f135,f88])).
0.14/0.44	fof(f135,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (nf(app(var(X0),lam(X1),X2)) | var(X0) = lam(proj1Lam(var(X0))) | ~nf(X1)) )),
0.14/0.44	  inference(resolution,[],[f120,f77])).
0.14/0.44	fof(f77,plain,(
0.14/0.44	  ( ! [X0] : (nf(var(X0))) )),
0.14/0.44	  inference(cnf_transformation,[],[f43])).
0.14/0.44	fof(f43,plain,(
0.14/0.44	  ! [X0] : nf(var(X0))),
0.14/0.44	  inference(rectify,[],[f11])).
0.14/0.44	fof(f11,axiom,(
0.14/0.44	  ! [X3] : nf(var(X3))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f120,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (~nf(X0) | nf(app(X0,lam(X1),X2)) | lam(proj1Lam(X0)) = X0 | ~nf(X1)) )),
0.14/0.44	  inference(resolution,[],[f104,f72])).
0.14/0.44	fof(f72,plain,(
0.14/0.44	  ( ! [X0] : (nf(lam(X0)) | ~nf(X0)) )),
0.14/0.44	  inference(cnf_transformation,[],[f57])).
0.14/0.44	fof(f57,plain,(
0.14/0.44	  ! [X0] : ((nf(X0) | ~nf(lam(X0))) & (nf(lam(X0)) | ~nf(X0)))),
0.14/0.44	  inference(nnf_transformation,[],[f41])).
0.14/0.44	fof(f41,plain,(
0.14/0.44	  ! [X0] : (nf(X0) <=> nf(lam(X0)))),
0.14/0.44	  inference(rectify,[],[f9])).
0.14/0.44	fof(f9,axiom,(
0.14/0.44	  ! [X8] : (nf(X8) <=> nf(lam(X8)))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f104,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (~nf(X1) | nf(app(X0,X1,X2)) | ~nf(X0) | lam(proj1Lam(X0)) = X0) )),
0.14/0.44	  inference(cnf_transformation,[],[f62])).
0.14/0.44	fof(f156,plain,(
0.14/0.44	  ( ! [X0] : (nf(lam(var(X0)))) )),
0.14/0.44	  inference(subsumption_resolution,[],[f147,f88])).
0.14/0.44	fof(f147,plain,(
0.14/0.44	  ( ! [X0,X1] : (nf(lam(var(X0))) | var(X1) = lam(proj1Lam(var(X1)))) )),
0.14/0.44	  inference(resolution,[],[f143,f103])).
0.14/0.44	fof(f143,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (nf(app(var(X0),lam(var(X1)),X2))) )),
0.14/0.44	  inference(resolution,[],[f140,f77])).
0.14/0.44	fof(f178,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (tc(X0,lam(lam(var(zero))),arr(X1,arr(X2,X2)))) )),
0.14/0.44	  inference(resolution,[],[f158,f89])).
0.14/0.44	fof(f89,plain,(
0.14/0.44	  ( ! [X2,X3,X0,X1] : (~tc(cons(X2,X0),X1,X3) | tc(X0,lam(X1),arr(X2,X3))) )),
0.14/0.44	  inference(cnf_transformation,[],[f60])).
0.14/0.44	fof(f60,plain,(
0.14/0.44	  ! [X0,X1,X2,X3] : ((tc(cons(X2,X0),X1,X3) | ~tc(X0,lam(X1),arr(X2,X3))) & (tc(X0,lam(X1),arr(X2,X3)) | ~tc(cons(X2,X0),X1,X3)))),
0.14/0.44	  inference(nnf_transformation,[],[f46])).
0.14/0.44	fof(f46,plain,(
0.14/0.44	  ! [X0,X1,X2,X3] : (tc(cons(X2,X0),X1,X3) <=> tc(X0,lam(X1),arr(X2,X3)))),
0.14/0.44	  inference(rectify,[],[f23])).
0.14/0.44	fof(f23,axiom,(
0.14/0.44	  ! [X0,X8,X12,X13] : (tc(cons(X12,X0),X8,X13) <=> tc(X0,lam(X8),arr(X12,X13)))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f158,plain,(
0.14/0.44	  ( ! [X0,X1] : (tc(X0,lam(var(zero)),arr(X1,X1))) )),
0.14/0.44	  inference(equality_resolution,[],[f141])).
0.14/0.44	fof(f141,plain,(
0.14/0.44	  ( ! [X2,X0,X1] : (just(X0) != just(X1) | tc(X2,lam(var(zero)),arr(X0,X1))) )),
0.14/0.44	  inference(superposition,[],[f117,f100])).
0.14/0.44	fof(f100,plain,(
0.14/0.44	  ( ! [X0,X1] : (just(X0) = index(cons(X0,X1),zero)) )),
0.14/0.44	  inference(cnf_transformation,[],[f49])).
0.14/0.44	fof(f49,plain,(
0.14/0.44	  ! [X0,X1] : just(X0) = index(cons(X0,X1),zero)),
0.14/0.44	  inference(rectify,[],[f34])).
0.14/0.44	fof(f34,axiom,(
0.14/0.44	  ! [X4,X6] : just(X4) = index(cons(X4,X6),zero)),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	fof(f117,plain,(
0.14/0.44	  ( ! [X2,X3,X0,X1] : (just(X3) != index(cons(X2,X0),X1) | tc(X0,lam(var(X1)),arr(X2,X3))) )),
0.14/0.44	  inference(resolution,[],[f89,f106])).
0.14/0.44	fof(f106,plain,(
0.14/0.44	  ( ! [X2,X3,X0] : (tc(X0,var(X2),X3) | index(X0,X2) != just(X3)) )),
0.14/0.44	  inference(equality_resolution,[],[f65])).
0.14/0.44	fof(f65,plain,(
0.14/0.44	  ( ! [X2,X3,X0,X1] : (tc(X0,var(X2),X1) | X1 != X3 | index(X0,X2) != just(X3)) )),
0.14/0.44	  inference(cnf_transformation,[],[f56])).
0.14/0.44	fof(f56,plain,(
0.14/0.44	  ! [X0,X1,X2,X3] : (((tc(X0,var(X2),X1) | X1 != X3) & (X1 = X3 | ~tc(X0,var(X2),X1))) | index(X0,X2) != just(X3))),
0.14/0.44	  inference(nnf_transformation,[],[f51])).
0.14/0.44	fof(f51,plain,(
0.14/0.44	  ! [X0,X1,X2,X3] : ((tc(X0,var(X2),X1) <=> X1 = X3) | index(X0,X2) != just(X3))),
0.14/0.44	  inference(ennf_transformation,[],[f38])).
0.14/0.44	fof(f38,plain,(
0.14/0.44	  ! [X0,X1,X2,X3] : (index(X0,X2) = just(X3) => (tc(X0,var(X2),X1) <=> X1 = X3))),
0.14/0.44	  inference(rectify,[],[f2])).
0.14/0.44	fof(f2,axiom,(
0.14/0.44	  ! [X0,X4,X2,X5] : (just(X5) = index(X0,X2) => (tc(X0,var(X2),X4) <=> X4 = X5))),
0.14/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.14/0.44	% SZS output end Proof for theBenchmark
0.14/0.44	% (985541)------------------------------
0.14/0.44	% (985541)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200)
0.14/0.44	% (985541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.14/0.44	% (985541)Termination reason: Refutation
0.14/0.44	
0.14/0.44	% (985541)Time elapsed: 0.006 s
0.14/0.44	% (985541)Peak memory usage: 12 MB
0.14/0.44	% (985541)Instructions burned: 16 (million)
0.14/0.44	% (985541)------------------------------
0.14/0.44	% (985541)------------------------------
0.14/0.44	% (985539)Success in time 0.059 s
0.14/0.45	EOF