0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -t %d %s 0.03/0.23 % Computer : n176.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:20:25 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.27 % lrs+10_1_av=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=5.0:sos=on:sp=reverse_arity_2 on theBenchmark 0.06/0.28 % Refutation found. Thanks to Tanya! 0.06/0.28 % SZS status Theorem for theBenchmark 0.06/0.28 % SZS output start Proof for theBenchmark 0.06/0.28 fof(f17,axiom,( 0.06/0.28 ! [X4,X8] : ((leq(X4,X8) & X4 != X8) => gt(X8,X4))), 0.06/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2)). 0.06/0.28 fof(f43,axiom,( 0.06/0.28 ! [X4,X8] : (gt(X8,X4) <=> leq(X4,pred(X8)))), 0.06/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred)). 0.06/0.28 fof(f76,conjecture,( 0.06/0.28 (sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X0] : ((leq(n0,X0) & leq(X0,pred(pv12))) => a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) & ! [X20] : ((leq(n0,X20) & leq(X20,pred(pv10))) => n1 = sum(n0,n4,a_select3(q,X20,tptp_sum_index))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)) => ! [X10] : ((leq(X10,pv12) & leq(n0,X10)) => (pv12 != X10 => a_select3(q,pv10,X10) = divide(sqrt(times(minus(a_select3(center,X10,n0),a_select2(x,pv10)),minus(a_select3(center,X10,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))))), 0.06/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0003)). 0.06/0.28 fof(f77,negated_conjecture,( 0.06/0.28 ~((sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X0] : ((leq(n0,X0) & leq(X0,pred(pv12))) => a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) & ! [X20] : ((leq(n0,X20) & leq(X20,pred(pv10))) => n1 = sum(n0,n4,a_select3(q,X20,tptp_sum_index))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)) => ! [X10] : ((leq(X10,pv12) & leq(n0,X10)) => (pv12 != X10 => a_select3(q,pv10,X10) = divide(sqrt(times(minus(a_select3(center,X10,n0),a_select2(x,pv10)),minus(a_select3(center,X10,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))))), 0.06/0.28 inference(negated_conjecture,[],[f76])). 0.06/0.28 fof(f94,plain,( 0.06/0.28 ~((sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X0] : ((leq(n0,X0) & leq(X0,pred(pv12))) => a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) & ! [X1] : ((leq(n0,X1) & leq(X1,pred(pv10))) => n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)) => ! [X2] : ((leq(X2,pv12) & leq(n0,X2)) => (pv12 != X2 => a_select3(q,pv10,X2) = divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))))), 0.06/0.28 inference(rectify,[],[f77])). 0.06/0.28 fof(f101,plain,( 0.06/0.28 ! [X0,X1] : ((leq(X0,X1) & X0 != X1) => gt(X1,X0))), 0.06/0.28 inference(rectify,[],[f17])). 0.06/0.28 fof(f128,plain,( 0.06/0.28 ! [X0,X1] : (gt(X1,X0) <=> leq(X0,pred(X1)))), 0.06/0.28 inference(rectify,[],[f43])). 0.06/0.28 fof(f143,plain,( 0.06/0.28 ? [X2] : ((a_select3(q,pv10,X2) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != X2) & (leq(X2,pv12) & leq(n0,X2))) & (sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X0] : (a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) | (~leq(n0,X0) | ~leq(X0,pred(pv12)))) & ! [X1] : (n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) | (~leq(n0,X1) | ~leq(X1,pred(pv10)))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10))), 0.06/0.28 inference(ennf_transformation,[],[f94])). 0.06/0.28 fof(f144,plain,( 0.06/0.28 ? [X2] : (a_select3(q,pv10,X2) != divide(sqrt(times(minus(a_select3(center,X2,n0),a_select2(x,pv10)),minus(a_select3(center,X2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != X2 & leq(X2,pv12) & leq(n0,X2)) & sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X0] : (a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) | ~leq(n0,X0) | ~leq(X0,pred(pv12))) & ! [X1] : (n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) | ~leq(n0,X1) | ~leq(X1,pred(pv10))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)), 0.06/0.28 inference(flattening,[],[f143])). 0.06/0.28 fof(f152,plain,( 0.06/0.28 ! [X0,X1] : (gt(X1,X0) | (~leq(X0,X1) | X0 = X1))), 0.06/0.28 inference(ennf_transformation,[],[f101])). 0.06/0.28 fof(f153,plain,( 0.06/0.28 ! [X0,X1] : (gt(X1,X0) | ~leq(X0,X1) | X0 = X1)), 0.06/0.28 inference(flattening,[],[f152])). 0.06/0.28 fof(f192,plain,( 0.06/0.28 ? [X0] : (a_select3(q,pv10,X0) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != X0 & leq(X0,pv12) & leq(n0,X0)) & sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X1] : (a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) | ~leq(n0,X1) | ~leq(X1,pred(pv12))) & ! [X2] : (n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) | ~leq(n0,X2) | ~leq(X2,pred(pv10))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)), 0.06/0.28 inference(rectify,[],[f144])). 0.06/0.28 fof(f193,plain,( 0.06/0.28 ? [X0] : (a_select3(q,pv10,X0) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != X0 & leq(X0,pv12) & leq(n0,X0)) => (a_select3(q,pv10,sK2) != divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != sK2 & leq(sK2,pv12) & leq(n0,sK2))), 0.06/0.28 introduced(choice_axiom,[])). 0.06/0.28 fof(f194,plain,( 0.06/0.28 (a_select3(q,pv10,sK2) != divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) & pv12 != sK2 & leq(sK2,pv12) & leq(n0,sK2)) & sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 & leq(pv10,n135299) & ! [X1] : (a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) | ~leq(n0,X1) | ~leq(X1,pred(pv12))) & ! [X2] : (n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) | ~leq(n0,X2) | ~leq(X2,pred(pv10))) & leq(pv12,n4) & leq(n0,pv12) & leq(n0,pv10)), 0.06/0.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f192,f193])). 0.06/0.28 fof(f211,plain,( 0.06/0.28 ! [X0,X1] : ((gt(X1,X0) | ~leq(X0,pred(X1))) & (leq(X0,pred(X1)) | ~gt(X1,X0)))), 0.06/0.28 inference(nnf_transformation,[],[f128])). 0.06/0.28 fof(f229,plain,( 0.06/0.28 ( ! [X1] : (a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) | ~leq(n0,X1) | ~leq(X1,pred(pv12))) )), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f231,plain,( 0.06/0.28 sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f232,plain,( 0.06/0.28 leq(n0,sK2)), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f233,plain,( 0.06/0.28 leq(sK2,pv12)), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f234,plain,( 0.06/0.28 pv12 != sK2), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f235,plain,( 0.06/0.28 a_select3(q,pv10,sK2) != divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))), 0.06/0.28 inference(cnf_transformation,[],[f194])). 0.06/0.28 fof(f251,plain,( 0.06/0.28 ( ! [X0,X1] : (~leq(X0,X1) | gt(X1,X0) | X0 = X1) )), 0.06/0.28 inference(cnf_transformation,[],[f153])). 0.06/0.28 fof(f310,plain,( 0.06/0.28 ( ! [X0,X1] : (~gt(X1,X0) | leq(X0,pred(X1))) )), 0.06/0.28 inference(cnf_transformation,[],[f211])). 0.06/0.28 fof(f360,plain,( 0.06/0.28 a_select3(q,pv10,sK2) != divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),pv70)), 0.06/0.28 inference(backward_demodulation,[],[f231,f235])). 0.06/0.28 fof(f361,plain,( 0.06/0.28 ( ! [X1] : (~leq(X1,pred(pv12)) | ~leq(n0,X1) | a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),pv70)) )), 0.06/0.28 inference(forward_demodulation,[],[f229,f231])). 0.06/0.28 fof(f481,plain,( 0.06/0.28 gt(pv12,sK2) | pv12 = sK2), 0.06/0.28 inference(resolution,[],[f233,f251])). 0.06/0.28 fof(f483,plain,( 0.06/0.28 gt(pv12,sK2)), 0.06/0.28 inference(subsumption_resolution,[],[f481,f234])). 0.06/0.28 fof(f487,plain,( 0.06/0.28 leq(sK2,pred(pv12))), 0.06/0.28 inference(resolution,[],[f483,f310])). 0.06/0.28 fof(f493,plain,( 0.06/0.28 ~leq(n0,sK2) | a_select3(q,pv10,sK2) = divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),pv70)), 0.06/0.28 inference(resolution,[],[f361,f487])). 0.06/0.28 fof(f495,plain,( 0.06/0.28 a_select3(q,pv10,sK2) = divide(sqrt(times(minus(a_select3(center,sK2,n0),a_select2(x,pv10)),minus(a_select3(center,sK2,n0),a_select2(x,pv10)))),pv70)), 0.06/0.28 inference(subsumption_resolution,[],[f493,f232])). 0.06/0.28 fof(f496,plain,( 0.06/0.28 $false), 0.06/0.28 inference(subsumption_resolution,[],[f495,f360])). 0.06/0.28 % SZS output end Proof for theBenchmark 0.06/0.28 % ------------------------------ 0.06/0.28 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 0.06/0.28 % Termination reason: Refutation 0.06/0.28 0.06/0.28 % Memory used [KB]: 1151 0.06/0.28 % Time elapsed: 0.011 s 0.06/0.28 % ------------------------------ 0.06/0.28 % ------------------------------ 0.06/0.28 % Success in time 0.047 s 0.06/0.29 EOF