0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : vampire --mode casc -t %d %s 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % DateTime : Thu Jul 2 06:54:36 EDT 2020 0.13/0.34 % CPUTime : 0.21/0.40 % ott+10_3:2_aac=none:add=large:afp=10000:afq=2.0:amm=off:fsr=off:fde=none:gs=on:gsaa=from_current:gsem=off:lcm=reverse:lma=on:nm=0:nwc=4:sas=z3:updr=off_22 on theBenchmark 0.21/0.49 % Refutation found. Thanks to Tanya! 0.21/0.49 % SZS status Theorem for theBenchmark 0.21/0.49 % SZS output start Proof for theBenchmark 0.21/0.49 tff(type_def_5, type, list: $tType). 0.21/0.49 tff(func_def_0, type, nil: list). 0.21/0.49 tff(func_def_1, type, cons: ($int * list) > list). 0.21/0.49 tff(func_def_2, type, head: list > $int). 0.21/0.49 tff(func_def_3, type, tail: list > list). 0.21/0.49 tff(func_def_4, type, length: list > $int). 0.21/0.49 tff(func_def_5, type, count: ($int * list) > $int). 0.21/0.49 tff(func_def_6, type, append: (list * list) > list). 0.21/0.49 tff(func_def_11, type, sK0: ($int * list) > $int). 0.21/0.49 tff(func_def_12, type, sK1: ($int * list) > list). 0.21/0.49 tff(func_def_13, type, sK2: ($int * list) > $int). 0.21/0.49 tff(func_def_14, type, sK3: ($int * list) > list). 0.21/0.49 tff(func_def_15, type, sK4: ($int * list) > $int). 0.21/0.49 tff(func_def_16, type, sK5: ($int * list) > list). 0.21/0.49 tff(pred_def_1, type, in: ($int * list) > $o). 0.21/0.49 tff(pred_def_2, type, inRange: ($int * list) > $o). 0.21/0.49 tff(f301,plain,( 0.21/0.49 $false), 0.21/0.49 inference(evaluation,[],[f300])). 0.21/0.49 tff(f300,plain,( 0.21/0.49 0 = -1), 0.21/0.49 inference(forward_demodulation,[],[f299,f64])). 0.21/0.49 tff(f64,plain,( 0.21/0.49 ( ! [X0:$int] : (count(X0,nil) = 0) )), 0.21/0.49 inference(cnf_transformation,[],[f6])). 0.21/0.49 tff(f6,axiom,( 0.21/0.49 ! [X0 : $int] : count(X0,nil) = 0), 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a)). 0.21/0.49 tff(f299,plain,( 0.21/0.49 ( ! [X0:$int] : (count(X0,nil) = -1) )), 0.21/0.49 inference(evaluation,[],[f282])). 0.21/0.49 tff(f282,plain,( 0.21/0.49 ( ! [X0:$int] : ($sum(1,count(X0,nil)) = 0) )), 0.21/0.49 inference(superposition,[],[f98,f154])). 0.21/0.49 tff(f154,plain,( 0.21/0.49 ( ! [X0:$int,X1:$int] : (count(X1,cons(X0,nil)) = 0) )), 0.21/0.49 inference(evaluation,[],[f153])). 0.21/0.49 tff(f153,plain,( 0.21/0.49 ( ! [X0:$int,X1:$int] : ($sum(1,0) = $sum(1,count(X1,cons(X0,nil)))) )), 0.21/0.49 inference(forward_demodulation,[],[f152,f64])). 0.21/0.49 tff(f152,plain,( 0.21/0.49 ( ! [X0:$int,X1:$int] : ($sum(1,count(X1,nil)) = $sum(1,count(X1,cons(X0,nil)))) )), 0.21/0.49 inference(superposition,[],[f138,f63])). 0.21/0.49 tff(f63,plain,( 0.21/0.49 ( ! [X0:list] : (append(nil,X0) = X0) )), 0.21/0.49 inference(cnf_transformation,[],[f33])). 0.21/0.49 tff(f33,plain,( 0.21/0.49 ! [X0 : list] : append(nil,X0) = X0), 0.21/0.49 inference(rectify,[],[f13])). 0.21/0.49 tff(f13,axiom,( 0.21/0.49 ! [X4 : list] : append(nil,X4) = X4), 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6)). 0.21/0.49 tff(f138,plain,( 0.21/0.49 ( ! [X2:list,X0:$int,X1:$int] : ($sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil))))) )), 0.21/0.49 inference(evaluation,[],[f137])). 0.21/0.49 tff(f137,plain,( 0.21/0.49 ( ! [X2:list,X0:$int,X1:$int] : ($less(0,0) | $sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil))))) )), 0.21/0.49 inference(superposition,[],[f128,f64])). 0.21/0.49 tff(f128,plain,( 0.21/0.49 ( ! [X4:$int,X2:$int,X5:list,X3:list] : ($less(0,count(X2,X3)) | $sum(1,count(X4,X5)) = $sum(1,count(X4,append(X5,cons(X2,X3))))) )), 0.21/0.49 inference(resolution,[],[f70,f102])). 0.21/0.49 tff(f102,plain,( 0.21/0.49 ( ! [X2:$int,X0:$int,X3:list,X1:list] : (in(X2,X3) | $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3))))) )), 0.21/0.49 inference(forward_demodulation,[],[f101,f98])). 0.21/0.49 tff(f101,plain,( 0.21/0.49 ( ! [X2:$int,X0:$int,X3:list,X1:list] : (count(X0,cons(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) | in(X2,X3)) )), 0.21/0.49 inference(forward_demodulation,[],[f100,f98])). 0.21/0.49 tff(f100,plain,( 0.21/0.49 ( ! [X2:$int,X0:$int,X3:list,X1:list] : (count(X0,cons(X0,X1)) = count(X0,cons(X0,append(X1,cons(X2,X3)))) | in(X2,X3)) )), 0.21/0.49 inference(forward_demodulation,[],[f99,f84])). 0.21/0.49 tff(f84,plain,( 0.21/0.49 ( ! [X2:list,X0:$int,X1:list] : (cons(X0,append(X1,X2)) = append(cons(X0,X1),X2)) )), 0.21/0.49 inference(cnf_transformation,[],[f42])). 0.21/0.49 tff(f42,plain,( 0.21/0.49 ! [X0 : $int,X1 : list,X2 : list] : cons(X0,append(X1,X2)) = append(cons(X0,X1),X2)), 0.21/0.49 inference(rectify,[],[f3])). 0.21/0.49 tff(f3,axiom,( 0.21/0.49 ! [X5 : $int,X0 : list,X4 : list] : cons(X5,append(X0,X4)) = append(cons(X5,X0),X4)), 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7)). 0.21/0.49 tff(f99,plain,( 0.21/0.49 ( ! [X2:$int,X0:$int,X3:list,X1:list] : (count(X0,cons(X0,X1)) = count(X0,append(cons(X0,X1),cons(X2,X3))) | in(X2,X3)) )), 0.21/0.49 inference(resolution,[],[f90,f87])). 0.21/0.49 tff(f87,plain,( 0.21/0.49 ( ! [X2:list,X0:$int,X3:list,X1:$int] : (~in(X1,X3) | count(X1,X3) = count(X1,append(X3,cons(X0,X2))) | in(X0,X2)) )), 0.21/0.49 inference(equality_resolution,[],[f61])). 0.21/0.49 tff(f61,plain,( 0.21/0.49 ( ! [X4:list,X2:list,X0:$int,X3:list,X1:$int] : (count(X1,X3) = count(X1,X4) | ~in(X1,X3) | append(X3,cons(X0,X2)) != X4 | in(X0,X2)) )), 0.21/0.49 inference(cnf_transformation,[],[f46])). 0.21/0.49 tff(f46,plain,( 0.21/0.49 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : (count(X1,X3) = count(X1,X4) | ~in(X1,X3) | append(X3,cons(X0,X2)) != X4 | in(X0,X2))), 0.21/0.49 inference(flattening,[],[f45])). 0.21/0.49 tff(f45,plain,( 0.21/0.49 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : (count(X1,X3) = count(X1,X4) | (~in(X1,X3) | append(X3,cons(X0,X2)) != X4 | in(X0,X2)))), 0.21/0.49 inference(ennf_transformation,[],[f32])). 0.21/0.49 tff(f32,plain,( 0.21/0.49 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : ((in(X1,X3) & append(X3,cons(X0,X2)) = X4 & ~in(X0,X2)) => count(X1,X3) = count(X1,X4))), 0.21/0.49 inference(flattening,[],[f31])). 0.21/0.49 tff(f31,plain,( 0.21/0.49 ~~! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : ((in(X1,X3) & append(X3,cons(X0,X2)) = X4 & ~in(X0,X2)) => count(X1,X3) = count(X1,X4))), 0.21/0.49 inference(rectify,[],[f12])). 0.21/0.49 tff(f12,negated_conjecture,( 0.21/0.49 ~~! [X7 : $int,X3 : $int,X0 : list,X4 : list,X8 : list] : ((in(X3,X4) & append(X4,cons(X7,X0)) = X8 & ~in(X7,X0)) => count(X3,X4) = count(X3,X8))), 0.21/0.49 inference(negated_conjecture,[],[f11])). 0.21/0.49 tff(f11,conjecture,( 0.21/0.49 ~! [X7 : $int,X3 : $int,X0 : list,X4 : list,X8 : list] : ((in(X3,X4) & append(X4,cons(X7,X0)) = X8 & ~in(X7,X0)) => count(X3,X4) = count(X3,X8))), 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',c)). 0.21/0.49 tff(f90,plain,( 0.21/0.49 ( ! [X4:$int,X5:list] : (in(X4,cons(X4,X5))) )), 0.21/0.49 inference(equality_resolution,[],[f89])). 0.21/0.49 tff(f89,plain,( 0.21/0.49 ( ! [X4:$int,X5:list,X1:list] : (in(X4,X1) | cons(X4,X5) != X1) )), 0.21/0.49 inference(equality_resolution,[],[f76])). 0.21/0.49 tff(f76,plain,( 0.21/0.49 ( ! [X4:$int,X0:$int,X5:list,X1:list] : (in(X0,X1) | X0 != X4 | cons(X4,X5) != X1) )), 0.21/0.49 inference(cnf_transformation,[],[f55])). 0.21/0.49 tff(f55,plain,( 0.21/0.49 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (~in(X0,X3) | cons(X2,X3) != X1) & ! [X4 : $int,X5 : list] : (X0 != X4 | cons(X4,X5) != X1))) & ((in(X0,sK1(X0,X1)) & cons(sK0(X0,X1),sK1(X0,X1)) = X1) | (sK2(X0,X1) = X0 & cons(sK2(X0,X1),sK3(X0,X1)) = X1) | ~in(X0,X1)))), 0.21/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f52,f54,f53])). 0.21/0.49 tff(f53,plain,( 0.21/0.49 ! [X1 : list,X0 : $int] : (? [X6 : $int,X7 : list] : (in(X0,X7) & cons(X6,X7) = X1) => (in(X0,sK1(X0,X1)) & cons(sK0(X0,X1),sK1(X0,X1)) = X1))), 0.21/0.49 introduced(choice_axiom,[])). 0.21/0.49 tff(f54,plain,( 0.21/0.49 ! [X1 : list,X0 : $int] : (? [X8 : $int,X9 : list] : (X0 = X8 & cons(X8,X9) = X1) => (sK2(X0,X1) = X0 & cons(sK2(X0,X1),sK3(X0,X1)) = X1))), 0.21/0.49 introduced(choice_axiom,[])). 0.21/0.50 tff(f52,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (~in(X0,X3) | cons(X2,X3) != X1) & ! [X4 : $int,X5 : list] : (X0 != X4 | cons(X4,X5) != X1))) & (? [X6 : $int,X7 : list] : (in(X0,X7) & cons(X6,X7) = X1) | ? [X8 : $int,X9 : list] : (X0 = X8 & cons(X8,X9) = X1) | ~in(X0,X1)))), 0.21/0.50 inference(rectify,[],[f51])). 0.21/0.50 tff(f51,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (~in(X0,X3) | cons(X2,X3) != X1) & ! [X4 : $int,X5 : list] : (X0 != X4 | cons(X4,X5) != X1))) & (? [X2 : $int,X3 : list] : (in(X0,X3) & cons(X2,X3) = X1) | ? [X4 : $int,X5 : list] : (X0 = X4 & cons(X4,X5) = X1) | ~in(X0,X1)))), 0.21/0.50 inference(flattening,[],[f50])). 0.21/0.50 tff(f50,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (~in(X0,X3) | cons(X2,X3) != X1) & ! [X4 : $int,X5 : list] : (X0 != X4 | cons(X4,X5) != X1))) & ((? [X2 : $int,X3 : list] : (in(X0,X3) & cons(X2,X3) = X1) | ? [X4 : $int,X5 : list] : (X0 = X4 & cons(X4,X5) = X1)) | ~in(X0,X1)))), 0.21/0.50 inference(nnf_transformation,[],[f40])). 0.21/0.50 tff(f40,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> (? [X2 : $int,X3 : list] : (in(X0,X3) & cons(X2,X3) = X1) | ? [X4 : $int,X5 : list] : (X0 = X4 & cons(X4,X5) = X1)))), 0.21/0.50 inference(rectify,[],[f10])). 0.21/0.50 tff(f10,axiom,( 0.21/0.50 ! [X6 : $int,X4 : list] : (in(X6,X4) <=> (? [X1 : $int,X2 : list] : (in(X6,X2) & cons(X1,X2) = X4) | ? [X1 : $int,X2 : list] : (X1 = X6 & cons(X1,X2) = X4)))), 0.21/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv)). 0.21/0.50 tff(f70,plain,( 0.21/0.50 ( ! [X0:$int,X1:list] : (~in(X0,X1) | $less(0,count(X0,X1))) )), 0.21/0.50 inference(cnf_transformation,[],[f49])). 0.21/0.50 tff(f49,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : ((in(X0,X1) | ~$less(0,count(X0,X1))) & ($less(0,count(X0,X1)) | ~in(X0,X1)))), 0.21/0.50 inference(nnf_transformation,[],[f39])). 0.21/0.50 tff(f39,plain,( 0.21/0.50 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> $less(0,count(X0,X1)))), 0.21/0.50 inference(rectify,[],[f17])). 0.21/0.50 tff(f17,plain,( 0.21/0.50 ! [X3 : $int,X4 : list] : (in(X3,X4) <=> $less(0,count(X3,X4)))), 0.21/0.50 inference(evaluation,[],[f2])). 0.21/0.50 tff(f2,axiom,( 0.21/0.50 ! [X3 : $int,X4 : list] : (in(X3,X4) <=> $greater(count(X3,X4),0))), 0.21/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8)). 0.21/0.50 tff(f98,plain,( 0.21/0.50 ( ! [X2:list,X1:$int] : (count(X1,cons(X1,X2)) = $sum(1,count(X1,X2))) )), 0.21/0.50 inference(forward_demodulation,[],[f93,f19])). 0.21/0.50 tff(f19,plain,( 0.21/0.50 ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )), 0.21/0.50 introduced(theory_axiom,[])). 0.21/0.50 tff(f93,plain,( 0.21/0.50 ( ! [X2:list,X1:$int] : (count(X1,cons(X1,X2)) = $sum(count(X1,X2),1)) )), 0.21/0.50 inference(equality_resolution,[],[f86])). 0.21/0.50 tff(f86,plain,( 0.21/0.50 ( ! [X2:list,X0:$int,X1:$int] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1) )), 0.21/0.50 inference(cnf_transformation,[],[f48])). 0.21/0.50 tff(f48,plain,( 0.21/0.50 ! [X0 : $int,X1 : $int,X2 : list] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1)), 0.21/0.50 inference(ennf_transformation,[],[f44])). 0.21/0.50 tff(f44,plain,( 0.21/0.50 ! [X0 : $int,X1 : $int,X2 : list] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))), 0.21/0.50 inference(rectify,[],[f1])). 0.21/0.50 tff(f1,axiom,( 0.21/0.50 ! [X0 : $int,X1 : $int,X2 : list,X3 : $int] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))), 0.21/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_4)). 0.21/0.50 % SZS output end Proof for theBenchmark 0.21/0.50 % ------------------------------ 0.21/0.50 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.21/0.50 % Termination reason: Refutation 0.21/0.50 0.21/0.50 % Memory used [KB]: 5373 0.21/0.50 % Time elapsed: 0.094 s 0.21/0.50 % ------------------------------ 0.21/0.50 % ------------------------------ 0.21/0.50 % Success in time 0.156 s 0.21/0.50 EOF