0.07/0.15 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s 0.12/0.36 % Computer : n028.cluster.edu 0.12/0.36 % Model : x86_64 x86_64 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.36 % Memory : 8042.1875MB 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.36 % CPULimit : 300 0.12/0.36 % WCLimit : 300 0.12/0.36 % DateTime : Fri Jul 5 04:23:54 EDT 2024 0.12/0.36 % CPUTime : 0.12/0.38 This is a TFF_ problem 0.12/0.38 Running vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.38 % (13244)Running in auto input_syntax mode. Trying TPTP 0.20/0.44 % (13251)lrs-1010_3_av=off:br=off:drc=off:er=known:fsd=off:fde=unused:nm=4:nwc=3.0:sp=scramble:urr=on:stl=180_280 on theBenchmark for (280ds/0Mi) 0.20/0.44 % (13247)dis-10_20_canc=force:fsd=off:gs=on:gsem=off:nm=0:sas=z3:sac=on:tha=off:thi=strong:tgt=ground_476 on theBenchmark for (476ds/0Mi) 0.20/0.44 % (13250)ott+10_1024_av=off:bd=preordered:br=off:ep=RSTC:fsr=off:fde=none:nm=2:urr=on_318 on theBenchmark for (318ds/0Mi) 0.20/0.44 % (13246)dis-1010_2:3_canc=force:fsd=off:fde=unused:gs=on:gsem=on:nm=0:nwc=1.3:sas=z3:tha=off:thf=on:uwa=ground_572 on theBenchmark for (572ds/0Mi) 0.20/0.44 % (13249)lrs+1010_2:1_amm=off:bs=on:bsr=on:canc=force:fsd=off:fsr=off:gs=on:gsaa=full_model:gsem=on:nm=0:nwc=1.3:sas=z3:sac=on:tha=off:thi=overlap:tgt=ground:uwa=ground:stl=60_408 on theBenchmark for (408ds/0Mi) 0.20/0.44 % (13248)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on theBenchmark for (472ds/0Mi) 0.20/0.44 % (13245)lrs+2_32_add=large:amm=off:bd=off:bs=unit_only:drc=off:flr=on:fsd=off:fde=none:nm=0:nwc=1.1:sos=theory:sp=reverse_arity:tgt=ground:stl=180_1034 on theBenchmark for (1034ds/0Mi) 3.96/0.99 % (13251)First to succeed. 3.96/0.99 % (13251)Refutation found. Thanks to Tanya! 3.96/0.99 % SZS status Theorem for theBenchmark 3.96/0.99 % SZS output start Proof for theBenchmark 3.96/0.99 tff(func_def_0, type, v0: ($int * $int * $int) > $int). 3.96/0.99 tff(func_def_1, type, u1: ($int * $int) > $int). 3.96/0.99 tff(func_def_2, type, w0: $int > $int). 3.96/0.99 tff(func_def_3, type, v1: $int > $int). 3.96/0.99 tff(func_def_4, type, g0: $int > $int). 3.96/0.99 tff(func_def_5, type, h1: $int > $int). 3.96/0.99 tff(func_def_6, type, i0: $int > $int). 3.96/0.99 tff(func_def_7, type, u0: ($int * $int * $int) > $int). 3.96/0.99 tff(func_def_8, type, f0: ($int * $int) > $int). 3.96/0.99 tff(func_def_9, type, h0: $int). 3.96/0.99 tff(func_def_10, type, g1: $int). 3.96/0.99 tff(func_def_11, type, j0: $int). 3.96/0.99 tff(func_def_12, type, fast: $int > $int). 3.96/0.99 tff(func_def_13, type, small: $int > $int). 3.96/0.99 tff(func_def_14, type, f1: $int > $int). 3.96/0.99 tff(func_def_22, type, sK0: $int). 3.96/0.99 tff(f24241,plain,( 3.96/0.99 $false), 3.96/0.99 inference(trivial_inequality_removal,[],[f24239])). 3.96/0.99 tff(f24239,plain,( 3.96/0.99 v1(sK0) != v1(sK0)), 3.96/0.99 inference(backward_demodulation,[],[f81,f24230])). 3.96/0.99 tff(f24230,plain,( 3.96/0.99 ( ! [X0 : $int] : (v1(X0) = small(X0)) )), 3.96/0.99 inference(forward_demodulation,[],[f24229,f1213])). 3.96/0.99 tff(f1213,plain,( 3.96/0.99 ( ! [X5 : $int] : (f0(1,X5) = X5) )), 3.96/0.99 inference(evaluation,[],[f1195])). 3.96/0.99 tff(f1195,plain,( 3.96/0.99 ( ! [X5 : $int] : (f0(1,X5) = $product(1,X5)) )), 3.96/0.99 inference(superposition,[],[f197,f35])). 3.96/0.99 tff(f35,plain,( 3.96/0.99 ( ! [X0 : $int] : ($product(X0,1) = X0) )), 3.96/0.99 introduced(theory_axiom_140,[])). 3.96/0.99 tff(f197,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X0,X1) = $product(X0,$product(X1,X0))) )), 3.96/0.99 inference(superposition,[],[f76,f33])). 3.96/0.99 tff(f33,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )), 3.96/0.99 introduced(theory_axiom_138,[])). 3.96/0.99 tff(f76,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X0,X1) = $product(X0,$product(X0,X1))) )), 3.96/0.99 inference(backward_demodulation,[],[f59,f34])). 3.96/0.99 tff(f34,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )), 3.96/0.99 introduced(theory_axiom_139,[])). 3.96/0.99 tff(f59,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X0,X1) = $product($product(X0,X0),X1)) )), 3.96/0.99 inference(cnf_transformation,[],[f13])). 3.96/0.99 tff(f13,axiom,( 3.96/0.99 ! [X0 : $int,X1 : $int] : f0(X0,X1) = $product($product(X0,X0),X1)), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_1)). 3.96/0.99 tff(f24229,plain,( 3.96/0.99 ( ! [X0 : $int] : (small(X0) = f0(1,v1(X0))) )), 3.96/0.99 inference(backward_demodulation,[],[f85,f24211])). 3.96/0.99 tff(f24211,plain,( 3.96/0.99 ( ! [X10 : $int,X11 : $int] : (u0(2,h1(X10),X11) = f0(X11,v1(X10))) )), 3.96/0.99 inference(superposition,[],[f24051,f744])). 3.96/0.99 tff(f744,plain,( 3.96/0.99 ( ! [X0 : $int] : (v1(X0) = f1(h1(X0))) )), 3.96/0.99 inference(backward_demodulation,[],[f72,f743])). 3.96/0.99 tff(f743,plain,( 3.96/0.99 ( ! [X0 : $int] : (f1(X0) = u1(1,X0)) )), 3.96/0.99 inference(forward_demodulation,[],[f742,f121])). 3.96/0.99 tff(f121,plain,( 3.96/0.99 ( ! [X0 : $int] : (u1(0,X0) = X0) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f27,f60])). 3.96/0.99 tff(f60,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u1(X0,X1) = X1 | $less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f41])). 3.96/0.99 tff(f41,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int] : ((u1(X0,X1) = f1(u1($sum(X0,$uminus(1)),X1)) | ~$less(0,X0)) & (u1(X0,X1) = X1 | $less(0,X0)))), 3.96/0.99 inference(ennf_transformation,[],[f19])). 3.96/0.99 tff(f19,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int] : (($less(0,X0) => u1(X0,X1) = f1(u1($sum(X0,$uminus(1)),X1))) & (~$less(0,X0) => u1(X0,X1) = X1))), 3.96/0.99 inference(theory_normalization,[],[f2])). 3.96/0.99 tff(f2,axiom,( 3.96/0.99 ! [X0 : $int,X1 : $int] : ((~$lesseq(X0,0) => u1(X0,X1) = f1(u1($difference(X0,1),X1))) & ($lesseq(X0,0) => u1(X0,X1) = X1))), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_13)). 3.96/0.99 tff(f27,plain,( 3.96/0.99 ( ! [X0 : $int] : (~$less(X0,X0)) )), 3.96/0.99 introduced(theory_axiom_145,[])). 3.96/0.99 tff(f742,plain,( 3.96/0.99 ( ! [X0 : $int] : (u1(1,X0) = f1(u1(0,X0))) )), 3.96/0.99 inference(evaluation,[],[f673])). 3.96/0.99 tff(f673,plain,( 3.96/0.99 ( ! [X0 : $int] : (u1($sum(0,1),X0) = f1(u1($sum($sum(0,1),-1),X0))) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f107,f69])). 3.96/0.99 tff(f69,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u1(X0,X1) = f1(u1($sum(X0,-1),X1)) | ~$less(0,X0)) )), 3.96/0.99 inference(evaluation,[],[f61])). 3.96/0.99 tff(f61,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u1(X0,X1) = f1(u1($sum(X0,$uminus(1)),X1)) | ~$less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f41])). 3.96/0.99 tff(f107,plain,( 3.96/0.99 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f27,f31])). 3.96/0.99 tff(f31,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )), 3.96/0.99 introduced(theory_axiom_150,[])). 3.96/0.99 tff(f72,plain,( 3.96/0.99 ( ! [X0 : $int] : (v1(X0) = u1(1,h1(X0))) )), 3.96/0.99 inference(forward_demodulation,[],[f54,f50])). 3.96/0.99 tff(f50,plain,( 3.96/0.99 1 = g1), 3.96/0.99 inference(cnf_transformation,[],[f15])). 3.96/0.99 tff(f15,axiom,( 3.96/0.99 1 = g1), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_11)). 3.96/0.99 tff(f54,plain,( 3.96/0.99 ( ! [X0 : $int] : (v1(X0) = u1(g1,h1(X0))) )), 3.96/0.99 inference(cnf_transformation,[],[f11])). 3.96/0.99 tff(f11,axiom,( 3.96/0.99 ! [X0 : $int] : v1(X0) = u1(g1,h1(X0))), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_14)). 3.96/0.99 tff(f24051,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X1,f1(X0)) = u0(2,X0,X1)) )), 3.96/0.99 inference(forward_demodulation,[],[f24050,f12859])). 3.96/0.99 tff(f12859,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(2,X0,X1) = f0(f0(X0,X1),X0)) )), 3.96/0.99 inference(forward_demodulation,[],[f12858,f748])). 3.96/0.99 tff(f748,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X0,X1) = u0(1,X0,X1)) )), 3.96/0.99 inference(forward_demodulation,[],[f747,f182])). 3.96/0.99 tff(f182,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(0,X0,X1) = X0) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f27,f65])). 3.96/0.99 tff(f65,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (u0(X0,X1,X2) = X1 | $less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f43])). 3.96/0.99 tff(f43,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : ((u0(X0,X1,X2) = X1 | $less(0,X0)) & (u0(X0,X1,X2) = f0(u0($sum(X0,$uminus(1)),X1,X2),v0($sum(X0,$uminus(1)),X1,X2)) | ~$less(0,X0)))), 3.96/0.99 inference(ennf_transformation,[],[f21])). 3.96/0.99 tff(f21,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : ((~$less(0,X0) => u0(X0,X1,X2) = X1) & ($less(0,X0) => u0(X0,X1,X2) = f0(u0($sum(X0,$uminus(1)),X1,X2),v0($sum(X0,$uminus(1)),X1,X2))))), 3.96/0.99 inference(theory_normalization,[],[f16])). 3.96/0.99 tff(f16,axiom,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : (($lesseq(X0,0) => u0(X0,X1,X2) = X1) & (~$lesseq(X0,0) => u0(X0,X1,X2) = f0(u0($difference(X0,1),X1,X2),v0($difference(X0,1),X1,X2))))), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6)). 3.96/0.99 tff(f747,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(1,X0,X1) = f0(u0(0,X0,X1),X1)) )), 3.96/0.99 inference(forward_demodulation,[],[f740,f175])). 3.96/0.99 tff(f175,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (v0(0,X0,X1) = X1) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f27,f63])). 3.96/0.99 tff(f63,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (v0(X0,X1,X2) = X2 | $less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f42])). 3.96/0.99 tff(f42,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : ((v0(X0,X1,X2) = X2 | $less(0,X0)) & (v0(X0,X1,X2) = g0(u0($sum(X0,$uminus(1)),X1,X2)) | ~$less(0,X0)))), 3.96/0.99 inference(ennf_transformation,[],[f20])). 3.96/0.99 tff(f20,plain,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : ((~$less(0,X0) => v0(X0,X1,X2) = X2) & ($less(0,X0) => v0(X0,X1,X2) = g0(u0($sum(X0,$uminus(1)),X1,X2))))), 3.96/0.99 inference(theory_normalization,[],[f4])). 3.96/0.99 tff(f4,axiom,( 3.96/0.99 ! [X0 : $int,X1 : $int,X2 : $int] : (($lesseq(X0,0) => v0(X0,X1,X2) = X2) & (~$lesseq(X0,0) => v0(X0,X1,X2) = g0(u0($difference(X0,1),X1,X2))))), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_7)). 3.96/0.99 tff(f740,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(1,X0,X1) = f0(u0(0,X0,X1),v0(0,X0,X1))) )), 3.96/0.99 inference(evaluation,[],[f671])). 3.96/0.99 tff(f671,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0($sum(0,1),X0,X1) = f0(u0($sum($sum(0,1),-1),X0,X1),v0($sum($sum(0,1),-1),X0,X1))) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f107,f67])). 3.96/0.99 tff(f67,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (u0(X0,X1,X2) = f0(u0($sum(X0,-1),X1,X2),v0($sum(X0,-1),X1,X2)) | ~$less(0,X0)) )), 3.96/0.99 inference(evaluation,[],[f64])). 3.96/0.99 tff(f64,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (u0(X0,X1,X2) = f0(u0($sum(X0,$uminus(1)),X1,X2),v0($sum(X0,$uminus(1)),X1,X2)) | ~$less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f43])). 3.96/0.99 tff(f12858,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(2,X0,X1) = f0(u0(1,X0,X1),X0)) )), 3.96/0.99 inference(forward_demodulation,[],[f12849,f746])). 3.96/0.99 tff(f746,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (v0(1,X0,X1) = X0) )), 3.96/0.99 inference(forward_demodulation,[],[f741,f182])). 3.96/0.99 tff(f741,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(0,X0,X1) = v0(1,X0,X1)) )), 3.96/0.99 inference(evaluation,[],[f672])). 3.96/0.99 tff(f672,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0($sum($sum(0,1),-1),X0,X1) = v0($sum(0,1),X0,X1)) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f107,f86])). 3.96/0.99 tff(f86,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (v0(X0,X1,X2) = u0($sum(X0,-1),X1,X2) | ~$less(0,X0)) )), 3.96/0.99 inference(forward_demodulation,[],[f68,f51])). 3.96/0.99 tff(f51,plain,( 3.96/0.99 ( ! [X0 : $int] : (g0(X0) = X0) )), 3.96/0.99 inference(cnf_transformation,[],[f8])). 3.96/0.99 tff(f8,axiom,( 3.96/0.99 ! [X0 : $int] : g0(X0) = X0), 3.96/0.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_2)). 3.96/0.99 tff(f68,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (v0(X0,X1,X2) = g0(u0($sum(X0,-1),X1,X2)) | ~$less(0,X0)) )), 3.96/0.99 inference(evaluation,[],[f62])). 3.96/0.99 tff(f62,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (v0(X0,X1,X2) = g0(u0($sum(X0,$uminus(1)),X1,X2)) | ~$less(0,X0)) )), 3.96/0.99 inference(cnf_transformation,[],[f42])). 3.96/0.99 tff(f12849,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0(2,X0,X1) = f0(u0(1,X0,X1),v0(1,X0,X1))) )), 3.96/0.99 inference(evaluation,[],[f12510])). 3.96/0.99 tff(f12510,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (u0($sum(2,0),X0,X1) = f0(u0($sum(-1,$sum(2,0)),X0,X1),v0($sum(-1,$sum(2,0)),X0,X1))) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f739,f563])). 3.96/0.99 tff(f563,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : (u0(X0,X1,X2) = f0(u0($sum(-1,X0),X1,X2),v0($sum(-1,X0),X1,X2)) | ~$less(0,X0)) )), 3.96/0.99 inference(superposition,[],[f67,f22])). 3.96/0.99 tff(f22,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )), 3.96/0.99 introduced(theory_axiom_138,[])). 3.96/0.99 tff(f739,plain,( 3.96/0.99 ( ! [X0 : $int] : ($less(X0,$sum(2,X0))) )), 3.96/0.99 inference(evaluation,[],[f668])). 3.96/0.99 tff(f668,plain,( 3.96/0.99 ( ! [X0 : $int] : ($less(X0,$sum($sum(X0,1),1))) )), 3.96/0.99 inference(unit_resulting_resolution,[],[f107,f107,f28])). 3.96/0.99 tff(f28,plain,( 3.96/0.99 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )), 3.96/0.99 introduced(theory_axiom_146,[])). 3.96/0.99 tff(f24050,plain,( 3.96/0.99 ( ! [X0 : $int,X1 : $int] : (f0(X1,f1(X0)) = f0(f0(X0,X1),X0)) )), 3.96/0.99 inference(backward_demodulation,[],[f3301,f24049])). 3.96/0.99 tff(f24049,plain,( 3.96/0.99 ( ! [X18 : $int,X19 : $int,X20 : $int] : (f0(f0(X18,X19),X20) = f0(X18,f0(X19,f0(X18,X20)))) )), 3.96/0.99 inference(forward_demodulation,[],[f24001,f1220])). 3.96/0.99 tff(f1220,plain,( 3.96/0.99 ( ! [X10 : $int,X8 : $int,X9 : $int] : (f0($product(X8,X9),X10) = f0(X8,f0(X9,X10))) )), 3.96/0.99 inference(forward_demodulation,[],[f1219,f197])). 3.96/0.99 tff(f1219,plain,( 3.96/0.99 ( ! [X10 : $int,X8 : $int,X9 : $int] : (f0($product(X8,X9),X10) = $product(X8,$product(f0(X9,X10),X8))) )), 3.96/0.99 inference(forward_demodulation,[],[f1203,f1217])). 3.96/0.99 tff(f1217,plain,( 3.96/0.99 ( ! [X14 : $int,X12 : $int,X13 : $int] : ($product(X14,$product(X12,$product(X13,X14))) = $product(f0(X14,X12),X13)) )), 3.96/0.99 inference(forward_demodulation,[],[f1200,f372])). 3.96/0.99 tff(f372,plain,( 3.96/0.99 ( ! [X10 : $int,X11 : $int,X12 : $int] : ($product(f0(X10,X11),X12) = f0(X10,$product(X11,X12))) )), 3.96/1.00 inference(forward_demodulation,[],[f371,f76])). 3.96/1.00 tff(f371,plain,( 3.96/1.00 ( ! [X10 : $int,X11 : $int,X12 : $int] : ($product(f0(X10,X11),X12) = $product(X10,$product(X10,$product(X11,X12)))) )), 3.96/1.00 inference(forward_demodulation,[],[f353,f34])). 3.96/1.00 tff(f353,plain,( 3.96/1.00 ( ! [X10 : $int,X11 : $int,X12 : $int] : ($product(X10,$product($product(X10,X11),X12)) = $product(f0(X10,X11),X12)) )), 3.96/1.00 inference(superposition,[],[f34,f76])). 3.96/1.00 tff(f1200,plain,( 3.96/1.00 ( ! [X14 : $int,X12 : $int,X13 : $int] : (f0(X14,$product(X12,X13)) = $product(X14,$product(X12,$product(X13,X14)))) )), 3.96/1.00 inference(superposition,[],[f197,f34])). 3.96/1.00 tff(f1203,plain,( 3.96/1.00 ( ! [X10 : $int,X8 : $int,X9 : $int] : ($product(X8,$product(X9,$product(X10,$product(X8,X9)))) = f0($product(X8,X9),X10)) )), 3.96/1.00 inference(superposition,[],[f197,f34])). 3.96/1.00 tff(f24001,plain,( 3.96/1.00 ( ! [X18 : $int,X19 : $int,X20 : $int] : (f0(X18,f0($product(X19,X18),X20)) = f0(f0(X18,X19),X20)) )), 3.96/1.00 inference(superposition,[],[f1220,f197])). 3.96/1.00 tff(f3301,plain,( 3.96/1.00 ( ! [X0 : $int,X1 : $int] : (f0(X0,f0(X1,f0(X0,X0))) = f0(X1,f1(X0))) )), 3.96/1.00 inference(superposition,[],[f2581,f80])). 3.96/1.00 tff(f80,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = f0(X0,f0(X0,X0))) )), 3.96/1.00 inference(forward_demodulation,[],[f79,f76])). 3.96/1.00 tff(f79,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = $product(X0,$product(X0,f0(X0,X0)))) )), 3.96/1.00 inference(forward_demodulation,[],[f78,f34])). 3.96/1.00 tff(f78,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = $product($product(X0,X0),f0(X0,X0))) )), 3.96/1.00 inference(backward_demodulation,[],[f77,f33])). 3.96/1.00 tff(f77,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = $product(f0(X0,X0),$product(X0,X0))) )), 3.96/1.00 inference(backward_demodulation,[],[f75,f34])). 3.96/1.00 tff(f75,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = $product($product(f0(X0,X0),X0),X0)) )), 3.96/1.00 inference(backward_demodulation,[],[f56,f59])). 3.96/1.00 tff(f56,plain,( 3.96/1.00 ( ! [X0 : $int] : (f1(X0) = $product($product($product($product(X0,X0),X0),X0),X0)) )), 3.96/1.00 inference(cnf_transformation,[],[f6])). 3.96/1.00 tff(f6,axiom,( 3.96/1.00 ! [X0 : $int] : f1(X0) = $product($product($product($product(X0,X0),X0),X0),X0)), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_10)). 3.96/1.00 tff(f2581,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0(X13,f0(X14,X15)) = f0(X14,f0(X13,X15))) )), 3.96/1.00 inference(forward_demodulation,[],[f2576,f76])). 3.96/1.00 tff(f2576,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0(X13,f0(X14,X15)) = $product(X14,$product(X14,f0(X13,X15)))) )), 3.96/1.00 inference(backward_demodulation,[],[f1227,f2574])). 3.96/1.00 tff(f2574,plain,( 3.96/1.00 ( ! [X14 : $int,X12 : $int,X13 : $int] : ($product(X14,f0(X12,X13)) = $product(f0(X12,X14),X13)) )), 3.96/1.00 inference(forward_demodulation,[],[f2497,f1225])). 3.96/1.00 tff(f1225,plain,( 3.96/1.00 ( ! [X6 : $int,X7 : $int,X5 : $int] : ($product(f0(X5,X6),X7) = $product(X5,$product(X6,$product(X5,X7)))) )), 3.96/1.00 inference(forward_demodulation,[],[f1204,f34])). 3.96/1.00 tff(f1204,plain,( 3.96/1.00 ( ! [X6 : $int,X7 : $int,X5 : $int] : ($product(X5,$product($product(X6,X5),X7)) = $product(f0(X5,X6),X7)) )), 3.96/1.00 inference(superposition,[],[f34,f197])). 3.96/1.00 tff(f2497,plain,( 3.96/1.00 ( ! [X14 : $int,X12 : $int,X13 : $int] : ($product(X14,f0(X12,X13)) = $product(X12,$product(X14,$product(X12,X13)))) )), 3.96/1.00 inference(superposition,[],[f368,f76])). 3.96/1.00 tff(f368,plain,( 3.96/1.00 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product(X1,$product(X0,X2))) )), 3.96/1.00 inference(forward_demodulation,[],[f349,f34])). 3.96/1.00 tff(f349,plain,( 3.96/1.00 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X1,X0),X2)) )), 3.96/1.00 inference(superposition,[],[f34,f33])). 3.96/1.00 tff(f1227,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0(X13,f0(X14,X15)) = $product(X14,$product(f0(X13,X14),X15))) )), 3.96/1.00 inference(forward_demodulation,[],[f1226,f368])). 3.96/1.00 tff(f1226,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0(X13,f0(X14,X15)) = $product(f0(X13,X14),$product(X14,X15))) )), 3.96/1.00 inference(backward_demodulation,[],[f1223,f1225])). 3.96/1.00 tff(f1223,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : ($product(X13,$product(X14,$product(X13,$product(X14,X15)))) = f0(X13,f0(X14,X15))) )), 3.96/1.00 inference(backward_demodulation,[],[f378,f1220])). 3.96/1.00 tff(f378,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0($product(X13,X14),X15) = $product(X13,$product(X14,$product(X13,$product(X14,X15))))) )), 3.96/1.00 inference(forward_demodulation,[],[f361,f34])). 3.96/1.00 tff(f361,plain,( 3.96/1.00 ( ! [X14 : $int,X15 : $int,X13 : $int] : (f0($product(X13,X14),X15) = $product(X13,$product(X14,$product($product(X13,X14),X15)))) )), 3.96/1.00 inference(superposition,[],[f34,f76])). 3.96/1.00 tff(f85,plain,( 3.96/1.00 ( ! [X0 : $int] : (small(X0) = u0(2,h1(X0),1)) )), 3.96/1.00 inference(forward_demodulation,[],[f84,f52])). 3.96/1.00 tff(f52,plain,( 3.96/1.00 ( ! [X0 : $int] : (w0(X0) = small(X0)) )), 3.96/1.00 inference(cnf_transformation,[],[f17])). 3.96/1.00 tff(f17,axiom,( 3.96/1.00 ! [X0 : $int] : w0(X0) = small(X0)), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_9)). 3.96/1.00 tff(f84,plain,( 3.96/1.00 ( ! [X0 : $int] : (w0(X0) = u0(2,h1(X0),1)) )), 3.96/1.00 inference(forward_demodulation,[],[f83,f48])). 3.96/1.00 tff(f48,plain,( 3.96/1.00 h0 = 2), 3.96/1.00 inference(cnf_transformation,[],[f5])). 3.96/1.00 tff(f5,axiom,( 3.96/1.00 h0 = 2), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_3)). 3.96/1.00 tff(f83,plain,( 3.96/1.00 ( ! [X0 : $int] : (w0(X0) = u0(h0,h1(X0),1)) )), 3.96/1.00 inference(forward_demodulation,[],[f82,f73])). 3.96/1.00 tff(f73,plain,( 3.96/1.00 ( ! [X0 : $int] : (i0(X0) = h1(X0)) )), 3.96/1.00 inference(forward_demodulation,[],[f70,f71])). 3.96/1.00 tff(f71,plain,( 3.96/1.00 ( ! [X0 : $int] : (i0(X0) = $product(5,$sum(1,$sum(X0,X0)))) )), 3.96/1.00 inference(evaluation,[],[f57])). 3.96/1.00 tff(f57,plain,( 3.96/1.00 ( ! [X0 : $int] : (i0(X0) = $product($sum(1,$sum(2,2)),$sum(1,$sum(X0,X0)))) )), 3.96/1.00 inference(cnf_transformation,[],[f12])). 3.96/1.00 tff(f12,axiom,( 3.96/1.00 ! [X0 : $int] : i0(X0) = $product($sum(1,$sum(2,2)),$sum(1,$sum(X0,X0)))), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_4)). 3.96/1.00 tff(f70,plain,( 3.96/1.00 ( ! [X0 : $int] : (h1(X0) = $product(5,$sum(1,$sum(X0,X0)))) )), 3.96/1.00 inference(evaluation,[],[f58])). 3.96/1.00 tff(f58,plain,( 3.96/1.00 ( ! [X0 : $int] : (h1(X0) = $product($sum(1,$sum(2,2)),$sum(1,$sum(X0,X0)))) )), 3.96/1.00 inference(cnf_transformation,[],[f14])). 3.96/1.00 tff(f14,axiom,( 3.96/1.00 ! [X0 : $int] : h1(X0) = $product($sum(1,$sum(2,2)),$sum(1,$sum(X0,X0)))), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_12)). 3.96/1.00 tff(f82,plain,( 3.96/1.00 ( ! [X0 : $int] : (w0(X0) = u0(h0,i0(X0),1)) )), 3.96/1.00 inference(forward_demodulation,[],[f55,f49])). 3.96/1.00 tff(f49,plain,( 3.96/1.00 j0 = 1), 3.96/1.00 inference(cnf_transformation,[],[f1])). 3.96/1.00 tff(f1,axiom,( 3.96/1.00 j0 = 1), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5)). 3.96/1.00 tff(f55,plain,( 3.96/1.00 ( ! [X0 : $int] : (w0(X0) = u0(h0,i0(X0),j0)) )), 3.96/1.00 inference(cnf_transformation,[],[f3])). 3.96/1.00 tff(f3,axiom,( 3.96/1.00 ! [X0 : $int] : w0(X0) = u0(h0,i0(X0),j0)), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_8)). 3.96/1.00 tff(f81,plain,( 3.96/1.00 small(sK0) != v1(sK0)), 3.96/1.00 inference(forward_demodulation,[],[f47,f53])). 3.96/1.00 tff(f53,plain,( 3.96/1.00 ( ! [X0 : $int] : (fast(X0) = v1(X0)) )), 3.96/1.00 inference(cnf_transformation,[],[f7])). 3.96/1.00 tff(f7,axiom,( 3.96/1.00 ! [X0 : $int] : fast(X0) = v1(X0)), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_15)). 3.96/1.00 tff(f47,plain,( 3.96/1.00 fast(sK0) != small(sK0)), 3.96/1.00 inference(cnf_transformation,[],[f45])). 3.96/1.00 tff(f45,plain,( 3.96/1.00 fast(sK0) != small(sK0) & ~$less(sK0,0)), 3.96/1.00 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f44])). 3.96/1.00 tff(f44,plain,( 3.96/1.00 ? [X0 : $int] : (fast(X0) != small(X0) & ~$less(X0,0)) => (fast(sK0) != small(sK0) & ~$less(sK0,0))), 3.96/1.00 introduced(choice_axiom,[])). 3.96/1.00 tff(f40,plain,( 3.96/1.00 ? [X0 : $int] : (fast(X0) != small(X0) & ~$less(X0,0))), 3.96/1.00 inference(rectify,[],[f18])). 3.96/1.00 tff(f18,plain,( 3.96/1.00 ? [X3 : $int] : (small(X3) != fast(X3) & ~$less(X3,0))), 3.96/1.00 inference(theory_normalization,[],[f10])). 3.96/1.00 tff(f10,negated_conjecture,( 3.96/1.00 ~~? [X3 : $int] : (small(X3) != fast(X3) & $greatereq(X3,0))), 3.96/1.00 inference(negated_conjecture,[],[f9])). 3.96/1.00 tff(f9,conjecture,( 3.96/1.00 ~? [X3 : $int] : (small(X3) != fast(X3) & $greatereq(X3,0))), 3.96/1.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1)). 3.96/1.00 % SZS output end Proof for theBenchmark 3.96/1.00 % (13251)------------------------------ 3.96/1.00 % (13251)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100) 3.96/1.00 % (13251)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 3.96/1.00 % (13251)Termination reason: Refutation 3.96/1.00 3.96/1.00 % (13251)Memory used [KB]: 13432 3.96/1.00 % (13251)Time elapsed: 0.556 s 3.96/1.00 % (13251)------------------------------ 3.96/1.00 % (13251)------------------------------ 3.96/1.00 % (13244)Success in time 0.586 s 3.96/1.00 % Vampire---4.8 exiting 3.96/1.00 EOF