0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -m 90000 -t %d %s 0.03/0.25 % Computer : n162.star.cs.uiowa.edu 0.03/0.25 % Model : x86_64 x86_64 0.03/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.25 % Memory : 32218.625MB 0.03/0.25 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.25 % CPULimit : 300 0.03/0.25 % DateTime : Sat Jul 14 04:17:55 CDT 2018 0.03/0.25 % CPUTime : 0.03/0.26 Hi Geoff, go and have some cold beer while I am trying to solve this very hard problem! 0.03/0.26 % remaining time: 3000 next slice time: 3 0.03/0.29 dis+1002_4_gs=on:inst=on:nm=64:nwc=1.3:sas=z3:sac=on:sfr=on:smm=off:ssnc=none:sp=occurrence:tha=off:thf=on:updr=off_1 on theBenchmark 0.07/0.33 % Refutation found. Thanks to Tanya! 0.07/0.33 % SZS status Theorem for theBenchmark 0.07/0.33 % SZS output start Proof for theBenchmark 0.07/0.33 tff(func_def_0, type, x: $int). 0.07/0.33 tff(func_def_1, type, y: $int). 0.07/0.33 tff(func_def_2, type, a: $int). 0.07/0.33 tff(func_def_3, type, z: $int). 0.07/0.33 tff(func_def_4, type, b: $int). 0.07/0.33 tff(f1,conjecture,( 0.07/0.33 1 = $product($product(z,y),x)), 0.07/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)). 0.07/0.33 tff(f2,negated_conjecture,( 0.07/0.33 ~1 = $product($product(z,y),x)), 0.07/0.33 inference(negated_conjecture,[],[f1])). 0.07/0.33 tff(f4,axiom,( 0.07/0.33 a = $product(x,y)), 0.07/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1)). 0.07/0.33 tff(f5,axiom,( 0.07/0.33 1 = $product(a,z)), 0.07/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq3)). 0.07/0.33 tff(f6,plain,( 0.07/0.33 1 != $product($product(z,y),x)), 0.07/0.33 inference(flattening,[],[f2])). 0.07/0.33 tff(f7,plain,( 0.07/0.33 1 != $product($product(z,y),x)), 0.07/0.33 inference(cnf_transformation,[],[f6])). 0.07/0.33 tff(f9,plain,( 0.07/0.33 a = $product(x,y)), 0.07/0.33 inference(cnf_transformation,[],[f4])). 0.07/0.33 tff(f10,plain,( 0.07/0.33 1 = $product(a,z)), 0.07/0.33 inference(cnf_transformation,[],[f5])). 0.07/0.33 tff(f11,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int,X1:$int] : (1 != $product($product(X1,X2),X3) | y != X2 | x != X3 | z != X1) )), 0.07/0.33 inference(theory_flattening,[],[f7])). 0.07/0.33 tff(f13,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int,X1:$int] : ($product(X2,X3) = X1 | x != X2 | y != X3 | a != X1) )), 0.07/0.33 inference(theory_flattening,[],[f9])). 0.07/0.33 tff(f14,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 = $product(X1,X2) | z != X2 | a != X1) )), 0.07/0.33 inference(theory_flattening,[],[f10])). 0.07/0.33 tff(f27,plain,( 0.07/0.33 1 = $product(a,z) | z != z | a != a), 0.07/0.33 inference(Instantiation,[],[f14])). 0.07/0.33 tff(f28,plain,( 0.07/0.33 1 = $product(a,a) | a != z | a != a), 0.07/0.33 inference(Instantiation,[],[f14])). 0.07/0.33 tff(f29,plain,( 0.07/0.33 1 = $product(a,a) | a != z), 0.07/0.33 inference(trivial_inequality_removal,[],[f28])). 0.07/0.33 tff(f30,plain,( 0.07/0.33 1 = $product(a,z)), 0.07/0.33 inference(trivial_inequality_removal,[],[f27])). 0.07/0.33 tff(f72,plain,( 0.07/0.33 spl0_0 <=> 1 = $product(a,z)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_0])])). 0.07/0.33 tff(f74,plain,( 0.07/0.33 spl0_0), 0.07/0.33 inference(AVATAR_split_clause,[],[f30,f72])). 0.07/0.33 tff(f77,plain,( 0.07/0.33 spl0_2 <=> a = z), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_2])])). 0.07/0.33 tff(f78,plain,( 0.07/0.33 a = z | ~spl0_2), 0.07/0.33 inference(AVATAR_component_clause,[],[f77])). 0.07/0.33 tff(f80,plain,( 0.07/0.33 spl0_3 <=> a != z), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_3])])). 0.07/0.33 tff(f86,plain,( 0.07/0.33 spl0_4 <=> 1 = $product(a,a)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_4])])). 0.07/0.33 tff(f87,plain,( 0.07/0.33 1 = $product(a,a) | ~spl0_4), 0.07/0.33 inference(AVATAR_component_clause,[],[f86])). 0.07/0.33 tff(f88,plain,( 0.07/0.33 ~spl0_3 | spl0_4), 0.07/0.33 inference(AVATAR_split_clause,[],[f29,f86,f80])). 0.07/0.33 tff(f90,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int,X1:$int] : (1 != $product($product(X1,X2),X3) | a != X1 | y != X2 | x != X3) ) | ~spl0_2), 0.07/0.33 inference(backward_demodulation,[],[f78,f11])). 0.07/0.33 tff(f91,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 = $product(X1,X2) | a != X2 | a != X1) ) | ~spl0_2), 0.07/0.33 inference(backward_demodulation,[],[f78,f14])). 0.07/0.33 tff(f103,plain,( 0.07/0.33 1 = $product(a,1) | a != 1 | a != a | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f91])). 0.07/0.33 tff(f109,plain,( 0.07/0.33 1 = $product(a,1) | a != 1 | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f103])). 0.07/0.33 tff(f123,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : (1 != $product($product(X1,y),X3) | a != X1 | y != y | x != X3) ) | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f90])). 0.07/0.33 tff(f124,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 != $product($product(a,X2),X3) | a != a | y != X2 | x != X3) ) | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f90])). 0.07/0.33 tff(f132,plain,( 0.07/0.33 1 != $product($product(a,y),b) | a != a | y != y | x != b | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f90])). 0.07/0.33 tff(f140,plain,( 0.07/0.33 1 != $product($product(a,a),1) | a != a | y != a | x != 1 | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f90])). 0.07/0.33 tff(f145,plain,( 0.07/0.33 1 != $product($product(a,a),1) | y != a | x != 1 | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f140])). 0.07/0.33 tff(f153,plain,( 0.07/0.33 1 != $product($product(a,y),b) | x != b | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f132])). 0.07/0.33 tff(f156,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 != $product($product(a,X2),X3) | y != X2 | x != X3) ) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f124])). 0.07/0.33 tff(f157,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : (1 != $product($product(X1,y),X3) | a != X1 | x != X3) ) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f123])). 0.07/0.33 tff(f169,plain,( 0.07/0.33 1 != $product(1,1) | y != a | x != 1 | (~spl0_2 | ~spl0_4)), 0.07/0.33 inference(forward_demodulation,[],[f145,f87])). 0.07/0.33 tff(f170,plain,( 0.07/0.33 y != a | x != 1 | (~spl0_2 | ~spl0_4)), 0.07/0.33 inference(evaluation,[],[f169])). 0.07/0.33 tff(f179,plain,( 0.07/0.33 spl0_7 <=> x != 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_7])])). 0.07/0.33 tff(f185,plain,( 0.07/0.33 spl0_9 <=> y != a), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_9])])). 0.07/0.33 tff(f186,plain,( 0.07/0.33 y != a | ~spl0_9), 0.07/0.33 inference(AVATAR_component_clause,[],[f185])). 0.07/0.33 tff(f187,plain,( 0.07/0.33 ~spl0_7 | ~spl0_9 | ~spl0_2 | ~spl0_4), 0.07/0.33 inference(AVATAR_split_clause,[],[f170,f86,f77,f185,f179])). 0.07/0.33 tff(f193,plain,( 0.07/0.33 spl0_11 <=> x != b), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_11])])). 0.07/0.33 tff(f199,plain,( 0.07/0.33 spl0_13 <=> 1 != $product($product(a,y),b)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_13])])). 0.07/0.33 tff(f200,plain,( 0.07/0.33 1 != $product($product(a,y),b) | ~spl0_13), 0.07/0.33 inference(AVATAR_component_clause,[],[f199])). 0.07/0.33 tff(f201,plain,( 0.07/0.33 ~spl0_11 | ~spl0_13 | ~spl0_2), 0.07/0.33 inference(AVATAR_split_clause,[],[f153,f77,f199,f193])). 0.07/0.33 tff(f203,plain,( 0.07/0.33 1 != 1 | a != b | a != $product(a,y) | (~spl0_2 | ~spl0_13)), 0.07/0.33 inference(superposition,[],[f200,f91])). 0.07/0.33 tff(f204,plain,( 0.07/0.33 a != b | a != $product(a,y) | (~spl0_2 | ~spl0_13)), 0.07/0.33 inference(trivial_inequality_removal,[],[f203])). 0.07/0.33 tff(f210,plain,( 0.07/0.33 spl0_15 <=> a != $product(a,y)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_15])])). 0.07/0.33 tff(f211,plain,( 0.07/0.33 a != $product(a,y) | ~spl0_15), 0.07/0.33 inference(AVATAR_component_clause,[],[f210])). 0.07/0.33 tff(f216,plain,( 0.07/0.33 spl0_17 <=> a != b), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_17])])). 0.07/0.33 tff(f217,plain,( 0.07/0.33 a != b | ~spl0_17), 0.07/0.33 inference(AVATAR_component_clause,[],[f216])). 0.07/0.33 tff(f218,plain,( 0.07/0.33 ~spl0_15 | ~spl0_17 | ~spl0_2 | spl0_13), 0.07/0.33 inference(AVATAR_split_clause,[],[f204,f199,f77,f216,f210])). 0.07/0.33 tff(f237,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : ($product(x,X3) = X1 | x != x | y != X3 | a != X1) )), 0.07/0.33 inference(Instantiation,[],[f13])). 0.07/0.33 tff(f270,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : ($product(x,X3) = X1 | y != X3 | a != X1) )), 0.07/0.33 inference(trivial_inequality_removal,[],[f237])). 0.07/0.33 tff(f282,plain,( 0.07/0.33 ( ! [X0:$int] : (a != X0 | x != a | y != y | a != X0) ) | ~spl0_15), 0.07/0.33 inference(superposition,[],[f211,f13])). 0.07/0.33 tff(f285,plain,( 0.07/0.33 ( ! [X0:$int] : (a != X0 | x != a | y != y) ) | ~spl0_15), 0.07/0.33 inference(duplicate_literal_removal,[],[f282])). 0.07/0.33 tff(f286,plain,( 0.07/0.33 ( ! [X0:$int] : (a != X0 | x != a) ) | ~spl0_15), 0.07/0.33 inference(trivial_inequality_removal,[],[f285])). 0.07/0.33 tff(f291,plain,( 0.07/0.33 spl0_19 <=> x != a), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_19])])). 0.07/0.33 tff(f294,plain,( 0.07/0.33 spl0_20 <=> ! [X0 : $int] : a != X0), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_20])])). 0.07/0.33 tff(f296,plain,( 0.07/0.33 ~spl0_19 | spl0_20 | spl0_15), 0.07/0.33 inference(AVATAR_split_clause,[],[f286,f210,f294,f291])). 0.07/0.33 tff(f373,plain,( 0.07/0.33 spl0_22 <=> a = 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_22])])). 0.07/0.33 tff(f374,plain,( 0.07/0.33 a = 1 | ~spl0_22), 0.07/0.33 inference(AVATAR_component_clause,[],[f373])). 0.07/0.33 tff(f376,plain,( 0.07/0.33 spl0_23 <=> a != 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_23])])). 0.07/0.33 tff(f382,plain,( 0.07/0.33 spl0_24 <=> 1 = $product(a,1)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_24])])). 0.07/0.33 tff(f384,plain,( 0.07/0.33 ~spl0_23 | spl0_24 | ~spl0_2), 0.07/0.33 inference(AVATAR_split_clause,[],[f109,f77,f382,f376])). 0.07/0.33 tff(f385,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int,X1:$int] : ($product(X2,X3) = X1 | 1 != X1 | x != X2 | y != X3) ) | ~spl0_22), 0.07/0.33 inference(backward_demodulation,[],[f374,f13])). 0.07/0.33 tff(f386,plain,( 0.07/0.33 z = 1 | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f78])). 0.07/0.33 tff(f388,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int,X1:$int] : (1 != $product($product(X1,X2),X3) | 1 != X1 | y != X2 | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f90])). 0.07/0.33 tff(f389,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 != X1 | 1 = $product(X1,X2) | a != X2) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f91])). 0.07/0.33 tff(f390,plain,( 0.07/0.33 y != 1 | (~spl0_9 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f186])). 0.07/0.33 tff(f392,plain,( 0.07/0.33 1 != $product($product(1,y),b) | (~spl0_13 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f200])). 0.07/0.33 tff(f393,plain,( 0.07/0.33 1 != $product(1,y) | (~spl0_15 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f211])). 0.07/0.33 tff(f394,plain,( 0.07/0.33 b != 1 | (~spl0_17 | ~spl0_22)), 0.07/0.33 inference(backward_demodulation,[],[f374,f217])). 0.07/0.33 tff(f396,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 = $product(X1,X2) | 1 != X1 | 1 != X2) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(forward_demodulation,[],[f389,f374])). 0.07/0.33 tff(f398,plain,( 0.07/0.33 ( ! [X2:$int] : (1 = $product(1,X2) | 1 != 1 | 1 != X2) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f396])). 0.07/0.33 tff(f415,plain,( 0.07/0.33 ( ! [X2:$int] : (1 = $product(1,X2) | 1 != X2) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f398])). 0.07/0.33 tff(f425,plain,( 0.07/0.33 spl0_27 <=> y != 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_27])])). 0.07/0.33 tff(f427,plain,( 0.07/0.33 ~spl0_27 | spl0_9 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f390,f373,f185,f425])). 0.07/0.33 tff(f432,plain,( 0.07/0.33 spl0_29 <=> b != 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_29])])). 0.07/0.33 tff(f434,plain,( 0.07/0.33 ~spl0_29 | spl0_17 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f394,f373,f216,f432])). 0.07/0.33 tff(f437,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 != $product($product(X1,X2),x) | 1 != X1 | y != X2 | x != x) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f388])). 0.07/0.33 tff(f438,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : (1 != $product($product(X1,y),X3) | 1 != X1 | y != y | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f388])). 0.07/0.33 tff(f439,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 != $product($product(1,X2),X3) | 1 != 1 | y != X2 | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f388])). 0.07/0.33 tff(f461,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 != $product($product(1,X2),X3) | y != X2 | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f439])). 0.07/0.33 tff(f462,plain,( 0.07/0.33 ( ! [X3:$int,X1:$int] : (1 != $product($product(X1,y),X3) | 1 != X1 | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f438])). 0.07/0.33 tff(f463,plain,( 0.07/0.33 ( ! [X2:$int,X1:$int] : (1 != $product($product(X1,X2),x) | 1 != X1 | y != X2) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f437])). 0.07/0.33 tff(f474,plain,( 0.07/0.33 spl0_30 <=> z = 1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_30])])). 0.07/0.33 tff(f476,plain,( 0.07/0.33 spl0_30 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f386,f373,f77,f474])). 0.07/0.33 tff(f481,plain,( 0.07/0.33 spl0_33 <=> 1 != $product(1,y)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_33])])). 0.07/0.33 tff(f483,plain,( 0.07/0.33 ~spl0_33 | spl0_15 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f393,f373,f210,f481])). 0.07/0.33 tff(f500,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 = $product(X2,X3) | 1 != 1 | x != X2 | y != X3) ) | ~spl0_22), 0.07/0.33 inference(Instantiation,[],[f385])). 0.07/0.33 tff(f510,plain,( 0.07/0.33 a = $product(x,b) | a != 1 | x != x | y != b | ~spl0_22), 0.07/0.33 inference(Instantiation,[],[f385])). 0.07/0.33 tff(f521,plain,( 0.07/0.33 a = $product(x,b) | a != 1 | y != b | ~spl0_22), 0.07/0.33 inference(trivial_inequality_removal,[],[f510])). 0.07/0.33 tff(f523,plain,( 0.07/0.33 ( ! [X2:$int,X3:$int] : (1 = $product(X2,X3) | x != X2 | y != X3) ) | ~spl0_22), 0.07/0.33 inference(trivial_inequality_removal,[],[f500])). 0.07/0.33 tff(f532,plain,( 0.07/0.33 a = $product(x,b) | y != b | ~spl0_22), 0.07/0.33 inference(subsumption_resolution,[],[f521,f374])). 0.07/0.33 tff(f533,plain,( 0.07/0.33 1 = $product(x,b) | y != b | ~spl0_22), 0.07/0.33 inference(forward_demodulation,[],[f532,f374])). 0.07/0.33 tff(f543,plain,( 0.07/0.33 spl0_35 <=> 1 != $product($product(1,y),b)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_35])])). 0.07/0.33 tff(f545,plain,( 0.07/0.33 ~spl0_35 | spl0_13 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f392,f373,f199,f543])). 0.07/0.33 tff(f643,plain,( 0.07/0.33 ( ! [X4:$int,X5:$int] : (1 != $product(1,X5) | 1 != 1 | y != X4 | x != X5 | 1 != X4) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(superposition,[],[f388,f415])). 0.07/0.33 tff(f653,plain,( 0.07/0.33 ( ! [X4:$int,X5:$int] : (1 != $product(1,X5) | y != X4 | x != X5 | 1 != X4) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f643])). 0.07/0.33 tff(f684,plain,( 0.07/0.33 spl0_37 <=> y != b), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_37])])). 0.07/0.33 tff(f690,plain,( 0.07/0.33 spl0_38 <=> 1 = $product(x,b)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_38])])). 0.07/0.33 tff(f692,plain,( 0.07/0.33 ~spl0_37 | spl0_38 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f533,f373,f690,f684])). 0.07/0.33 tff(f727,plain,( 0.07/0.33 ( ! [X6:$int,X7:$int] : (1 != 1 | y != X6 | x != X7 | 1 != $product(1,X6) | 1 != X7) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(superposition,[],[f461,f396])). 0.07/0.33 tff(f730,plain,( 0.07/0.33 ( ! [X3:$int] : (1 != $product($product(1,y),X3) | y != y | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f461])). 0.07/0.33 tff(f746,plain,( 0.07/0.33 ( ! [X3:$int] : (1 != $product($product(1,y),X3) | x != X3) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f730])). 0.07/0.33 tff(f749,plain,( 0.07/0.33 ( ! [X6:$int,X7:$int] : (y != X6 | x != X7 | 1 != $product(1,X6) | 1 != X7) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f727])). 0.07/0.33 tff(f769,plain,( 0.07/0.33 1 != $product($product(1,y),x) | x != x | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f746])). 0.07/0.33 tff(f772,plain,( 0.07/0.33 1 != $product($product(1,y),x) | x != x | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f746])). 0.07/0.33 tff(f776,plain,( 0.07/0.33 1 != $product($product(1,y),x) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f772])). 0.07/0.33 tff(f777,plain,( 0.07/0.33 1 != $product($product(1,y),x) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f769])). 0.07/0.33 tff(f788,plain,( 0.07/0.33 spl0_41 <=> 1 != $product($product(1,y),x)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_41])])). 0.07/0.33 tff(f789,plain,( 0.07/0.33 1 != $product($product(1,y),x) | ~spl0_41), 0.07/0.33 inference(AVATAR_component_clause,[],[f788])). 0.07/0.33 tff(f790,plain,( 0.07/0.33 ~spl0_41 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f776,f373,f77,f788])). 0.07/0.33 tff(f813,plain,( 0.07/0.33 1 != $product($product(a,y),x) | a != 1 | x != x | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(Instantiation,[],[f462])). 0.07/0.33 tff(f817,plain,( 0.07/0.33 1 != $product($product(a,y),x) | a != 1 | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f813])). 0.07/0.33 tff(f827,plain,( 0.07/0.33 1 != $product($product(a,y),x) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(subsumption_resolution,[],[f817,f374])). 0.07/0.33 tff(f828,plain,( 0.07/0.33 1 != $product($product(1,y),x) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(forward_demodulation,[],[f827,f374])). 0.07/0.33 tff(f829,plain,( 0.07/0.33 ~spl0_41 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f828,f373,f77,f788])). 0.07/0.33 tff(f830,plain,( 0.07/0.33 ~spl0_41 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f777,f373,f77,f788])). 0.07/0.33 tff(f840,plain,( 0.07/0.33 ( ! [X1:$int] : (1 != X1 | 1 != X1 | x != $product(1,y) | x != y) ) | (~spl0_22 | ~spl0_41)), 0.07/0.33 inference(superposition,[],[f789,f385])). 0.07/0.33 tff(f843,plain,( 0.07/0.33 ( ! [X1:$int] : (1 != X1 | x != $product(1,y) | x != y) ) | (~spl0_22 | ~spl0_41)), 0.07/0.33 inference(duplicate_literal_removal,[],[f840])). 0.07/0.33 tff(f880,plain,( 0.07/0.33 ( ! [X9:$int] : (1 != $product(1,x) | 1 != 1 | y != X9 | 1 != X9) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(superposition,[],[f463,f415])). 0.07/0.33 tff(f906,plain,( 0.07/0.33 ( ! [X9:$int] : (1 != $product(1,x) | y != X9 | 1 != X9) ) | (~spl0_2 | ~spl0_22)), 0.07/0.33 inference(trivial_inequality_removal,[],[f880])). 0.07/0.33 tff(f938,plain,( 0.07/0.33 spl0_42 <=> ! [X9 : $int] : (y != X9 | 1 != X9)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_42])])). 0.07/0.33 tff(f944,plain,( 0.07/0.33 spl0_45 <=> 1 != $product(1,x)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_45])])). 0.07/0.33 tff(f946,plain,( 0.07/0.33 spl0_42 | ~spl0_45 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f906,f373,f77,f944,f938])). 0.07/0.33 tff(f961,plain,( 0.07/0.33 spl0_47 <=> x != y), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_47])])). 0.07/0.33 tff(f967,plain,( 0.07/0.33 spl0_49 <=> x != $product(1,y)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_49])])). 0.07/0.33 tff(f970,plain,( 0.07/0.33 spl0_50 <=> ! [X1 : $int] : 1 != X1), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_50])])). 0.07/0.33 tff(f972,plain,( 0.07/0.33 ~spl0_47 | ~spl0_49 | spl0_50 | ~spl0_22 | spl0_41), 0.07/0.33 inference(AVATAR_split_clause,[],[f843,f788,f373,f970,f967,f961])). 0.07/0.33 tff(f984,plain,( 0.07/0.33 spl0_52 <=> ! [X5 : $int] : (1 != $product(1,X5) | x != X5)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_52])])). 0.07/0.33 tff(f986,plain,( 0.07/0.33 spl0_42 | spl0_52 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f653,f373,f77,f984,f938])). 0.07/0.33 tff(f1001,plain,( 0.07/0.33 spl0_54 <=> ! [X7 : $int] : (x != X7 | 1 != X7)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_54])])). 0.07/0.33 tff(f1004,plain,( 0.07/0.33 spl0_56 <=> ! [X6 : $int] : (y != X6 | 1 != $product(1,X6))), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_56])])). 0.07/0.33 tff(f1006,plain,( 0.07/0.33 spl0_54 | spl0_56 | ~spl0_2 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f749,f373,f77,f1004,f1001])). 0.07/0.33 tff(f1055,plain,( 0.07/0.33 ( ! [X3:$int] : (1 = $product(x,X3) | x != x | y != X3) ) | ~spl0_22), 0.07/0.33 inference(Instantiation,[],[f523])). 0.07/0.33 tff(f1070,plain,( 0.07/0.33 ( ! [X3:$int] : (1 = $product(x,X3) | y != X3) ) | ~spl0_22), 0.07/0.33 inference(trivial_inequality_removal,[],[f1055])). 0.07/0.33 tff(f1113,plain,( 0.07/0.33 1 = $product(x,y) | y != y | ~spl0_22), 0.07/0.33 inference(Instantiation,[],[f1070])). 0.07/0.33 tff(f1118,plain,( 0.07/0.33 1 = $product(x,y) | ~spl0_22), 0.07/0.33 inference(trivial_inequality_removal,[],[f1113])). 0.07/0.33 tff(f1131,plain,( 0.07/0.33 spl0_58 <=> 1 = $product(x,y)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_58])])). 0.07/0.33 tff(f1133,plain,( 0.07/0.33 spl0_58 | ~spl0_22), 0.07/0.33 inference(AVATAR_split_clause,[],[f1118,f373,f1131])). 0.07/0.33 tff(f1477,plain,( 0.07/0.33 ( ! [X3:$int] : (1 != $product($product(a,y),X3) | y != y | x != X3) ) | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f156])). 0.07/0.33 tff(f1492,plain,( 0.07/0.33 ( ! [X3:$int] : (1 != $product($product(a,y),X3) | x != X3) ) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f1477])). 0.07/0.33 tff(f1511,plain,( 0.07/0.33 1 != $product($product(a,y),x) | x != x | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f1492])). 0.07/0.33 tff(f1514,plain,( 0.07/0.33 1 != $product($product(a,y),x) | x != x | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f1492])). 0.07/0.33 tff(f1518,plain,( 0.07/0.33 1 != $product($product(a,y),x) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f1514])). 0.07/0.33 tff(f1519,plain,( 0.07/0.33 1 != $product($product(a,y),x) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f1511])). 0.07/0.33 tff(f1529,plain,( 0.07/0.33 spl0_61 <=> 1 != $product($product(a,y),x)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_61])])). 0.07/0.33 tff(f1531,plain,( 0.07/0.33 ~spl0_61 | ~spl0_2), 0.07/0.33 inference(AVATAR_split_clause,[],[f1518,f77,f1529])). 0.07/0.33 tff(f1554,plain,( 0.07/0.33 1 != $product($product(a,y),x) | a != a | x != x | ~spl0_2), 0.07/0.33 inference(Instantiation,[],[f157])). 0.07/0.33 tff(f1561,plain,( 0.07/0.33 1 != $product($product(a,y),x) | ~spl0_2), 0.07/0.33 inference(trivial_inequality_removal,[],[f1554])). 0.07/0.33 tff(f1572,plain,( 0.07/0.33 ~spl0_61 | ~spl0_2), 0.07/0.33 inference(AVATAR_split_clause,[],[f1561,f77,f1529])). 0.07/0.33 tff(f1573,plain,( 0.07/0.33 ~spl0_61 | ~spl0_2), 0.07/0.33 inference(AVATAR_split_clause,[],[f1519,f77,f1529])). 0.07/0.33 tff(f1741,plain,( 0.07/0.33 a = $product(x,y) | y != y | a != a), 0.07/0.33 inference(Instantiation,[],[f270])). 0.07/0.33 tff(f1750,plain,( 0.07/0.33 a = $product(x,y)), 0.07/0.33 inference(trivial_inequality_removal,[],[f1741])). 0.07/0.33 tff(f1772,plain,( 0.07/0.33 spl0_62 <=> a = $product(x,y)), 0.07/0.33 introduced(AVATAR_definition,[new_symbols(naming,[spl0_62])])). 0.07/0.33 tff(f1774,plain,( 0.07/0.33 spl0_62), 0.07/0.33 inference(AVATAR_split_clause,[],[f1750,f1772])). 0.07/0.33 tff(f1775,plain,( 0.07/0.33 $false), 0.07/0.33 inference(AVATAR_sat_refutation,[],[f74,f88,f187,f201,f218,f296,f384,f427,f434,f476,f483,f545,f692,f790,f829,f830,f946,f972,f986,f1006,f1133,f1531,f1572,f1573,f1774])). 0.07/0.33 % SZS output end Proof for theBenchmark 0.07/0.33 % ------------------------------ 0.07/0.33 % Version: Vampire 4.1 for CASC J8 Entry 0.07/0.33 % Termination reason: Refutation 0.07/0.33 0.07/0.33 % Memory used [KB]: 1023 0.07/0.33 % Time elapsed: 0.048 s 0.07/0.33 % ------------------------------ 0.07/0.33 % ------------------------------ 0.07/0.33 % Success in time 0.077 s 0.15/0.39 EOF