%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV171^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:05 AM UTC 2026
% Result : Theorem 0.72s 0.38s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV171^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n010.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:18:48 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.28 Running first-order model finding
% 0.10/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.72/0.38 % (2984269)Will run a generic schedule for satisfiability detection.
% 0.72/0.38 % (2984278)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1818283658:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.72/0.38 % (2984278)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.72/0.38 % (2984275)% WARNING: option uhcvi not known.
% 0.72/0.38 % (2984274)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1133366235_3000 on theBenchmark for (3000ds/0Mi)
% 0.72/0.38 % (2984275)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3996778143:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.72/0.38 % (2984277)dis+10_1_sil=32000:sp=arity:random_seed=2415145008:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.72/0.38 % (2984276)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1222635376:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.72/0.38 % (2984275)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.72/0.38 % Exception at run slice level
% 0.72/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.72/0.38 % (2984275)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.72/0.38 % (2984279)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4142159444:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.72/0.38 % (2984280)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3347991569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.72/0.38 % (2984286)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=935975174:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.72/0.38 % Exception at run slice level
% 0.72/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.72/0.38 % (2984290)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2734490798:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.72/0.38 % (2984280) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2984269-2984280"...
% 0.72/0.38 % (2984280)...printing done.
% 0.72/0.38 % (2984280)Refutation found. Thanks to Tanya!
% 0.72/0.38 % SZS status Theorem for theBenchmark
% 0.72/0.38 % SZS output start Proof for theBenchmark
% 0.72/0.38 thf(type_def_5, type, a: $tType).
% 0.72/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.72/0.38 thf(func_def_1, type, db0: !>[X0: $tType]:(X0)).
% 0.72/0.38 thf(func_def_2, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.72/0.38 thf(func_def_3, type, sK0: ((a > (a > a > a) > a) > a)).
% 0.72/0.38 thf(func_def_4, type, sK1: ((a > (a > a > a) > a) > a)).
% 0.72/0.38 thf(func_def_5, type, sK2: ((a > (a > a > a) > a) > a)).
% 0.72/0.38 thf(func_def_6, type, sK3: ((a > (a > a > a) > a) > a > a > a > a)).
% 0.72/0.38 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.72/0.38 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.72/0.38 thf(func_def_9, type, db3: !>[X0: $tType]:(X0)).
% 0.72/0.38 thf(func_def_10, type, db4: !>[X0: $tType]:(X0)).
% 0.72/0.38 thf(func_def_12, type, sK5: (a > a > a > a)).
% 0.72/0.38 thf(func_def_13, type, sK6: (a > a > a > a)).
% 0.72/0.38 thf(func_def_14, type, sK7: ((a > (a > a > a) > a) > a > a > a)).
% 0.72/0.38 thf(f1,conjecture,(
% 0.72/0.38 ? [X0 : (a > (a > a > a) > a)] : (! [X3 : a] : ? [X4 : a,X5 : a] : (((X0 @ X3)) = (^[X6 : (a > a > a)] : ((X6 @ X3 @ X4)))) & ! [X1 : a,X2 : a] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)))),
% 0.72/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM33_pme)).
% 0.72/0.38 thf(f2,negated_conjecture,(
% 0.72/0.38 ~ ? [X0 : (a > (a > a > a) > a)] : (! [X3 : a] : ? [X4 : a,X5 : a] : (((X0 @ X3)) = (^[X6 : (a > a > a)] : ((X6 @ X3 @ X4)))) & ! [X1 : a,X2 : a] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)))),
% 0.72/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.72/0.38 thf(f3,plain,(
% 0.72/0.38 ~ ? [X0 : (a > (a > a > a) > a)] : (! [X1 : a] : ? [X2 : a] : (((X0 @ X1)) = (^[X4 : (a > a > a)] : ((X4 @ X1 @ X2)))) & ! [X5 : a,X6 : a] : ((((X0 @ X5)) = ((X0 @ X6))) => (X5 = X6)))),
% 0.72/0.38 inference(rectify,[],[f2])).
% 0.72/0.38 thf(f4,plain,(
% 0.72/0.38 ~ ? [X0 : (a > (a > a > a) > a)] : (! [X1 : a] : ? [X2 : a] : (((X0 @ X1)) = (^[Y0 : a > a > a]: (Y0 @ X1 @ X2))) & ! [X5 : a,X6 : a] : ((((X0 @ X5)) = ((X0 @ X6))) => (X5 = X6)))),
% 0.72/0.38 inference(fool_elimination,[],[f3])).
% 0.72/0.38 thf(f5,plain,(
% 0.72/0.38 ~ ? [X0 : (a > (a > a > a) > a)] : (! [X1 : a] : ? [X2 : a] : (((X0 @ X1)) = (^[Y0 : a > a > a]: (Y0 @ X1 @ X2))) & ! [X3 : a,X4 : a] : ((((X0 @ X3)) = ((X0 @ X4))) => (X3 = X4)))),
% 0.72/0.38 inference(rectify,[],[f4])).
% 0.72/0.38 thf(f6,plain,(
% 0.72/0.38 ! [X0 : (a > (a > a > a) > a)] : (? [X1 : a] : ! [X2 : a] : (((X0 @ X1)) != (^[Y0 : a > a > a]: (Y0 @ X1 @ X2))) | ? [X3 : a,X4 : a] : ((X3 != X4) & (((X0 @ X3)) = ((X0 @ X4)))))),
% 0.72/0.38 inference(ennf_transformation,[],[f5])).
% 0.72/0.38 thf(f7,plain,(
% 0.72/0.38 ! [X0 : (a > (a > a > a) > a)] : (! [X2 : a] : (((X0 @ (sK0 @ X0))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X0) @ X2))) | ((((sK1 @ X0)) != ((sK2 @ X0))) & (((X0 @ (sK1 @ X0))) = ((X0 @ (sK2 @ X0))))))),
% 0.72/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X4,sK2 @ X0),skolemize(X4,sK2 @ X0),skolemize(X4,sK2 @ X0)],[f6])).
% 0.72/0.38 thf(f8,plain,(
% 0.72/0.38 ( ! [X2 : a,X0 : (a > (a > a > a) > a)] : ((((X0 @ (sK0 @ X0))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X0) @ X2))) | (((X0 @ (sK1 @ X0))) = ((X0 @ (sK2 @ X0))))) )),
% 0.72/0.38 inference(cnf_transformation,[],[f7])).
% 0.72/0.38 thf(f9,plain,(
% 0.72/0.38 ( ! [X2 : a,X0 : (a > (a > a > a) > a)] : ((((sK1 @ X0)) != ((sK2 @ X0))) | (((X0 @ (sK0 @ X0))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X0) @ X2)))) )),
% 0.72/0.38 inference(cnf_transformation,[],[f7])).
% 0.72/0.38 thf(f11,plain,(
% 0.72/0.38 ( ! [X0 : (a > (a > a > a) > a),X1 : a] : (((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1)))))))) = (((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))))))) | ((^[Y0 : a > a > a]: (X1)) != ((X0 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))))))) | ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ ((^[Y3 : a]: ((^[Y4 : a > a > a]: (Y3)))) @ Y1 @ Y2) @ (X0 @ Y1 @ Y2))))))))) )),
% 0.72/0.38 inference(equality_resolution,[],[f8])).
% 0.72/0.38 thf(f14,plain,(
% 0.72/0.38 ( ! [X0 : (a > (a > a > a) > a),X1 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0))) = (^[Y0 : a > a > a]: (Y0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0)))) | ((^[Y0 : a > a > a]: (X1)) != ((X0 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1))))))))) | ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2))))))))) )),
% 0.72/0.38 inference(beta-eta_normalization,[],[f11])).
% 0.72/0.38 thf(f15,plain,(
% 0.72/0.38 ( ! [X0 : (a > (a > a > a) > a),X1 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0))) = (^[Y0 : a > a > a]: (Y0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0)))) | ((^[Y0 : a > a > a]: (X1)) != ((X0 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.72/0.38 inference(trivial_inequality_removal,[],[f14])).
% 0.72/0.38 thf(f27,plain,(
% 0.72/0.38 ( ! [X2 : (a > a > a),X0 : (a > (a > a > a) > a),X1 : a] : (((((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0))) @ X2)) = (((^[Y0 : a > a > a]: (Y0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ (X0 @ (sK2 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0))) @ X2))) | ((^[Y0 : a > a > a]: (X1)) != ((X0 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.72/0.38 inference(argument_congruence,[],[f15])).
% 0.72/0.38 thf(f31,plain,(
% 0.72/0.38 ( ! [X2 : (a > a > a),X0 : (a > (a > a > a) > a),X1 : a] : ((((X2 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))) @ (X0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))) @ X2))) = ((X2 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))) @ (X0 @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))) @ X2)))) | ((^[Y0 : a > a > a]: (X1)) != ((X0 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.72/0.38 inference(beta-eta_normalization,[],[f27])).
% 0.72/0.38 thf(f41,plain,(
% 0.72/0.38 ( ! [X3 : a,X4 : a,X5 : (a > (a > a > a) > a)] : (((((^[Y0 : a]: ((^[Y1 : a]: (Y1)))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1)))))) @ ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1)))))) @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))) != ((sK1 @ X5))) | (((X5 @ (sK0 @ X5))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X5) @ X3))) | ((^[Y0 : a > a > a]: (X4)) != (((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y0)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ ((^[Y2 : a]: ((^[Y3 : a > a > a]: (Y2)))) @ Y0 @ Y1))))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != X5)) )),
% 0.72/0.38 inference(constrained_superposition,[],[f9,f31])).
% 0.72/0.38 thf(f61,plain,(
% 0.72/0.38 ( ! [X3 : a,X4 : a,X5 : (a > (a > a > a) > a)] : ((((sK1 @ X5)) != ((sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))))) | (((X5 @ (sK0 @ X5))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X5) @ X3))) | ((^[Y0 : a > a > a]: (X4)) != (^[Y0 : a > a > a]: (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != X5)) )),
% 0.72/0.38 inference(beta-eta_normalization,[],[f41])).
% 0.72/0.38 thf(f70,definition,(
% 0.72/0.38 spl4_1 <=> ! [X4 : a] : ((^[Y0 : a > a > a]: (X4)) != (^[Y0 : a > a > a]: (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))))),
% 0.72/0.38 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.72/0.38 thf(f71,plain,(
% 0.72/0.38 ( ! [X4 : a] : (((^[Y0 : a > a > a]: (X4)) != (^[Y0 : a > a > a]: (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))))) ) | ~spl4_1),
% 0.72/0.38 inference(avatar_component_clause,[],[f70])).
% 0.72/0.38 thf(f73,definition,(
% 0.72/0.38 spl4_2 <=> ! [X5 : (a > (a > a > a) > a),X3 : a] : ((((sK1 @ X5)) != ((sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != X5) | (((X5 @ (sK0 @ X5))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X5) @ X3))))),
% 0.72/0.38 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.72/0.38 thf(f74,plain,(
% 0.72/0.38 ( ! [X3 : a,X5 : (a > (a > a > a) > a)] : ((((sK1 @ X5)) != ((sK1 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))))) | ((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != X5) | (((X5 @ (sK0 @ X5))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ X5) @ X3)))) ) | ~spl4_2),
% 0.72/0.38 inference(avatar_component_clause,[],[f73])).
% 0.72/0.38 thf(f75,plain,(
% 0.72/0.38 spl4_1 | spl4_2),
% 0.72/0.38 inference(avatar_split_clause,[],[f61,f73,f70])).
% 0.72/0.38 thf(f83,plain,(
% 0.72/0.38 ( ! [X0 : a] : (((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) != (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))) | ((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))) @ X0)))) ) | ~spl4_2),
% 0.72/0.38 inference(equality_resolution,[],[f74])).
% 0.72/0.38 thf(f84,plain,(
% 0.72/0.38 ( ! [X0 : a] : (((((^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0))))))) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))) @ X0)))) ) | ~spl4_2),
% 0.72/0.38 inference(trivial_inequality_removal,[],[f83])).
% 0.72/0.38 thf(f85,plain,(
% 0.72/0.38 ( ! [X0 : a] : (((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))) @ X0)) != (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1))))))))) ) | ~spl4_2),
% 0.72/0.38 inference(beta-eta_normalization,[],[f84])).
% 0.72/0.38 thf(f90,plain,(
% 0.72/0.38 ( ! [X0 : (a > (a > a > a) > a),X1 : (a > (a > a > a) > a)] : (((^[Y0 : a > a > a]: (X0)) != (^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1))))))) | ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))) ) | ~spl4_2),
% 0.72/0.38 inference(equality_resolution,[],[f85])).
% 0.72/0.38 thf(f93,definition,(
% 0.72/0.38 spl4_4 <=> ! [X1 : (a > (a > a > a) > a)] : ((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))),
% 0.72/0.38 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.72/0.38 thf(f94,plain,(
% 0.72/0.38 ( ! [X1 : (a > (a > a > a) > a)] : (((^[Y0 : a > a > a]: ((^[Y1 : a]: ((^[Y2 : a > a > a]: (Y1)))))) != (^[Y0 : a > a > a]: (X1)))) ) | ~spl4_4),
% 0.72/0.38 inference(avatar_component_clause,[],[f93])).
% 0.72/0.38 thf(f95,plain,(
% 0.72/0.38 spl4_4 | spl4_4 | ~spl4_2),
% 0.72/0.38 inference(avatar_split_clause,[],[f90,f73,f93,f93])).
% 0.72/0.38 thf(f96,plain,(
% 0.72/0.38 ( ! [X4 : a] : (((((^[Y0 : a > a > a]: (X4)) @ (sK6 @ X4))) != (((^[Y0 : a > a > a]: (sK0 @ (^[Y1 : a]: ((^[Y2 : a > a > a]: (Y2 @ Y1 @ Y1)))))) @ (sK6 @ X4))))) ) | ~spl4_1),
% 0.72/0.38 inference(negative_extensionality,[],[f71])).
% 0.72/0.38 thf(f98,plain,(
% 0.72/0.38 ( ! [X4 : a] : ((((sK0 @ (^[Y0 : a]: ((^[Y1 : a > a > a]: (Y1 @ Y0 @ Y0)))))) != X4)) ) | ~spl4_1),
% 0.72/0.38 inference(beta-eta_normalization,[],[f96])).
% 0.72/0.38 thf(f100,plain,(
% 0.72/0.38 $false | ~spl4_1),
% 0.72/0.38 inference(equality_resolution,[],[f98])).
% 0.72/0.38 thf(f101,plain,(
% 0.72/0.38 ~spl4_1),
% 0.72/0.38 inference(avatar_contradiction_clause,[],[f100])).
% 0.72/0.38 thf(f104,plain,(
% 0.72/0.38 $false | ~spl4_4),
% 0.72/0.38 inference(equality_resolution,[],[f94])).
% 0.72/0.38 thf(f105,plain,(
% 0.72/0.38 ~spl4_4),
% 0.72/0.38 inference(avatar_contradiction_clause,[],[f104])).
% 0.72/0.38 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f75])).
% 0.72/0.38 cnf(s3, plain, spl4_4 | ~spl4_2 | spl4_4, inference(sat_conversion,[],[f95])).
% 0.72/0.38 cnf(s4, plain, ~spl4_2 | spl4_4, inference(rat,[],[s3])).
% 0.72/0.38 cnf(s7, plain, ~spl4_1, inference(sat_conversion,[],[f101])).
% 0.72/0.38 cnf(s8, plain, ~spl4_4, inference(sat_conversion,[],[f105])).
% 0.72/0.38 cnf(s9, plain, ~spl4_2, inference(rat,[],[s4,s8])).
% 0.72/0.38 cnf(s11, plain, $false, inference(rat,[],[s1,s9,s7])).
% 0.72/0.38 thf(f107,plain,(
% 0.72/0.38 $false),
% 0.72/0.38 inference(avatar_sat_refutation,[],[s11])).
% 0.72/0.38 % SZS output end Proof for theBenchmark
% 0.72/0.38 % (2984280)------------------------------
% 0.72/0.38 % (2984280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.72/0.38 % (2984280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.72/0.38 % (2984280)CaDiCaL version: 2.1.3
% 0.72/0.38 % (2984280)Termination reason: Refutation
% 0.72/0.38 % (2984280)Time elapsed: 0.047 s
% 0.72/0.38 % (2984280)Peak memory usage: 13 MB
% 0.72/0.38 % (2984280)Instructions burned: 55 (million)
% 0.72/0.38 % (2984269)Success in time 0.091 s
% 0.72/0.38 % Vampire exiting
%------------------------------------------------------------------------------