%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL597^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:15:01 AM UTC 2026
% Result : Theorem 0.10s 0.31s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL597^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 % Computer : n018.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 09:13:14 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 Running first-order model finding
% 0.10/0.27 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
% 0.10/0.31 % (4024062)Will run a generic schedule for satisfiability detection.
% 0.10/0.31 % (4024068)% WARNING: option uhcvi not known.
% 0.10/0.31 % (4024068)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=85181509:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.31 % (4024068)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.31 % (4024067)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2656142172_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.31 % (4024068)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.31 % Exception at run slice level
% 0.10/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.31 % (4024068) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4024062-4024068"...
% 0.10/0.31 % (4024068)...printing done.
% 0.10/0.31 % (4024068)Refutation found. Thanks to Tanya!
% 0.10/0.31 % SZS status Theorem for theBenchmark
% 0.10/0.31 % SZS output start Proof for theBenchmark
% 0.10/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.31 thf(type_def_6, type, individuals: $tType).
% 0.10/0.31 thf(func_def_1, type, prop_a: ($i > $o)).
% 0.10/0.31 thf(func_def_2, type, prop_b: ($i > $o)).
% 0.10/0.31 thf(func_def_3, type, prop_c: ($i > $o)).
% 0.10/0.31 thf(func_def_4, type, mfalse: ($i > $o)).
% 0.10/0.31 thf(func_def_5, type, mtrue: ($i > $o)).
% 0.10/0.31 thf(func_def_6, type, mnot: (($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_8, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_9, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_10, type, mimpl: (($i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_11, type, miff: (($i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_12, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_13, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_14, type, mall: ((individuals > $i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_15, type, mexists: ((individuals > $i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_16, type, mvalid: (($i > $o) > $o)).
% 0.10/0.31 thf(func_def_17, type, msatisfiable: (($i > $o) > $o)).
% 0.10/0.31 thf(func_def_18, type, mcountersatisfiable: (($i > $o) > $o)).
% 0.10/0.31 thf(func_def_19, type, minvalid: (($i > $o) > $o)).
% 0.10/0.31 thf(func_def_22, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.31 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.10/0.31 thf(func_def_24, type, db1: !>[X0: $tType]:(X0)).
% 0.10/0.31 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.31 thf(func_def_26, type, vOR: ($o > $o > $o)).
% 0.10/0.31 thf(func_def_27, type, db2: !>[X0: $tType]:(X0)).
% 0.10/0.31 thf(func_def_28, type, vAND: ($o > $o > $o)).
% 0.10/0.31 thf(func_def_29, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.10/0.31 thf(func_def_30, type, vIMP: ($o > $o > $o)).
% 0.10/0.31 thf(func_def_31, type, db3: !>[X0: $tType]:(X0)).
% 0.10/0.31 thf(func_def_32, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.10/0.31 thf(func_def_33, type, sK0: (($i > $i > $o) > $i > $o)).
% 0.10/0.31 thf(func_def_34, type, sK1: (($i > $i > $o) > $i)).
% 0.10/0.31 thf(func_def_35, type, sK2: (($i > $i > $o) > $i)).
% 0.10/0.31 thf(func_def_36, type, sK3: (($i > $i > $o) > $i)).
% 0.10/0.31 thf(func_def_37, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.10/0.31 thf(f3,axiom,(
% 0.10/0.31 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot)).
% 0.10/0.31 thf(f4,axiom,(
% 0.10/0.31 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor)).
% 0.10/0.31 thf(f6,axiom,(
% 0.10/0.31 (mimpl = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl)).
% 0.10/0.31 thf(f8,axiom,(
% 0.10/0.31 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox)).
% 0.10/0.31 thf(f12,axiom,(
% 0.10/0.31 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid)).
% 0.10/0.31 thf(f16,conjecture,(
% 0.10/0.31 ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))),
% 0.10/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.10/0.31 thf(f17,negated_conjecture,(
% 0.10/0.31 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))),
% 0.10/0.31 inference(negated_conjecture,[status(cth)],[f16])).
% 0.10/0.31 thf(f20,plain,(
% 0.10/0.31 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.10/0.31 inference(rectify,[],[f3])).
% 0.10/0.31 thf(f21,plain,(
% 0.10/0.31 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.10/0.31 inference(fool_elimination,[],[f20])).
% 0.10/0.31 thf(f22,plain,(
% 0.10/0.31 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.10/0.31 inference(rectify,[],[f4])).
% 0.10/0.31 thf(f23,plain,(
% 0.10/0.31 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.10/0.31 inference(fool_elimination,[],[f22])).
% 0.10/0.31 thf(f26,plain,(
% 0.10/0.31 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.10/0.31 inference(fool_elimination,[],[f6])).
% 0.10/0.31 thf(f28,plain,(
% 0.10/0.31 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.10/0.31 inference(rectify,[],[f8])).
% 0.10/0.31 thf(f29,plain,(
% 0.10/0.31 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.10/0.31 inference(fool_elimination,[],[f28])).
% 0.10/0.31 thf(f36,plain,(
% 0.10/0.31 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.10/0.31 inference(rectify,[],[f12])).
% 0.10/0.31 thf(f37,plain,(
% 0.10/0.31 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.10/0.31 inference(fool_elimination,[],[f36])).
% 0.10/0.31 thf(f44,plain,(
% 0.10/0.31 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))),
% 0.10/0.31 inference(rectify,[],[f17])).
% 0.10/0.31 thf(f45,plain,(
% 0.10/0.31 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))) = $true)),
% 0.10/0.31 inference(fool_elimination,[],[f44])).
% 0.10/0.31 thf(f46,plain,(
% 0.10/0.31 ! [X0 : ($i > $i > $o)] : ? [X1 : ($i > $o)] : (((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ (mbox @ X0 @ (mbox @ X0 @ X1))))) != $true)),
% 0.10/0.31 inference(ennf_transformation,[],[f45])).
% 0.10/0.31 thf(f47,plain,(
% 0.10/0.31 ! [X0 : ($i > $i > $o)] : ($true != ((mvalid @ (mimpl @ (mbox @ X0 @ (sK0 @ X0)) @ (mbox @ X0 @ (mbox @ X0 @ (sK0 @ X0)))))))),
% 0.10/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f46])).
% 0.10/0.31 thf(f50,plain,(
% 0.10/0.31 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.10/0.31 inference(cnf_transformation,[],[f21])).
% 0.10/0.31 thf(f51,plain,(
% 0.10/0.31 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.10/0.31 inference(cnf_transformation,[],[f23])).
% 0.10/0.31 thf(f53,plain,(
% 0.10/0.31 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.10/0.31 inference(cnf_transformation,[],[f26])).
% 0.10/0.31 thf(f55,plain,(
% 0.10/0.31 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.10/0.31 inference(cnf_transformation,[],[f29])).
% 0.10/0.31 thf(f59,plain,(
% 0.10/0.31 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.10/0.31 inference(cnf_transformation,[],[f37])).
% 0.10/0.31 thf(f63,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($true != ((mvalid @ (mimpl @ (mbox @ X0 @ (sK0 @ X0)) @ (mbox @ X0 @ (mbox @ X0 @ (sK0 @ X0)))))))) )),
% 0.10/0.31 inference(cnf_transformation,[],[f47])).
% 0.10/0.31 thf(f66,plain,(
% 0.10/0.31 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.10/0.31 inference(definition_unfolding,[],[f53,f51,f50])).
% 0.10/0.31 thf(f68,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ X0 @ (sK0 @ X0)) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ X0 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ X0 @ (sK0 @ X0)))))))) )),
% 0.10/0.31 inference(definition_unfolding,[],[f63,f59,f66,f55,f55,f55])).
% 0.10/0.31 thf(f69,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($true != ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((X0 @ Y1 @ Y2) => (sK0 @ X0 @ Y2))))))))))))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f68])).
% 0.10/0.31 thf(f70,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((X0 @ Y1 @ Y2) => (sK0 @ X0 @ Y2))))))))) @ (sK1 @ X0))))) )),
% 0.10/0.31 inference(sigma_proxy_clausification,[],[f69])).
% 0.10/0.31 thf(f71,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1))))))))))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f70])).
% 0.10/0.31 thf(f72,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1)))))))))) )),
% 0.10/0.31 inference(or_proxy_clausification,[],[f71])).
% 0.10/0.31 thf(f73,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0)))))))) )),
% 0.10/0.31 inference(or_proxy_clausification,[],[f71])).
% 0.10/0.31 thf(f74,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))))))) )),
% 0.10/0.31 inference(not_proxy_clausification,[],[f73])).
% 0.10/0.31 thf(f75,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))) @ X1)))) )),
% 0.10/0.31 inference(pi_proxy_clausification,[],[f74])).
% 0.10/0.31 thf(f76,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = (((X0 @ (sK1 @ X0) @ X1) => (sK0 @ X0 @ X1))))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f75])).
% 0.10/0.31 thf(f77,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($false = ((X0 @ (sK1 @ X0) @ X1))) | ($true = ((sK0 @ X0 @ X1)))) )),
% 0.10/0.31 inference(imp_proxy_clausification,[],[f76])).
% 0.10/0.31 thf(f78,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1)))))) @ (sK2 @ X0))))) )),
% 0.10/0.31 inference(sigma_proxy_clausification,[],[f72])).
% 0.10/0.31 thf(f79,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((X0 @ (sK1 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK2 @ X0) @ Y0) => (sK0 @ X0 @ Y0)))))))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f78])).
% 0.10/0.31 thf(f80,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK2 @ X0) @ Y0) => (sK0 @ X0 @ Y0))))))) )),
% 0.10/0.31 inference(imp_proxy_clausification,[],[f79])).
% 0.10/0.31 thf(f82,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((X0 @ (sK2 @ X0) @ Y0) => (sK0 @ X0 @ Y0))) @ (sK3 @ X0))))) )),
% 0.10/0.31 inference(sigma_proxy_clausification,[],[f80])).
% 0.10/0.31 thf(f83,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) => (sK0 @ X0 @ (sK3 @ X0)))))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f82])).
% 0.10/0.31 thf(f84,plain,(
% 0.10/0.31 ( ! [X0 : ($i > $i > $o)] : (($false = ((sK0 @ X0 @ (sK3 @ X0))))) )),
% 0.10/0.31 inference(imp_proxy_clausification,[],[f83])).
% 0.10/0.31 thf(f97,plain,(
% 0.10/0.31 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) @ X1))) | ($true = ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)))) )),
% 0.10/0.31 inference(primitive_instantiation,[],[f77])).
% 0.10/0.31 thf(f116,plain,(
% 0.10/0.31 ( ! [X1 : $i] : (($false = $true) | ($true = ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)))) )),
% 0.10/0.31 inference(beta-eta_normalization,[],[f97])).
% 0.10/0.31 thf(f117,plain,(
% 0.10/0.31 ( ! [X1 : $i] : (($true = ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)))) )),
% 0.10/0.31 inference(trivial_inequality_removal,[],[f116])).
% 0.10/0.31 thf(f125,definition,(
% 0.10/0.31 spl4_1 <=> ! [X1 : $i] : ($true = ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)))),
% 0.10/0.31 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.10/0.31 thf(f126,plain,(
% 0.10/0.31 ( ! [X1 : $i] : (($true = ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)))) ) | ~spl4_1),
% 0.10/0.31 inference(avatar_component_clause,[],[f125])).
% 0.10/0.31 thf(f132,plain,(
% 0.10/0.31 spl4_1),
% 0.10/0.31 inference(avatar_split_clause,[],[f117,f125])).
% 0.10/0.31 thf(f133,plain,(
% 0.10/0.31 ($false = $true) | ~spl4_1),
% 0.10/0.31 inference(constrained_superposition,[],[f126,f84])).
% 0.10/0.31 thf(f143,plain,(
% 0.10/0.31 $false | ~spl4_1),
% 0.10/0.31 inference(trivial_inequality_removal,[],[f133])).
% 0.10/0.31 thf(f144,plain,(
% 0.10/0.31 ~spl4_1),
% 0.10/0.31 inference(avatar_contradiction_clause,[],[f143])).
% 0.10/0.31 cnf(s3, plain, spl4_1, inference(sat_conversion,[],[f132])).
% 0.10/0.31 cnf(s6, plain, ~spl4_1, inference(sat_conversion,[],[f144])).
% 0.10/0.31 cnf(s7, plain, $false, inference(rat,[],[s3,s6])).
% 0.10/0.31 thf(f145,plain,(
% 0.10/0.31 $false),
% 0.10/0.31 inference(avatar_sat_refutation,[],[s7])).
% 0.10/0.31 % SZS output end Proof for theBenchmark
% 0.10/0.31 % (4024068)------------------------------
% 0.10/0.31 % (4024068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.31 % (4024068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.31 % (4024068)CaDiCaL version: 2.1.3
% 0.10/0.31 % (4024068)Termination reason: Refutation
% 0.10/0.31 % (4024068)Time elapsed: 0.007 s
% 0.10/0.31 % (4024068)Peak memory usage: 13 MB
% 0.10/0.31 % (4024068)Instructions burned: 11 (million)
% 0.10/0.31 % (4024062)Success in time 0.031 s
% 0.10/0.31 % Vampire exiting
%------------------------------------------------------------------------------