%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL594^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:14:25 AM UTC 2026
% Result : Theorem 0.33s 0.39s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL594^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n006.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 09:08:10 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.39 % (447340)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.39 % (447351)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.39 % (447351)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.33/0.39 % (447351)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1963555520:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.39 % (447351)Refutation not found, incomplete strategy
% 0.33/0.39 % (447351)------------------------------
% 0.33/0.39 % (447351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.39 % (447351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.39 % (447351)CaDiCaL version: 2.1.3
% 0.33/0.39 % (447351)Termination reason: Refutation not found, incomplete strategy
% 0.33/0.39 % (447351)Time elapsed: 0.003 s
% 0.33/0.39 % (447351)Peak memory usage: 12 MB
% 0.33/0.39 % (447351)Instructions burned: 4 (million)
% 0.33/0.39 % (447351)------------------------------
% 0.33/0.39 % (447351)------------------------------
% 0.33/0.39 % (447345)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3118078358:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.39 % (447347)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1866709920:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.39 % (447346)lrs+10_16_si=on:nwc=1.5:random_seed=310241769:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.39 % (447349)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3201883204:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.39 % (447348)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2565309553:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.33/0.39 % (447350)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1115630061:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.39 % (447347)Refutation not found, incomplete strategy
% 0.33/0.39 % (447347)------------------------------
% 0.33/0.39 % (447347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.39 % (447347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.39 % (447347)CaDiCaL version: 2.1.3
% 0.33/0.39 % (447347)Termination reason: Refutation not found, incomplete strategy
% 0.33/0.39 % (447347)Time elapsed: 0.003 s
% 0.33/0.39 % (447347)Peak memory usage: 12 MB
% 0.33/0.39 % (447347)Instructions burned: 3 (million)
% 0.33/0.39 % (447345) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-447340-447345"...
% 0.33/0.39 % (447347)------------------------------
% 0.33/0.39 % (447347)------------------------------
% 0.33/0.39 % (447346) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-447340-447346"...
% 0.33/0.39 % (447345)...printing done.
% 0.33/0.39 % (447345)Refutation found. Thanks to Tanya!
% 0.33/0.39 % SZS status Theorem for theBenchmark
% 0.33/0.39 % SZS output start Proof for theBenchmark
% 0.33/0.39 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.39 thf(type_def_6, type, individuals: $tType).
% 0.33/0.39 thf(func_def_1, type, prop_a: ($i > $o)).
% 0.33/0.39 thf(func_def_2, type, prop_b: ($i > $o)).
% 0.33/0.39 thf(func_def_3, type, prop_c: ($i > $o)).
% 0.33/0.39 thf(func_def_4, type, mfalse: ($i > $o)).
% 0.33/0.39 thf(func_def_5, type, mtrue: ($i > $o)).
% 0.33/0.39 thf(func_def_6, type, mnot: (($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_8, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_9, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_10, type, mimpl: (($i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_11, type, miff: (($i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_12, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_13, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_14, type, mall: ((individuals > $i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_15, type, mexists: ((individuals > $i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_16, type, mvalid: (($i > $o) > $o)).
% 0.33/0.39 thf(func_def_17, type, msatisfiable: (($i > $o) > $o)).
% 0.33/0.39 thf(func_def_18, type, mcountersatisfiable: (($i > $o) > $o)).
% 0.33/0.39 thf(func_def_19, type, minvalid: (($i > $o) > $o)).
% 0.33/0.39 thf(func_def_22, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.39 thf(func_def_23, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.39 thf(func_def_24, type, vNOT: ($o > $o)).
% 0.33/0.39 thf(func_def_25, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.39 thf(func_def_26, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.39 thf(func_def_27, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.39 thf(func_def_28, type, vIMP: ($o > $o > $o)).
% 0.33/0.39 thf(func_def_29, type, db3: !>[X0: $tType]:(X0)).
% 0.33/0.39 thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
% 0.33/0.39 thf(func_def_31, type, vAND: ($o > $o > $o)).
% 0.33/0.39 thf(func_def_32, type, vOR: ($o > $o > $o)).
% 0.33/0.39 thf(func_def_33, type, sK0: (($i > $i > $o) > $i > $o)).
% 0.33/0.39 thf(func_def_34, type, sK1: (($i > $i > $o) > $i)).
% 0.33/0.39 thf(func_def_35, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.39 thf(f3,axiom,(
% 0.33/0.39 ((^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot)).
% 0.33/0.39 thf(f4,axiom,(
% 0.33/0.39 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor)).
% 0.33/0.39 thf(f6,axiom,(
% 0.33/0.39 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))) = mimpl)),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl)).
% 0.33/0.39 thf(f8,axiom,(
% 0.33/0.39 ((^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox)).
% 0.33/0.39 thf(f12,axiom,(
% 0.33/0.39 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid)).
% 0.33/0.39 thf(f16,conjecture,(
% 0.33/0.39 ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))),
% 0.33/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.33/0.39 thf(f17,negated_conjecture,(
% 0.33/0.39 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))),
% 0.33/0.39 inference(negated_conjecture,[status(cth)],[f16])).
% 0.33/0.39 thf(f22,plain,(
% 0.33/0.39 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.33/0.39 inference(rectify,[],[f12])).
% 0.33/0.39 thf(f23,plain,(
% 0.33/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.33/0.39 inference(fool_elimination,[],[f22])).
% 0.33/0.39 thf(f24,plain,(
% 0.33/0.39 ((^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.33/0.39 inference(rectify,[],[f3])).
% 0.33/0.39 thf(f25,plain,(
% 0.33/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.33/0.39 inference(fool_elimination,[],[f24])).
% 0.33/0.39 thf(f28,plain,(
% 0.33/0.39 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.33/0.39 inference(fool_elimination,[],[f6])).
% 0.33/0.39 thf(f29,plain,(
% 0.33/0.39 ((^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 0.33/0.39 inference(rectify,[],[f8])).
% 0.33/0.39 thf(f30,plain,(
% 0.33/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.33/0.39 inference(fool_elimination,[],[f29])).
% 0.33/0.39 thf(f32,plain,(
% 0.33/0.39 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))),
% 0.33/0.39 inference(rectify,[],[f17])).
% 0.33/0.39 thf(f33,plain,(
% 0.33/0.39 ~ ? [X0 : ($i > $i > $o)] : ! [X1 : ($i > $o)] : (((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))) = $true)),
% 0.33/0.39 inference(fool_elimination,[],[f32])).
% 0.33/0.39 thf(f38,plain,(
% 0.33/0.39 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.33/0.39 inference(rectify,[],[f4])).
% 0.33/0.39 thf(f39,plain,(
% 0.33/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.33/0.39 inference(fool_elimination,[],[f38])).
% 0.33/0.39 thf(f46,plain,(
% 0.33/0.39 ! [X0 : ($i > $i > $o)] : ? [X1 : ($i > $o)] : (((mvalid @ (mimpl @ (mbox @ X0 @ X1) @ X1))) != $true)),
% 0.33/0.39 inference(ennf_transformation,[],[f33])).
% 0.33/0.39 thf(f47,plain,(
% 0.33/0.39 ! [X0 : ($i > $i > $o)] : (((mvalid @ (mimpl @ (mbox @ X0 @ (sK0 @ X0)) @ (sK0 @ X0)))) != $true)),
% 0.33/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f46])).
% 0.33/0.39 thf(f51,plain,(
% 0.33/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.33/0.39 inference(cnf_transformation,[],[f23])).
% 0.33/0.39 thf(f52,plain,(
% 0.33/0.39 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.33/0.39 inference(cnf_transformation,[],[f28])).
% 0.33/0.39 thf(f53,plain,(
% 0.33/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.33/0.39 inference(cnf_transformation,[],[f25])).
% 0.33/0.39 thf(f54,plain,(
% 0.33/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.33/0.39 inference(cnf_transformation,[],[f30])).
% 0.33/0.39 thf(f55,plain,(
% 0.33/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.33/0.39 inference(cnf_transformation,[],[f39])).
% 0.33/0.39 thf(f60,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : ((((mvalid @ (mimpl @ (mbox @ X0 @ (sK0 @ X0)) @ (sK0 @ X0)))) != $true)) )),
% 0.33/0.39 inference(cnf_transformation,[],[f47])).
% 0.33/0.39 thf(f66,plain,(
% 0.33/0.39 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.33/0.39 inference(definition_unfolding,[],[f52,f55,f53])).
% 0.33/0.39 thf(f68,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : (((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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)) @ (sK0 @ X0)))) != $true)) )),
% 0.33/0.39 inference(definition_unfolding,[],[f60,f51,f66,f54])).
% 0.33/0.39 thf(f69,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : (($true != ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ X0 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1))))))))))) )),
% 0.33/0.39 inference(beta-eta_normalization,[],[f68])).
% 0.33/0.39 thf(f70,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((sK0 @ X0 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) => (sK0 @ X0 @ Y1))))))) @ (sK1 @ X0))))) )),
% 0.33/0.39 inference(sigma_proxy_clausification,[],[f69])).
% 0.33/0.39 thf(f71,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : (($false = (((sK0 @ X0 @ (sK1 @ X0)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))))))))) )),
% 0.33/0.39 inference(beta-eta_normalization,[],[f70])).
% 0.33/0.39 thf(f72,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0)))))) = $false)) )),
% 0.33/0.39 inference(or_proxy_clausification,[],[f71])).
% 0.33/0.39 thf(f73,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $false)) )),
% 0.33/0.39 inference(or_proxy_clausification,[],[f71])).
% 0.33/0.39 thf(f74,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))))) = $true)) )),
% 0.33/0.39 inference(not_proxy_clausification,[],[f72])).
% 0.33/0.39 thf(f75,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: ((X0 @ (sK1 @ X0) @ Y0) => (sK0 @ X0 @ Y0))) @ X1)) = $true)) )),
% 0.33/0.39 inference(pi_proxy_clausification,[],[f74])).
% 0.33/0.39 thf(f76,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = (((X0 @ (sK1 @ X0) @ X1) => (sK0 @ X0 @ X1))))) )),
% 0.33/0.39 inference(beta-eta_normalization,[],[f75])).
% 0.33/0.39 thf(f77,plain,(
% 0.33/0.39 ( ! [X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ (sK1 @ X0) @ X1)) = $false) | ($true = ((sK0 @ X0 @ X1)))) )),
% 0.33/0.39 inference(imp_proxy_clausification,[],[f76])).
% 0.33/0.39 thf(f80,plain,(
% 0.33/0.39 ( ! [X1 : $i] : ((((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = $true) | ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) @ X1)))) )),
% 0.33/0.39 inference(primitive_instantiation,[],[f77])).
% 0.33/0.39 thf(f86,plain,(
% 0.33/0.39 ( ! [X1 : $i] : (($false = $true) | (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = $true)) )),
% 0.33/0.39 inference(beta-eta_normalization,[],[f80])).
% 0.33/0.39 thf(f87,plain,(
% 0.33/0.39 ( ! [X1 : $i] : ((((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = $true)) )),
% 0.33/0.39 inference(trivial_inequality_removal,[],[f86])).
% 0.33/0.39 thf(f93,plain,(
% 0.33/0.39 ($false = $true)),
% 0.33/0.39 inference(constrained_superposition,[],[f87,f73])).
% 0.33/0.39 thf(f95,plain,(
% 0.33/0.39 $false),
% 0.33/0.39 inference(trivial_inequality_removal,[],[f93])).
% 0.33/0.39 % SZS output end Proof for theBenchmark
% 0.33/0.39 % (447345)------------------------------
% 0.33/0.39 % (447345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.39 % (447345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.39 % (447345)CaDiCaL version: 2.1.3
% 0.33/0.39 % (447345)Termination reason: Refutation
% 0.33/0.39 % (447345)Time elapsed: 0.008 s
% 0.33/0.39 % (447345)Peak memory usage: 12 MB
% 0.33/0.39 % (447345)Instructions burned: 6 (million)
% 0.33/0.39 % (447340)Success in time 0.046 s
% 0.33/0.39 % Vampire exiting
%------------------------------------------------------------------------------