%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO224^5 : 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 : n002.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 08:49:33 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO224^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25 % Computer : n002.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 16:42:52 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.30 Running first-order model finding
% 0.25/0.30 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
% 0.25/0.36 % (1525398)Will run a generic schedule for satisfiability detection.
% 0.25/0.36 % (1525404)% WARNING: option uhcvi not known.
% 0.25/0.36 % (1525408)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1808254239:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.25/0.36 % (1525404)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2810833641:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.25/0.36 % (1525404)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.36 % (1525404)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.25/0.36 % (1525403)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1150327524_3000 on theBenchmark for (3000ds/0Mi)
% 0.25/0.36 % (1525405)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2268837415:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.25/0.36 % (1525406)dis+10_1_sil=32000:sp=arity:random_seed=492179573:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.25/0.36 % (1525407)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=128023161:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.25/0.36 % (1525409)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3848385412:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.25/0.36 % Exception at run slice level
% 0.25/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.36 % (1525407)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.36 % (1525408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1525398-1525408"...
% 0.25/0.36 % (1525408)...printing done.
% 0.25/0.36 % (1525408)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% 0.25/0.36 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.36 thf(func_def_1, type, cLIKE: ($i > $i > $o)).
% 0.25/0.36 thf(func_def_2, type, cWRH: ($i > $o)).
% 0.25/0.36 thf(func_def_3, type, cW: ($i > $o)).
% 0.25/0.36 thf(func_def_4, type, cUNIQUE: ($i > $o)).
% 0.25/0.36 thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.25/0.36 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.25/0.36 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.36 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.36 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.25/0.36 thf(func_def_17, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.25/0.36 thf(f1,conjecture,(
% 0.25/0.36 ((cWRH @ cS) & (cW @ cS) & (cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cW @ X1) & (cWRH @ X1)) => (X0 = X1)))) => ? [X2 : ($i > $o)] : ((((X2 @ cJ)) = ? [X0 : $i] : ((cLIKE @ cJ @ X0) & (cWRH @ X0) & (cW @ X0) & (cUNIQUE @ X0))) & (((X2 @ cP)) = ((cLIKE @ cP @ cS))))),
% 0.25/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLING1)).
% 0.25/0.36 thf(f2,negated_conjecture,(
% 0.25/0.36 ~(((cWRH @ cS) & (cW @ cS) & (cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cW @ X1) & (cWRH @ X1)) => (X0 = X1)))) => ? [X2 : ($i > $o)] : ((((X2 @ cJ)) = ? [X0 : $i] : ((cLIKE @ cJ @ X0) & (cWRH @ X0) & (cW @ X0) & (cUNIQUE @ X0))) & (((X2 @ cP)) = ((cLIKE @ cP @ cS)))))),
% 0.25/0.36 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.36 thf(f3,plain,(
% 0.25/0.36 ~(((cWRH @ cS) & (cW @ cS) & (cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cW @ X1) & (cWRH @ X1)) => (X0 = X1)))) => ? [X2 : ($i > $o)] : ((((X2 @ cJ)) = ? [X3 : $i] : ((cLIKE @ cJ @ X3) & (cWRH @ X3) & (cW @ X3) & (cUNIQUE @ X3))) & (((X2 @ cP)) = ((cLIKE @ cP @ cS)))))),
% 0.25/0.36 inference(rectify,[],[f2])).
% 0.25/0.36 thf(f4,plain,(
% 0.25/0.36 ~(((((cWRH @ cS)) = $true) & (((cW @ cS)) = $true) & (((cUNIQUE @ cS)) = $true) & ! [X0 : $i] : ((((cUNIQUE @ X0)) = $true) => ! [X1 : $i] : (((((cW @ X1)) = $true) & (((cWRH @ X1)) = $true)) => (X0 = X1)))) => ? [X2 : ($i > $o)] : ((((X2 @ cJ)) = ((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0)))))) & (((X2 @ cP)) = ((cLIKE @ cP @ cS)))))),
% 0.25/0.36 inference(fool_elimination,[],[f3])).
% 0.25/0.36 thf(f5,plain,(
% 0.25/0.36 ! [X2 : ($i > $o)] : ((((X2 @ cJ)) != ((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0)))))) | (((X2 @ cP)) != ((cLIKE @ cP @ cS)))) & ((((cWRH @ cS)) = $true) & (((cW @ cS)) = $true) & (((cUNIQUE @ cS)) = $true) & ! [X0 : $i] : (! [X1 : $i] : ((X0 = X1) | ((((cW @ X1)) != $true) | (((cWRH @ X1)) != $true))) | (((cUNIQUE @ X0)) != $true)))),
% 0.25/0.36 inference(ennf_transformation,[],[f4])).
% 0.25/0.36 thf(f6,plain,(
% 0.25/0.36 ! [X2 : ($i > $o)] : ((((X2 @ cJ)) != ((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0)))))) | (((X2 @ cP)) != ((cLIKE @ cP @ cS)))) & (((cWRH @ cS)) = $true) & (((cW @ cS)) = $true) & (((cUNIQUE @ cS)) = $true) & ! [X0 : $i] : (! [X1 : $i] : ((X0 = X1) | (((cW @ X1)) != $true) | (((cWRH @ X1)) != $true)) | (((cUNIQUE @ X0)) != $true))),
% 0.25/0.36 inference(flattening,[],[f5])).
% 0.25/0.36 thf(f7,plain,(
% 0.25/0.36 ! [X0 : ($i > $o)] : ((((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))))) != ((X0 @ cJ))) | (((cLIKE @ cP @ cS)) != ((X0 @ cP)))) & (((cWRH @ cS)) = $true) & (((cW @ cS)) = $true) & (((cUNIQUE @ cS)) = $true) & ! [X1 : $i] : (! [X2 : $i] : ((X1 = X2) | ($true != ((cW @ X2))) | ($true != ((cWRH @ X2)))) | ($true != ((cUNIQUE @ X1))))),
% 0.25/0.36 inference(rectify,[],[f6])).
% 0.25/0.36 thf(f8,plain,(
% 0.25/0.36 ( ! [X2 : $i,X1 : $i] : (($true != ((cW @ X2))) | (X1 = X2) | ($true != ((cWRH @ X2))) | ($true != ((cUNIQUE @ X1)))) )),
% 0.25/0.36 inference(cnf_transformation,[],[f7])).
% 0.25/0.36 thf(f9,plain,(
% 0.25/0.36 (((cUNIQUE @ cS)) = $true)),
% 0.25/0.36 inference(cnf_transformation,[],[f7])).
% 0.25/0.36 thf(f10,plain,(
% 0.25/0.36 (((cW @ cS)) = $true)),
% 0.25/0.36 inference(cnf_transformation,[],[f7])).
% 0.25/0.36 thf(f11,plain,(
% 0.25/0.36 (((cWRH @ cS)) = $true)),
% 0.25/0.36 inference(cnf_transformation,[],[f7])).
% 0.25/0.36 thf(f12,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : ((((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))))) != ((X0 @ cJ))) | (((cLIKE @ cP @ cS)) != ((X0 @ cP)))) )),
% 0.25/0.36 inference(cnf_transformation,[],[f7])).
% 0.25/0.36 thf(f14,definition,(
% 0.25/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.25/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.25/0.36 thf(f15,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0)))))) | (((cLIKE @ cP @ cS)) != ((X0 @ cP))) | ($true = ((X0 @ cJ)))) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f12])).
% 0.25/0.36 thf(f16,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : ((((?? @ $i @ (^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))))) = $false) | (((cLIKE @ cP @ cS)) != ((X0 @ cP))) | (((X0 @ cJ)) = $false)) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f12])).
% 0.25/0.36 thf(f17,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ X1))) | (((cLIKE @ cP @ cS)) != ((X0 @ cP))) | (((X0 @ cJ)) = $false)) )),
% 0.25/0.36 inference(pi_proxy_clausification,[],[f16])).
% 0.25/0.36 thf(f18,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ X1))) | (((cLIKE @ cP @ cS)) = $true) | (((X0 @ cJ)) = $false) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f17])).
% 0.25/0.36 thf(f19,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ X1))) | (((cLIKE @ cP @ cS)) = $false) | (((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f17])).
% 0.25/0.36 thf(f20,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = (((((cUNIQUE @ X1) & (cW @ X1)) & (cWRH @ X1)) & (cLIKE @ cJ @ X1)))) | (((cLIKE @ cP @ cS)) = $false) | (((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(beta-eta_normalization,[],[f19])).
% 0.25/0.36 thf(f21,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $false) | (((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false) | ($false = ((((cUNIQUE @ X1) & (cW @ X1)) & (cWRH @ X1))))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f20])).
% 0.25/0.36 thf(f22,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $false) | (((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false) | (((cWRH @ X1)) = $false) | ($false = (((cUNIQUE @ X1) & (cW @ X1))))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f21])).
% 0.25/0.36 thf(f23,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $false) | (((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false) | (((cWRH @ X1)) = $false) | (((cW @ X1)) = $false) | (((cUNIQUE @ X1)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f22])).
% 0.25/0.36 thf(f24,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = (((((cUNIQUE @ X1) & (cW @ X1)) & (cWRH @ X1)) & (cLIKE @ cJ @ X1)))) | (((cLIKE @ cP @ cS)) = $true) | (((X0 @ cJ)) = $false) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(beta-eta_normalization,[],[f18])).
% 0.25/0.36 thf(f25,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $true) | (((X0 @ cJ)) = $false) | ($true = ((X0 @ cP))) | ($false = ((((cUNIQUE @ X1) & (cW @ X1)) & (cWRH @ X1))))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f24])).
% 0.25/0.36 thf(f26,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $true) | (((X0 @ cJ)) = $false) | ($true = ((X0 @ cP))) | (((cWRH @ X1)) = $false) | ($false = (((cUNIQUE @ X1) & (cW @ X1))))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f25])).
% 0.25/0.36 thf(f27,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cLIKE @ cP @ cS)) = $true) | (((X0 @ cJ)) = $false) | ($true = ((X0 @ cP))) | (((cWRH @ X1)) = $false) | (((cW @ X1)) = $false) | (((cUNIQUE @ X1)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f26])).
% 0.25/0.36 thf(f28,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ sK0))) | (((cLIKE @ cP @ cS)) != ((X0 @ cP))) | ($true = ((X0 @ cJ)))) )),
% 0.25/0.36 inference(sigma_proxy_clausification,[],[f15])).
% 0.25/0.36 thf(f29,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ sK0))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f28])).
% 0.25/0.36 thf(f30,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((^[Y0 : $i]: ((((cUNIQUE @ Y0) & (cW @ Y0)) & (cWRH @ Y0)) & (cLIKE @ cJ @ Y0))) @ sK0))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f28])).
% 0.25/0.36 thf(f31,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((((cUNIQUE @ sK0) & (cW @ sK0)) & (cWRH @ sK0)) & (cLIKE @ cJ @ sK0)))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(beta-eta_normalization,[],[f30])).
% 0.25/0.36 thf(f32,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cLIKE @ cJ @ sK0))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f31])).
% 0.25/0.36 thf(f33,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((((cUNIQUE @ sK0) & (cW @ sK0)) & (cWRH @ sK0)))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f31])).
% 0.25/0.36 thf(f35,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((cUNIQUE @ sK0) & (cW @ sK0)))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f33])).
% 0.25/0.36 thf(f37,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cUNIQUE @ sK0))) | (((cLIKE @ cP @ cS)) = $false) | ($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false)) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f35])).
% 0.25/0.36 thf(f38,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((((cUNIQUE @ sK0) & (cW @ sK0)) & (cWRH @ sK0)) & (cLIKE @ cJ @ sK0)))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(beta-eta_normalization,[],[f29])).
% 0.25/0.36 thf(f39,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cLIKE @ cJ @ sK0))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f38])).
% 0.25/0.36 thf(f40,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((((cUNIQUE @ sK0) & (cW @ sK0)) & (cWRH @ sK0)))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f38])).
% 0.25/0.36 thf(f41,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cWRH @ sK0))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f40])).
% 0.25/0.36 thf(f42,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = (((cUNIQUE @ sK0) & (cW @ sK0)))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f40])).
% 0.25/0.36 thf(f43,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cW @ sK0))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f42])).
% 0.25/0.36 thf(f44,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((cUNIQUE @ sK0))) | (((cLIKE @ cP @ cS)) = $true) | ($true = ((X0 @ cJ))) | ($true = ((X0 @ cP)))) )),
% 0.25/0.36 inference(and_proxy_clausification,[],[f42])).
% 0.25/0.36 thf(f46,definition,(
% 0.25/0.36 spl1_1 <=> ! [X0 : ($i > $o)] : ((((X0 @ cJ)) = $false) | (((X0 @ cP)) = $false))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.25/0.36 thf(f47,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : ((((X0 @ cP)) = $false) | (((X0 @ cJ)) = $false)) ) | ~spl1_1),
% 0.25/0.36 inference(avatar_component_clause,[],[f46])).
% 0.25/0.36 thf(f49,definition,(
% 0.25/0.36 spl1_2 <=> (((cLIKE @ cP @ cS)) = $false)),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.25/0.36 thf(f50,plain,(
% 0.25/0.36 (((cLIKE @ cP @ cS)) != $false) | spl1_2),
% 0.25/0.36 inference(avatar_component_clause,[],[f49])).
% 0.25/0.36 thf(f51,plain,(
% 0.25/0.36 (((cLIKE @ cP @ cS)) = $false) | ~spl1_2),
% 0.25/0.36 inference(avatar_component_clause,[],[f49])).
% 0.25/0.36 thf(f53,definition,(
% 0.25/0.36 spl1_3 <=> ! [X1 : $i] : (($false = ((cLIKE @ cJ @ X1))) | (((cUNIQUE @ X1)) = $false) | (((cW @ X1)) = $false) | (((cWRH @ X1)) = $false))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.25/0.36 thf(f54,plain,(
% 0.25/0.36 ( ! [X1 : $i] : ((((cUNIQUE @ X1)) = $false) | ($false = ((cLIKE @ cJ @ X1))) | (((cW @ X1)) = $false) | (((cWRH @ X1)) = $false)) ) | ~spl1_3),
% 0.25/0.36 inference(avatar_component_clause,[],[f53])).
% 0.25/0.36 thf(f55,plain,(
% 0.25/0.36 spl1_1 | spl1_2 | spl1_3),
% 0.25/0.36 inference(avatar_split_clause,[],[f23,f53,f49,f46])).
% 0.25/0.36 thf(f57,definition,(
% 0.25/0.36 spl1_4 <=> ! [X0 : ($i > $o)] : ((((X0 @ cJ)) = $false) | ($true = ((X0 @ cP))))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.25/0.36 thf(f58,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ cP))) | (((X0 @ cJ)) = $false)) ) | ~spl1_4),
% 0.25/0.36 inference(avatar_component_clause,[],[f57])).
% 0.25/0.36 thf(f60,definition,(
% 0.25/0.36 spl1_5 <=> (((cLIKE @ cP @ cS)) = $true)),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.25/0.36 thf(f61,plain,(
% 0.25/0.36 (((cLIKE @ cP @ cS)) != $true) | spl1_5),
% 0.25/0.36 inference(avatar_component_clause,[],[f60])).
% 0.25/0.36 thf(f62,plain,(
% 0.25/0.36 (((cLIKE @ cP @ cS)) = $true) | ~spl1_5),
% 0.25/0.36 inference(avatar_component_clause,[],[f60])).
% 0.25/0.36 thf(f63,plain,(
% 0.25/0.36 spl1_4 | spl1_5 | spl1_3),
% 0.25/0.36 inference(avatar_split_clause,[],[f27,f53,f60,f57])).
% 0.25/0.36 thf(f65,definition,(
% 0.25/0.36 spl1_6 <=> ! [X0 : ($i > $o)] : (($true = ((X0 @ cJ))) | (((X0 @ cP)) = $false))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 0.25/0.36 thf(f66,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : ((((X0 @ cP)) = $false) | ($true = ((X0 @ cJ)))) ) | ~spl1_6),
% 0.25/0.36 inference(avatar_component_clause,[],[f65])).
% 0.25/0.36 thf(f68,definition,(
% 0.25/0.36 spl1_7 <=> ($true = ((cUNIQUE @ sK0)))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
% 0.25/0.36 thf(f70,plain,(
% 0.25/0.36 ($true = ((cUNIQUE @ sK0))) | ~spl1_7),
% 0.25/0.36 inference(avatar_component_clause,[],[f68])).
% 0.25/0.36 thf(f71,plain,(
% 0.25/0.36 spl1_6 | spl1_2 | spl1_7),
% 0.25/0.36 inference(avatar_split_clause,[],[f37,f68,f49,f65])).
% 0.25/0.36 thf(f73,definition,(
% 0.25/0.36 spl1_8 <=> ($true = ((cW @ sK0)))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition])).
% 0.25/0.36 thf(f75,plain,(
% 0.25/0.36 ($true = ((cW @ sK0))) | ~spl1_8),
% 0.25/0.36 inference(avatar_component_clause,[],[f73])).
% 0.25/0.36 thf(f78,definition,(
% 0.25/0.36 spl1_9 <=> ($true = ((cWRH @ sK0)))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
% 0.25/0.36 thf(f80,plain,(
% 0.25/0.36 ($true = ((cWRH @ sK0))) | ~spl1_9),
% 0.25/0.36 inference(avatar_component_clause,[],[f78])).
% 0.25/0.36 thf(f83,definition,(
% 0.25/0.36 spl1_10 <=> ($true = ((cLIKE @ cJ @ sK0)))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition])).
% 0.25/0.36 thf(f85,plain,(
% 0.25/0.36 ($true = ((cLIKE @ cJ @ sK0))) | ~spl1_10),
% 0.25/0.36 inference(avatar_component_clause,[],[f83])).
% 0.25/0.36 thf(f86,plain,(
% 0.25/0.36 spl1_6 | spl1_2 | spl1_10),
% 0.25/0.36 inference(avatar_split_clause,[],[f32,f83,f49,f65])).
% 0.25/0.36 thf(f88,definition,(
% 0.25/0.36 spl1_11 <=> ! [X0 : ($i > $o)] : (($true = ((X0 @ cJ))) | ($true = ((X0 @ cP))))),
% 0.25/0.36 introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition])).
% 0.25/0.36 thf(f89,plain,(
% 0.25/0.36 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ cP))) | ($true = ((X0 @ cJ)))) ) | ~spl1_11),
% 0.25/0.36 inference(avatar_component_clause,[],[f88])).
% 0.25/0.36 thf(f90,plain,(
% 0.25/0.36 spl1_11 | spl1_5 | spl1_7),
% 0.25/0.36 inference(avatar_split_clause,[],[f44,f68,f60,f88])).
% 0.25/0.36 thf(f91,plain,(
% 0.25/0.36 spl1_11 | spl1_5 | spl1_8),
% 0.25/0.36 inference(avatar_split_clause,[],[f43,f73,f60,f88])).
% 0.25/0.36 thf(f92,plain,(
% 0.25/0.36 spl1_11 | spl1_5 | spl1_9),
% 0.25/0.36 inference(avatar_split_clause,[],[f41,f78,f60,f88])).
% 0.25/0.36 thf(f93,plain,(
% 0.25/0.36 spl1_11 | spl1_5 | spl1_10),
% 0.25/0.36 inference(avatar_split_clause,[],[f39,f83,f60,f88])).
% 0.25/0.36 thf(f94,plain,(
% 0.25/0.36 ($true = $false) | (~spl1_2 | ~spl1_5)),
% 0.25/0.36 inference(forward_demodulation,[],[f62,f51])).
% 0.25/0.36 thf(f95,plain,(
% 0.25/0.36 $false | (~spl1_2 | ~spl1_5)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f94])).
% 0.25/0.36 thf(f96,plain,(
% 0.25/0.36 ~spl1_2 | ~spl1_5),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f95])).
% 0.25/0.36 thf(f98,plain,(
% 0.25/0.36 ( ! [X0 : $i] : (($true != $true) | (cS = X0) | (((cWRH @ cS)) != $true) | (((cUNIQUE @ X0)) != $true)) )),
% 0.25/0.36 inference(constrained_superposition,[],[f8,f10])).
% 0.25/0.36 thf(f99,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((cS = X0) | (((cWRH @ cS)) != $true) | (((cUNIQUE @ X0)) != $true)) )),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f98])).
% 0.25/0.36 thf(f100,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((((cUNIQUE @ X0)) != $true) | (cS = X0)) )),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f99,f11])).
% 0.25/0.36 thf(f110,plain,(
% 0.25/0.36 ( ! [X0 : $i] : (($true != $true) | (sK0 = X0) | ($true != ((cWRH @ sK0))) | (((cUNIQUE @ X0)) != $true)) ) | ~spl1_8),
% 0.25/0.36 inference(constrained_superposition,[],[f8,f75])).
% 0.25/0.36 thf(f111,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((sK0 = X0) | ($true != ((cWRH @ sK0))) | (((cUNIQUE @ X0)) != $true)) ) | ~spl1_8),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f110])).
% 0.25/0.36 thf(f112,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((((cUNIQUE @ X0)) != $true) | (sK0 = X0)) ) | (~spl1_8 | ~spl1_9)),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f111,f80])).
% 0.25/0.36 thf(f113,plain,(
% 0.25/0.36 ($true != $true) | (cS = sK0) | ~spl1_7),
% 0.25/0.36 inference(constrained_superposition,[],[f100,f70])).
% 0.25/0.36 thf(f114,plain,(
% 0.25/0.36 ( ! [X0 : $i] : (($true != $true) | (cS = X0) | (((cUNIQUE @ X0)) = $false)) )),
% 0.25/0.36 inference(constrained_superposition,[],[f100,f14])).
% 0.25/0.36 thf(f115,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((cS = X0) | (((cUNIQUE @ X0)) = $false)) )),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f114])).
% 0.25/0.36 thf(f116,plain,(
% 0.25/0.36 (cS = sK0) | ~spl1_7),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f113])).
% 0.25/0.36 thf(f141,plain,(
% 0.25/0.36 ($true != $true) | (cS = sK0) | (~spl1_8 | ~spl1_9)),
% 0.25/0.36 inference(constrained_superposition,[],[f112,f9])).
% 0.25/0.36 thf(f145,plain,(
% 0.25/0.36 (cS = sK0) | (~spl1_8 | ~spl1_9)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f141])).
% 0.25/0.36 thf(f148,plain,(
% 0.25/0.36 (cP = cJ) | ~spl1_4),
% 0.25/0.36 inference(leibniz_equality_elimination,[],[f58])).
% 0.25/0.36 thf(f197,plain,(
% 0.25/0.36 ($true = ((cLIKE @ cJ @ cS))) | (~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(constrained_superposition,[],[f85,f116])).
% 0.25/0.36 thf(f200,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ cP))) | ($false = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(primitive_instantiation,[],[f47])).
% 0.25/0.36 thf(f224,plain,(
% 0.25/0.36 ( ! [X0 : $o] : (($false = X0) | ($false = X0) | ($false = (((^[Y0 : $i]: ($true)) @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(constrained_superposition,[],[f14,f47])).
% 0.25/0.36 thf(f237,plain,(
% 0.25/0.36 ( ! [X0 : $o] : (($false = X0) | ($false = (((^[Y0 : $i]: ($true)) @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(duplicate_literal_removal,[],[f224])).
% 0.25/0.36 thf(f238,plain,(
% 0.25/0.36 ( ! [X0 : $o] : (($false = X0) | ($true = $false)) ) | ~spl1_1),
% 0.25/0.36 inference(beta-eta_normalization,[],[f237])).
% 0.25/0.36 thf(f239,plain,(
% 0.25/0.36 ( ! [X0 : $o] : (($false = X0)) ) | ~spl1_1),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f238])).
% 0.25/0.36 thf(f282,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($false = ((~ (X1 @ cP)))) | ($false = ((~ (X1 @ cJ))))) ) | ~spl1_1),
% 0.25/0.36 inference(beta-eta_normalization,[],[f200])).
% 0.25/0.36 thf(f283,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ cP))) | ($false = ((~ (X1 @ cJ))))) ) | ~spl1_1),
% 0.25/0.36 inference(not_proxy_clausification,[],[f282])).
% 0.25/0.36 thf(f284,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ cP))) | ($true = ((X1 @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(not_proxy_clausification,[],[f283])).
% 0.25/0.36 thf(f291,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = $false) | ($true = ((X1 @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(forward_demodulation,[],[f284,f239])).
% 0.25/0.36 thf(f292,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ cJ)))) ) | ~spl1_1),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f291])).
% 0.25/0.36 thf(f293,plain,(
% 0.25/0.36 ($true = $false) | ~spl1_1),
% 0.25/0.36 inference(forward_demodulation,[],[f292,f239])).
% 0.25/0.36 thf(f294,plain,(
% 0.25/0.36 $false | ~spl1_1),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f293])).
% 0.25/0.36 thf(f295,plain,(
% 0.25/0.36 ~spl1_1),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f294])).
% 0.25/0.36 thf(f324,plain,(
% 0.25/0.36 ($true = $false) | ($false = ((cLIKE @ cJ @ cS))) | (((cW @ cS)) = $false) | (((cWRH @ cS)) = $false) | ~spl1_3),
% 0.25/0.36 inference(constrained_superposition,[],[f9,f54])).
% 0.25/0.36 thf(f327,plain,(
% 0.25/0.36 ($false = ((cLIKE @ cJ @ cS))) | (((cW @ cS)) = $false) | (((cWRH @ cS)) = $false) | ~spl1_3),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f324])).
% 0.25/0.36 thf(f333,plain,(
% 0.25/0.36 ($true = $false) | (((cW @ cS)) = $false) | (((cWRH @ cS)) = $false) | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(forward_demodulation,[],[f327,f197])).
% 0.25/0.36 thf(f334,plain,(
% 0.25/0.36 (((cW @ cS)) = $false) | (((cWRH @ cS)) = $false) | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f333])).
% 0.25/0.36 thf(f341,plain,(
% 0.25/0.36 ($true = $false) | (((cWRH @ cS)) = $false) | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(forward_demodulation,[],[f334,f10])).
% 0.25/0.36 thf(f342,plain,(
% 0.25/0.36 (((cWRH @ cS)) = $false) | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f341])).
% 0.25/0.36 thf(f350,plain,(
% 0.25/0.36 ($true = $false) | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(constrained_superposition,[],[f342,f11])).
% 0.25/0.36 thf(f357,plain,(
% 0.25/0.36 $false | (~spl1_3 | ~spl1_7 | ~spl1_10)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f350])).
% 0.25/0.36 thf(f358,plain,(
% 0.25/0.36 ~spl1_3 | ~spl1_7 | ~spl1_10),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f357])).
% 0.25/0.36 thf(f359,plain,(
% 0.25/0.36 ($true = $false) | ($false = ((cLIKE @ cJ @ cS))) | (((cWRH @ cS)) = $false) | ~spl1_3),
% 0.25/0.36 inference(forward_demodulation,[],[f327,f10])).
% 0.25/0.36 thf(f360,plain,(
% 0.25/0.36 ($false = ((cLIKE @ cJ @ cS))) | (((cWRH @ cS)) = $false) | ~spl1_3),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f359])).
% 0.25/0.36 thf(f363,plain,(
% 0.25/0.36 ($true = $false) | ($false = ((cLIKE @ cJ @ cS))) | ~spl1_3),
% 0.25/0.36 inference(forward_demodulation,[],[f360,f11])).
% 0.25/0.36 thf(f364,plain,(
% 0.25/0.36 ($false = ((cLIKE @ cJ @ cS))) | ~spl1_3),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f363])).
% 0.25/0.36 thf(f367,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((((cUNIQUE @ X0)) = $false) | (((cLIKE @ cJ @ X0)) = $false)) ) | ~spl1_3),
% 0.25/0.36 inference(constrained_superposition,[],[f364,f115])).
% 0.25/0.36 thf(f370,plain,(
% 0.25/0.36 ($true = ((cLIKE @ cJ @ cS))) | (~spl1_8 | ~spl1_9 | ~spl1_10)),
% 0.25/0.36 inference(constrained_superposition,[],[f85,f145])).
% 0.25/0.36 thf(f471,plain,(
% 0.25/0.36 ($true = $false) | ($false = ((cLIKE @ cJ @ cS))) | ~spl1_3),
% 0.25/0.36 inference(constrained_superposition,[],[f367,f9])).
% 0.25/0.36 thf(f484,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ cP))) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ cJ)))) ) | ~spl1_6),
% 0.25/0.36 inference(primitive_instantiation,[],[f66])).
% 0.25/0.36 thf(f566,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($false = ((~ (X1 @ cP)))) | ($true = ((~ (X1 @ cJ))))) ) | ~spl1_6),
% 0.25/0.36 inference(beta-eta_normalization,[],[f484])).
% 0.25/0.36 thf(f567,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ cP))) | ($true = ((~ (X1 @ cJ))))) ) | ~spl1_6),
% 0.25/0.36 inference(not_proxy_clausification,[],[f566])).
% 0.25/0.36 thf(f568,plain,(
% 0.25/0.36 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ cP))) | ($false = ((X1 @ cJ)))) ) | ~spl1_6),
% 0.25/0.36 inference(not_proxy_clausification,[],[f567])).
% 0.25/0.36 thf(f572,plain,(
% 0.25/0.36 spl1_4 | ~spl1_6),
% 0.25/0.36 inference(avatar_split_clause,[],[f568,f65,f57])).
% 0.25/0.36 thf(f580,plain,(
% 0.25/0.36 ($true = (((^[Y0 : $i]: ($false)) @ cP))) | ($true = (((^[Y0 : $i]: ($false)) @ cJ))) | ~spl1_11),
% 0.25/0.36 inference(primitive_instantiation,[],[f89])).
% 0.25/0.36 thf(f705,plain,(
% 0.25/0.36 ($true = $false) | ($true = $false) | ~spl1_11),
% 0.25/0.36 inference(beta-eta_normalization,[],[f580])).
% 0.25/0.36 thf(f706,plain,(
% 0.25/0.36 ($true = $false) | ~spl1_11),
% 0.25/0.36 inference(duplicate_literal_removal,[],[f705])).
% 0.25/0.36 thf(f707,plain,(
% 0.25/0.36 $false | ~spl1_11),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f706])).
% 0.25/0.36 thf(f708,plain,(
% 0.25/0.36 ~spl1_11),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f707])).
% 0.25/0.36 thf(f751,plain,(
% 0.25/0.36 ($false = ((cLIKE @ cJ @ cS))) | ~spl1_3),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f471])).
% 0.25/0.36 thf(f760,plain,(
% 0.25/0.36 ($false != ((cLIKE @ cJ @ cS))) | (spl1_2 | ~spl1_4)),
% 0.25/0.36 inference(forward_demodulation,[],[f50,f148])).
% 0.25/0.36 thf(f768,plain,(
% 0.25/0.36 $false | (spl1_2 | ~spl1_3 | ~spl1_4)),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f760,f751])).
% 0.25/0.36 thf(f769,plain,(
% 0.25/0.36 spl1_2 | ~spl1_3 | ~spl1_4),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f768])).
% 0.25/0.36 thf(f776,plain,(
% 0.25/0.36 ($true != ((cLIKE @ cJ @ cS))) | (~spl1_4 | spl1_5)),
% 0.25/0.36 inference(forward_demodulation,[],[f61,f148])).
% 0.25/0.36 thf(f781,plain,(
% 0.25/0.36 $false | (~spl1_4 | spl1_5 | ~spl1_8 | ~spl1_9 | ~spl1_10)),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f776,f370])).
% 0.25/0.36 thf(f782,plain,(
% 0.25/0.36 ~spl1_4 | spl1_5 | ~spl1_8 | ~spl1_9 | ~spl1_10),
% 0.25/0.36 inference(avatar_contradiction_clause,[],[f781])).
% 0.25/0.36 cnf(s1, plain, spl1_1 | spl1_2 | spl1_3, inference(sat_conversion,[],[f55])).
% 0.25/0.36 cnf(s2, plain, spl1_3 | spl1_4 | spl1_5, inference(sat_conversion,[],[f63])).
% 0.25/0.36 cnf(s3, plain, spl1_2 | spl1_6 | spl1_7, inference(sat_conversion,[],[f71])).
% 0.25/0.36 cnf(s6, plain, spl1_2 | spl1_6 | spl1_10, inference(sat_conversion,[],[f86])).
% 0.25/0.36 cnf(s7, plain, spl1_5 | spl1_7 | spl1_11, inference(sat_conversion,[],[f90])).
% 0.25/0.36 cnf(s8, plain, spl1_5 | spl1_8 | spl1_11, inference(sat_conversion,[],[f91])).
% 0.25/0.36 cnf(s9, plain, spl1_5 | spl1_9 | spl1_11, inference(sat_conversion,[],[f92])).
% 0.25/0.36 cnf(s10, plain, spl1_5 | spl1_10 | spl1_11, inference(sat_conversion,[],[f93])).
% 0.25/0.36 cnf(s11, plain, ~spl1_2 | ~spl1_5, inference(sat_conversion,[],[f96])).
% 0.25/0.36 cnf(s15, plain, ~spl1_1, inference(sat_conversion,[],[f295])).
% 0.25/0.36 cnf(s17, plain, ~spl1_3 | ~spl1_7 | ~spl1_10, inference(sat_conversion,[],[f358])).
% 0.25/0.36 cnf(s21, plain, spl1_4 | ~spl1_6, inference(sat_conversion,[],[f572])).
% 0.25/0.36 cnf(s22, plain, ~spl1_11, inference(sat_conversion,[],[f708])).
% 0.25/0.36 cnf(s34, plain, spl1_2 | ~spl1_3 | ~spl1_4, inference(sat_conversion,[],[f769])).
% 0.25/0.36 cnf(s36, plain, ~spl1_4 | spl1_5 | ~spl1_8 | ~spl1_9 | ~spl1_10, inference(sat_conversion,[],[f782])).
% 0.25/0.36 cnf(s37, plain, spl1_5 | spl1_10, inference(rat,[],[s10,s22])).
% 0.25/0.36 cnf(s38, plain, spl1_5 | spl1_9, inference(rat,[],[s9,s22])).
% 0.25/0.36 cnf(s39, plain, spl1_5 | spl1_8, inference(rat,[],[s8,s22])).
% 0.25/0.36 cnf(s40, plain, spl1_5 | spl1_7, inference(rat,[],[s7,s22])).
% 0.25/0.36 cnf(s41, plain, spl1_2 | spl1_3, inference(rat,[],[s1,s15])).
% 0.25/0.36 cnf(s42, plain, ~spl1_3 | spl1_2, inference(rat,[],[s17,s3,s6,s21,s34])).
% 0.25/0.36 cnf(s43, plain, spl1_2, inference(rat,[],[s42,s41])).
% 0.25/0.36 cnf(s44, plain, ~spl1_5, inference(rat,[],[s11,s43])).
% 0.25/0.36 cnf(s45, plain, spl1_10, inference(rat,[],[s37,s44])).
% 0.25/0.36 cnf(s46, plain, spl1_9, inference(rat,[],[s38,s44])).
% 0.25/0.36 cnf(s47, plain, spl1_8, inference(rat,[],[s39,s44])).
% 0.25/0.36 cnf(s48, plain, spl1_7, inference(rat,[],[s40,s44])).
% 0.25/0.36 cnf(s49, plain, ~spl1_4, inference(rat,[],[s36,s45,s46,s47,s44])).
% 0.25/0.36 cnf(s50, plain, spl1_3, inference(rat,[],[s2,s49,s44])).
% 0.25/0.36 cnf(s51, plain, $false, inference(rat,[],[s17,s50,s45,s48])).
% 0.25/0.36 thf(f784,plain,(
% 0.25/0.36 $false),
% 0.25/0.36 inference(avatar_sat_refutation,[],[s51])).
% 0.25/0.36 % SZS output end Proof for theBenchmark
% 0.25/0.36 % (1525408)------------------------------
% 0.25/0.36 % (1525408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (1525408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (1525408)CaDiCaL version: 2.1.3
% 0.25/0.36 % (1525408)Termination reason: Refutation
% 0.25/0.36 % (1525408)Time elapsed: 0.021 s
% 0.25/0.36 % (1525408)Peak memory usage: 12 MB
% 0.25/0.36 % (1525408)Instructions burned: 42 (million)
% 0.25/0.36 % (1525398)Success in time 0.044 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------