%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET582^5 : 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 : n015.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 08:23:38 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET582^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:41:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.21/0.28 % (3533852)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3533866)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1991489577:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (3533866)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (3533863)% WARNING: option uhcvi not known.
% 0.21/0.28 % (3533866) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3533852-3533866"...
% 0.21/0.28 % (3533866)...printing done.
% 0.21/0.28 % (3533866)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, a: $tType).
% 0.21/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_3, type, vOR: ($o > $o > $o)).
% 0.21/0.28 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.21/0.28 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_8, type, sK0: (a > $o)).
% 0.21/0.28 thf(func_def_9, type, sK1: (a > $o)).
% 0.21/0.28 thf(func_def_10, type, sK2: (a > $o)).
% 0.21/0.28 thf(func_def_11, type, sK3: a).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((~(X0 @ X3) <=> (X1 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : ((~(X1 @ X4) & (X2 @ X4)) | (~(X2 @ X4) & (X1 @ X4))))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_25_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((~(X0 @ X3) <=> (X1 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : ((~(X1 @ X4) & (X2 @ X4)) | (~(X2 @ X4) & (X1 @ X4))))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((~(X0 @ X3) <=> (X1 @ X3)) <=> (X2 @ X3)) => (X0 = (^[X4 : a] : ((~(X1 @ X4) & (X2 @ X4)) | (~(X2 @ X4) & (X1 @ X4))))))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((~ (((X0 @ X3)) = $true) <=> (((X1 @ X3)) = $true)) <=> (((X2 @ X3)) = $true)) => ((^[Y0 : a]: (((X1 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X1 @ Y0))))) = X0))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : (((((X0 @ X3)) != $true) <=> (((X1 @ X3)) = $true)) <=> (((X2 @ X3)) = $true)) => ((^[Y0 : a]: (((X1 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X1 @ Y0))))) = X0))),
% 0.21/0.28 inference(flattening,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (((X1 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X1 @ Y0))))) != X0) & ! [X3 : a] : (((((X0 @ X3)) != $true) <=> (((X1 @ X3)) = $true)) <=> (((X2 @ X3)) = $true)))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((^[Y0 : a]: (((X1 @ Y0) & (~ (X2 @ Y0))) | ((X2 @ Y0) & (~ (X1 @ Y0))))) != X0) & ! [X3 : a] : (((((((X0 @ X3)) != $true) | (((X1 @ X3)) != $true)) & ((((X1 @ X3)) = $true) | (((X0 @ X3)) = $true))) | (((X2 @ X3)) != $true)) & ((((X2 @ X3)) = $true) | (((((X1 @ X3)) != $true) | (((X0 @ X3)) = $true)) & ((((X1 @ X3)) = $true) | (((X0 @ X3)) != $true))))))),
% 0.21/0.28 inference(nnf_transformation,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (sK0 != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK1 @ Y0)))))) & ! [X3 : a] : ((((($true != ((sK0 @ X3))) | ($true != ((sK1 @ X3)))) & (($true = ((sK1 @ X3))) | ($true = ((sK0 @ X3))))) | ($true != ((sK2 @ X3)))) & (($true = ((sK2 @ X3))) | ((($true != ((sK1 @ X3))) | ($true = ((sK0 @ X3)))) & (($true = ((sK1 @ X3))) | ($true != ((sK0 @ X3)))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true != ((sK0 @ X3))) | ($true = ((sK1 @ X3))) | ($true = ((sK2 @ X3)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true != ((sK1 @ X3))) | ($true = ((sK2 @ X3)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true = ((sK1 @ X3))) | ($true != ((sK2 @ X3)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ( ! [X3 : a] : (($true != ((sK0 @ X3))) | ($true != ((sK1 @ X3))) | ($true != ((sK2 @ X3)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (sK0 != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK1 @ Y0))))))),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f15,definition,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ( ! [X0 : a] : (($true != $true) | ($true != ((sK1 @ X0))) | ($true != ((sK2 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.21/0.29 inference(constrained_superposition,[],[f12,f15])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ( ! [X0 : a] : (($true != $true) | ($true = ((sK1 @ X0))) | ($true = ((sK2 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.21/0.29 inference(constrained_superposition,[],[f9,f15])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ( ! [X0 : a] : (($false = ((sK0 @ X0))) | ($true = ((sK2 @ X0))) | ($true = ((sK1 @ X0)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f27])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ( ! [X0 : a] : (($false = ((sK0 @ X0))) | ($true != ((sK2 @ X0))) | ($true != ((sK1 @ X0)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f26])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 (((sK0 @ sK3)) != (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK1 @ Y0))))) @ sK3)))),
% 0.21/0.29 inference(negative_extensionality,[],[f13])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK1 @ Y0))))) @ sK3)))),
% 0.21/0.29 inference(xor_proxy_clausification,[],[f48])).
% 0.21/0.29 thf(f50,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK2 @ Y0))) | ((sK2 @ Y0) & (~ (sK1 @ Y0))))) @ sK3)))),
% 0.21/0.29 inference(xor_proxy_clausification,[],[f48])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = ((((sK1 @ sK3) & (~ (sK2 @ sK3))) | ((sK2 @ sK3) & (~ (sK1 @ sK3))))))),
% 0.21/0.29 inference(beta-eta_normalization,[],[f50])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = (((sK2 @ sK3) & (~ (sK1 @ sK3)))))),
% 0.21/0.29 inference(or_proxy_clausification,[],[f51])).
% 0.21/0.29 thf(f53,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = (((sK1 @ sK3) & (~ (sK2 @ sK3)))))),
% 0.21/0.29 inference(or_proxy_clausification,[],[f51])).
% 0.21/0.29 thf(f54,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = ((~ (sK2 @ sK3)))) | ($false = ((sK1 @ sK3)))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f53])).
% 0.21/0.29 thf(f55,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($true = ((sK2 @ sK3))) | ($false = ((sK1 @ sK3)))),
% 0.21/0.29 inference(not_proxy_clausification,[],[f54])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($false = ((~ (sK1 @ sK3)))) | ($false = ((sK2 @ sK3)))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f52])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | ($false = ((sK2 @ sK3)))),
% 0.21/0.29 inference(not_proxy_clausification,[],[f56])).
% 0.21/0.29 thf(f58,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = ((((sK1 @ sK3) & (~ (sK2 @ sK3))) | ((sK2 @ sK3) & (~ (sK1 @ sK3))))))),
% 0.21/0.29 inference(beta-eta_normalization,[],[f49])).
% 0.21/0.29 thf(f59,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = (((sK2 @ sK3) & (~ (sK1 @ sK3))))) | ($true = (((sK1 @ sK3) & (~ (sK2 @ sK3)))))),
% 0.21/0.29 inference(or_proxy_clausification,[],[f58])).
% 0.21/0.29 thf(f60,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = ((~ (sK1 @ sK3)))) | ($true = (((sK1 @ sK3) & (~ (sK2 @ sK3)))))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f59])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = ((sK2 @ sK3))) | ($true = (((sK1 @ sK3) & (~ (sK2 @ sK3)))))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f59])).
% 0.21/0.29 thf(f63,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = ((sK2 @ sK3))) | ($true = ((sK1 @ sK3)))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f61])).
% 0.21/0.29 thf(f65,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($false = ((sK1 @ sK3))) | ($true = (((sK1 @ sK3) & (~ (sK2 @ sK3)))))),
% 0.21/0.29 inference(not_proxy_clausification,[],[f60])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($false = ((sK1 @ sK3))) | ($true = ((~ (sK2 @ sK3))))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f65])).
% 0.21/0.29 thf(f68,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($false = ((sK1 @ sK3))) | ($false = ((sK2 @ sK3)))),
% 0.21/0.29 inference(not_proxy_clausification,[],[f66])).
% 0.21/0.29 thf(f70,definition,(
% 0.21/0.29 spl4_1 <=> ($false = ((sK1 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ($false = ((sK1 @ sK3))) | ~spl4_1),
% 0.21/0.29 inference(avatar_component_clause,[],[f70])).
% 0.21/0.29 thf(f74,definition,(
% 0.21/0.29 spl4_2 <=> ($true = ((sK2 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.21/0.29 thf(f75,plain,(
% 0.21/0.29 ($true != ((sK2 @ sK3))) | spl4_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f74])).
% 0.21/0.29 thf(f76,plain,(
% 0.21/0.29 ($true = ((sK2 @ sK3))) | ~spl4_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f74])).
% 0.21/0.29 thf(f78,definition,(
% 0.21/0.29 spl4_3 <=> ($false = ((sK0 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.21/0.29 thf(f80,plain,(
% 0.21/0.29 ($false = ((sK0 @ sK3))) | ~spl4_3),
% 0.21/0.29 inference(avatar_component_clause,[],[f78])).
% 0.21/0.29 thf(f81,plain,(
% 0.21/0.29 spl4_1 | spl4_2 | spl4_3),
% 0.21/0.29 inference(avatar_split_clause,[],[f55,f78,f74,f70])).
% 0.21/0.29 thf(f83,definition,(
% 0.21/0.29 spl4_4 <=> ($false = ((sK2 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.21/0.29 thf(f85,plain,(
% 0.21/0.29 ($false = ((sK2 @ sK3))) | ~spl4_4),
% 0.21/0.29 inference(avatar_component_clause,[],[f83])).
% 0.21/0.29 thf(f87,definition,(
% 0.21/0.29 spl4_5 <=> ($true = ((sK1 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.21/0.29 thf(f88,plain,(
% 0.21/0.29 ($true != ((sK1 @ sK3))) | spl4_5),
% 0.21/0.29 inference(avatar_component_clause,[],[f87])).
% 0.21/0.29 thf(f89,plain,(
% 0.21/0.29 ($true = ((sK1 @ sK3))) | ~spl4_5),
% 0.21/0.29 inference(avatar_component_clause,[],[f87])).
% 0.21/0.29 thf(f90,plain,(
% 0.21/0.29 spl4_4 | spl4_5 | spl4_3),
% 0.21/0.29 inference(avatar_split_clause,[],[f57,f78,f87,f83])).
% 0.21/0.29 thf(f91,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ($true = ((sK2 @ sK3)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f63,f10])).
% 0.21/0.29 thf(f93,definition,(
% 0.21/0.29 spl4_6 <=> ($true = ((sK0 @ sK3)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.21/0.29 thf(f95,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK3))) | ~spl4_6),
% 0.21/0.29 inference(avatar_component_clause,[],[f93])).
% 0.21/0.29 thf(f96,plain,(
% 0.21/0.29 spl4_4 | spl4_1 | spl4_6),
% 0.21/0.29 inference(avatar_split_clause,[],[f68,f93,f70,f83])).
% 0.21/0.29 thf(f97,plain,(
% 0.21/0.29 spl4_2 | spl4_6),
% 0.21/0.29 inference(avatar_split_clause,[],[f91,f93,f74])).
% 0.21/0.29 thf(f111,plain,(
% 0.21/0.29 ($true = $false) | (~spl4_2 | ~spl4_4)),
% 0.21/0.29 inference(constrained_superposition,[],[f85,f76])).
% 0.21/0.29 thf(f117,plain,(
% 0.21/0.29 $false | (~spl4_2 | ~spl4_4)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f111])).
% 0.21/0.29 thf(f118,plain,(
% 0.21/0.29 ~spl4_2 | ~spl4_4),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f117])).
% 0.21/0.29 thf(f121,plain,(
% 0.21/0.29 ($true = $false) | ($true = ((sK2 @ sK3))) | ($true = ((sK1 @ sK3))) | ~spl4_6),
% 0.21/0.29 inference(constrained_superposition,[],[f95,f29])).
% 0.21/0.29 thf(f122,plain,(
% 0.21/0.29 ($true = $false) | ($true != ((sK2 @ sK3))) | ($true != ((sK1 @ sK3))) | ~spl4_6),
% 0.21/0.29 inference(constrained_superposition,[],[f30,f95])).
% 0.21/0.29 thf(f129,plain,(
% 0.21/0.29 ($true != ((sK2 @ sK3))) | ($true != ((sK1 @ sK3))) | ~spl4_6),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f122])).
% 0.21/0.29 thf(f130,plain,(
% 0.21/0.29 ($true = ((sK2 @ sK3))) | ($true = ((sK1 @ sK3))) | ~spl4_6),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.29 thf(f133,plain,(
% 0.21/0.29 ($true != ((sK1 @ sK3))) | (~spl4_2 | ~spl4_6)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f129,f76])).
% 0.21/0.29 thf(f143,plain,(
% 0.21/0.29 ($true = ((sK1 @ sK3))) | (spl4_2 | ~spl4_6)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f130,f75])).
% 0.21/0.29 thf(f150,plain,(
% 0.21/0.29 ($true = $false) | (~spl4_1 | spl4_2 | ~spl4_6)),
% 0.21/0.29 inference(forward_demodulation,[],[f143,f72])).
% 0.21/0.29 thf(f151,plain,(
% 0.21/0.29 $false | (~spl4_1 | spl4_2 | ~spl4_6)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.21/0.29 thf(f152,plain,(
% 0.21/0.29 ~spl4_1 | spl4_2 | ~spl4_6),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f151])).
% 0.21/0.29 thf(f154,plain,(
% 0.21/0.29 ~spl4_5 | ~spl4_2 | ~spl4_6),
% 0.21/0.29 inference(avatar_split_clause,[],[f133,f93,f74,f87])).
% 0.21/0.29 thf(f157,plain,(
% 0.21/0.29 ($true = $false) | ($true = ((sK1 @ sK3))) | ($true != ((sK2 @ sK3))) | ~spl4_3),
% 0.21/0.29 inference(constrained_superposition,[],[f80,f11])).
% 0.21/0.29 thf(f159,plain,(
% 0.21/0.29 ($true = $false) | (~spl4_3 | ~spl4_6)),
% 0.21/0.29 inference(constrained_superposition,[],[f80,f95])).
% 0.21/0.29 thf(f165,plain,(
% 0.21/0.29 ($true = $false) | (~spl4_3 | ~spl4_6)),
% 0.21/0.29 inference(constrained_superposition,[],[f95,f80])).
% 0.21/0.29 thf(f166,plain,(
% 0.21/0.29 $false | (~spl4_3 | ~spl4_6)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f165])).
% 0.21/0.29 thf(f167,plain,(
% 0.21/0.29 ~spl4_3 | ~spl4_6),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f166])).
% 0.21/0.29 thf(f171,plain,(
% 0.21/0.29 $false | (~spl4_3 | ~spl4_6)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f159])).
% 0.21/0.29 thf(f172,plain,(
% 0.21/0.29 ~spl4_3 | ~spl4_6),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f171])).
% 0.21/0.29 thf(f174,plain,(
% 0.21/0.29 ($true = ((sK1 @ sK3))) | ($true != ((sK2 @ sK3))) | ~spl4_3),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f157])).
% 0.21/0.29 thf(f176,plain,(
% 0.21/0.29 ($true != ((sK2 @ sK3))) | (~spl4_3 | spl4_5)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f174,f88])).
% 0.21/0.29 thf(f179,plain,(
% 0.21/0.29 $false | (~spl4_2 | ~spl4_3 | spl4_5)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f176,f76])).
% 0.21/0.29 thf(f180,plain,(
% 0.21/0.29 ~spl4_2 | ~spl4_3 | spl4_5),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f179])).
% 0.21/0.29 thf(f181,plain,(
% 0.21/0.29 ($true = $false) | (~spl4_1 | ~spl4_5)),
% 0.21/0.29 inference(forward_demodulation,[],[f89,f72])).
% 0.21/0.29 thf(f182,plain,(
% 0.21/0.29 $false | (~spl4_1 | ~spl4_5)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f181])).
% 0.21/0.29 thf(f183,plain,(
% 0.21/0.29 ~spl4_1 | ~spl4_5),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f182])).
% 0.21/0.29 cnf(s1, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f81])).
% 0.21/0.29 cnf(s2, plain, spl4_3 | spl4_4 | spl4_5, inference(sat_conversion,[],[f90])).
% 0.21/0.29 cnf(s3, plain, spl4_1 | spl4_4 | spl4_6, inference(sat_conversion,[],[f96])).
% 0.21/0.29 cnf(s4, plain, spl4_2 | spl4_6, inference(sat_conversion,[],[f97])).
% 0.21/0.29 cnf(s6, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f118])).
% 0.21/0.29 cnf(s12, plain, ~spl4_1 | spl4_2 | ~spl4_6, inference(sat_conversion,[],[f152])).
% 0.21/0.29 cnf(s16, plain, ~spl4_2 | ~spl4_5 | ~spl4_6, inference(sat_conversion,[],[f154])).
% 0.21/0.29 cnf(s18, plain, ~spl4_3 | ~spl4_6, inference(sat_conversion,[],[f167])).
% 0.21/0.29 cnf(s19, plain, ~spl4_3 | ~spl4_6, inference(sat_conversion,[],[f172])).
% 0.21/0.29 cnf(s21, plain, ~spl4_2 | ~spl4_3 | spl4_5, inference(sat_conversion,[],[f180])).
% 0.21/0.29 cnf(s22, plain, ~spl4_1 | ~spl4_5, inference(sat_conversion,[],[f183])).
% 0.21/0.29 cnf(s23, plain, spl4_2 | spl4_1, inference(rat,[],[s18,s1,s4])).
% 0.21/0.29 cnf(s24, plain, spl4_1, inference(rat,[],[s2,s16,s19,s3,s6,s23])).
% 0.21/0.29 cnf(s25, plain, ~spl4_5, inference(rat,[],[s22,s24])).
% 0.21/0.29 cnf(s26, plain, spl4_2, inference(rat,[],[s4,s12,s24])).
% 0.21/0.29 cnf(s27, plain, ~spl4_4, inference(rat,[],[s6,s26])).
% 0.21/0.29 cnf(s28, plain, ~spl4_3, inference(rat,[],[s21,s25,s26])).
% 0.21/0.29 cnf(s29, plain, $false, inference(rat,[],[s2,s25,s27,s28])).
% 0.21/0.29 thf(f184,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s29])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (3533866)------------------------------
% 0.21/0.29 % (3533866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3533866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3533866)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3533866)Termination reason: Refutation
% 0.21/0.29 % (3533866)Time elapsed: 0.004 s
% 0.21/0.29 % (3533866)Peak memory usage: 12 MB
% 0.21/0.29 % (3533866)Instructions burned: 8 (million)
% 0.21/0.29 % (3533852)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------