%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO175^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:05 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO175^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:37:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.27 % (34580)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (34585)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3433382533_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.27 % Exception at run slice level
% 0.09/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.27 % (34586)% WARNING: option uhcvi not known.
% 0.09/0.27 % (34586)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2225220131:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.27 % (34587)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1150845367:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.27 % (34588)dis+10_1_sil=32000:sp=arity:random_seed=1187791776:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.27 % (34590)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1758686901:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.27 % (34586)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (34586)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.27 % (34589)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2480043693:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.27 % (34589)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (34590) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-34580-34590"...
% 0.09/0.27 % (34590)...printing done.
% 0.09/0.27 % (34588) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-34580-34588"...
% 0.09/0.27 % (34587) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-34580-34587"...
% 0.09/0.27 % (34590)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% 0.09/0.27 thf(type_def_5, type, p: $tType).
% 0.09/0.27 thf(type_def_6, type, a: $tType).
% 0.09/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.27 thf(func_def_0, type, cGRAIN: p).
% 0.09/0.27 thf(func_def_1, type, cVEG_EATS: (a > p > $o)).
% 0.09/0.27 thf(func_def_2, type, cMEAT_EATS: (a > a > $o)).
% 0.09/0.27 thf(func_def_3, type, cSNAIL: a).
% 0.09/0.27 thf(func_def_4, type, cCATERPILLAR: a).
% 0.09/0.27 thf(func_def_5, type, cBIRD: a).
% 0.09/0.27 thf(func_def_6, type, cWOLF: a).
% 0.09/0.27 thf(func_def_7, type, cFOX: a).
% 0.09/0.27 thf(func_def_8, type, cSMALLER: (a > a > $o)).
% 0.09/0.27 thf(func_def_12, type, sK0: p).
% 0.09/0.27 thf(func_def_13, type, sK1: p).
% 0.09/0.27 thf(f1,conjecture,(
% 0.09/0.27 (? [X1 : p] : (cVEG_EATS @ cSNAIL @ X1) & ? [X1 : p] : (cVEG_EATS @ cCATERPILLAR @ X1) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ~(cMEAT_EATS @ cWOLF @ cFOX) & (cSMALLER @ cFOX @ cWOLF) & (cSMALLER @ cBIRD @ cFOX) & (cSMALLER @ cSNAIL @ cBIRD) & (cSMALLER @ cCATERPILLAR @ cBIRD) & ! [X0 : a] : (! [X2 : a] : ((? [X3 : p] : (cVEG_EATS @ X2 @ X3) & (cSMALLER @ X2 @ X0)) => (cMEAT_EATS @ X0 @ X2)) | ! [X1 : p] : (cVEG_EATS @ X0 @ X1))) => ? [X0 : a,X1 : a] : ((cVEG_EATS @ X1 @ cGRAIN) & (cMEAT_EATS @ X0 @ X1))),
% 0.09/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPUZ031_1_HO)).
% 0.09/0.27 thf(f2,negated_conjecture,(
% 0.09/0.27 ~((? [X1 : p] : (cVEG_EATS @ cSNAIL @ X1) & ? [X1 : p] : (cVEG_EATS @ cCATERPILLAR @ X1) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ~(cMEAT_EATS @ cWOLF @ cFOX) & (cSMALLER @ cFOX @ cWOLF) & (cSMALLER @ cBIRD @ cFOX) & (cSMALLER @ cSNAIL @ cBIRD) & (cSMALLER @ cCATERPILLAR @ cBIRD) & ! [X0 : a] : (! [X2 : a] : ((? [X3 : p] : (cVEG_EATS @ X2 @ X3) & (cSMALLER @ X2 @ X0)) => (cMEAT_EATS @ X0 @ X2)) | ! [X1 : p] : (cVEG_EATS @ X0 @ X1))) => ? [X0 : a,X1 : a] : ((cVEG_EATS @ X1 @ cGRAIN) & (cMEAT_EATS @ X0 @ X1)))),
% 0.09/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.27 thf(f3,plain,(
% 0.09/0.27 ~((? [X0 : p] : (cVEG_EATS @ cSNAIL @ X0) & ? [X1 : p] : (cVEG_EATS @ cCATERPILLAR @ X1) & ~(cMEAT_EATS @ cBIRD @ cSNAIL) & (cMEAT_EATS @ cBIRD @ cCATERPILLAR) & ~(cVEG_EATS @ cWOLF @ cGRAIN) & ~(cMEAT_EATS @ cWOLF @ cFOX) & (cSMALLER @ cFOX @ cWOLF) & (cSMALLER @ cBIRD @ cFOX) & (cSMALLER @ cSNAIL @ cBIRD) & (cSMALLER @ cCATERPILLAR @ cBIRD) & ! [X2 : a] : (! [X3 : a] : ((? [X4 : p] : (cVEG_EATS @ X3 @ X4) & (cSMALLER @ X3 @ X2)) => (cMEAT_EATS @ X2 @ X3)) | ! [X5 : p] : (cVEG_EATS @ X2 @ X5))) => ? [X6 : a,X7 : a] : ((cVEG_EATS @ X7 @ cGRAIN) & (cMEAT_EATS @ X6 @ X7)))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f4,plain,(
% 0.19/0.27 ~((? [X0 : p] : (((cVEG_EATS @ cSNAIL @ X0)) = $true) & ? [X1 : p] : (((cVEG_EATS @ cCATERPILLAR @ X1)) = $true) & ~ (((cMEAT_EATS @ cBIRD @ cSNAIL)) = $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & ~ (((cVEG_EATS @ cWOLF @ cGRAIN)) = $true) & ~ (((cMEAT_EATS @ cWOLF @ cFOX)) = $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X2 : a] : (! [X3 : a] : ((? [X4 : p] : (((cVEG_EATS @ X3 @ X4)) = $true) & (((cSMALLER @ X3 @ X2)) = $true)) => (((cMEAT_EATS @ X2 @ X3)) = $true)) | ! [X5 : p] : (((cVEG_EATS @ X2 @ X5)) = $true))) => ? [X6 : a,X7 : a] : ((((cVEG_EATS @ X7 @ cGRAIN)) = $true) & (((cMEAT_EATS @ X6 @ X7)) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ~((? [X0 : p] : (((cVEG_EATS @ cSNAIL @ X0)) = $true) & ? [X1 : p] : (((cVEG_EATS @ cCATERPILLAR @ X1)) = $true) & (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true) & (((cMEAT_EATS @ cWOLF @ cFOX)) != $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X2 : a] : (! [X3 : a] : ((? [X4 : p] : (((cVEG_EATS @ X3 @ X4)) = $true) & (((cSMALLER @ X3 @ X2)) = $true)) => (((cMEAT_EATS @ X2 @ X3)) = $true)) | ! [X5 : p] : (((cVEG_EATS @ X2 @ X5)) = $true))) => ? [X6 : a,X7 : a] : ((((cVEG_EATS @ X7 @ cGRAIN)) = $true) & (((cMEAT_EATS @ X6 @ X7)) = $true)))),
% 0.19/0.27 inference(flattening,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 ! [X6 : a,X7 : a] : ((((cVEG_EATS @ X7 @ cGRAIN)) != $true) | (((cMEAT_EATS @ X6 @ X7)) != $true)) & (? [X0 : p] : (((cVEG_EATS @ cSNAIL @ X0)) = $true) & ? [X1 : p] : (((cVEG_EATS @ cCATERPILLAR @ X1)) = $true) & (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true) & (((cMEAT_EATS @ cWOLF @ cFOX)) != $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X2 : a] : (! [X3 : a] : ((((cMEAT_EATS @ X2 @ X3)) = $true) | (! [X4 : p] : (((cVEG_EATS @ X3 @ X4)) != $true) | (((cSMALLER @ X3 @ X2)) != $true))) | ! [X5 : p] : (((cVEG_EATS @ X2 @ X5)) = $true)))),
% 0.19/0.27 inference(ennf_transformation,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 ! [X6 : a,X7 : a] : ((((cVEG_EATS @ X7 @ cGRAIN)) != $true) | (((cMEAT_EATS @ X6 @ X7)) != $true)) & ? [X0 : p] : (((cVEG_EATS @ cSNAIL @ X0)) = $true) & ? [X1 : p] : (((cVEG_EATS @ cCATERPILLAR @ X1)) = $true) & (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true) & (((cMEAT_EATS @ cWOLF @ cFOX)) != $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X2 : a] : (! [X3 : a] : ((((cMEAT_EATS @ X2 @ X3)) = $true) | ! [X4 : p] : (((cVEG_EATS @ X3 @ X4)) != $true) | (((cSMALLER @ X3 @ X2)) != $true)) | ! [X5 : p] : (((cVEG_EATS @ X2 @ X5)) = $true))),
% 0.19/0.27 inference(flattening,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ! [X0 : a,X1 : a] : ((((cVEG_EATS @ X1 @ cGRAIN)) != $true) | (((cMEAT_EATS @ X0 @ X1)) != $true)) & ? [X2 : p] : ($true = ((cVEG_EATS @ cSNAIL @ X2))) & ? [X3 : p] : ($true = ((cVEG_EATS @ cCATERPILLAR @ X3))) & (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true) & (((cMEAT_EATS @ cWOLF @ cFOX)) != $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X4 : a] : (! [X5 : a] : (($true = ((cMEAT_EATS @ X4 @ X5))) | ! [X6 : p] : ($true != ((cVEG_EATS @ X5 @ X6))) | ($true != ((cSMALLER @ X5 @ X4)))) | ! [X7 : p] : ($true = ((cVEG_EATS @ X4 @ X7))))),
% 0.19/0.27 inference(rectify,[],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ! [X0 : a,X1 : a] : ((((cVEG_EATS @ X1 @ cGRAIN)) != $true) | (((cMEAT_EATS @ X0 @ X1)) != $true)) & ($true = ((cVEG_EATS @ cSNAIL @ sK0))) & ($true = ((cVEG_EATS @ cCATERPILLAR @ sK1))) & (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true) & (((cMEAT_EATS @ cBIRD @ cCATERPILLAR)) = $true) & (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true) & (((cMEAT_EATS @ cWOLF @ cFOX)) != $true) & (((cSMALLER @ cFOX @ cWOLF)) = $true) & (((cSMALLER @ cBIRD @ cFOX)) = $true) & (((cSMALLER @ cSNAIL @ cBIRD)) = $true) & (((cSMALLER @ cCATERPILLAR @ cBIRD)) = $true) & ! [X4 : a] : (! [X5 : a] : (($true = ((cMEAT_EATS @ X4 @ X5))) | ! [X6 : p] : ($true != ((cVEG_EATS @ X5 @ X6))) | ($true != ((cSMALLER @ X5 @ X4)))) | ! [X7 : p] : ($true = ((cVEG_EATS @ X4 @ X7))))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f8])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ( ! [X6 : p,X7 : p,X4 : a,X5 : a] : (($true != ((cVEG_EATS @ X5 @ X6))) | ($true = ((cMEAT_EATS @ X4 @ X5))) | ($true != ((cSMALLER @ X5 @ X4))) | ($true = ((cVEG_EATS @ X4 @ X7)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 (((cSMALLER @ cSNAIL @ cBIRD)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 (((cSMALLER @ cBIRD @ cFOX)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 (((cSMALLER @ cFOX @ cWOLF)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 (((cMEAT_EATS @ cWOLF @ cFOX)) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 (((cVEG_EATS @ cWOLF @ cGRAIN)) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 (((cMEAT_EATS @ cBIRD @ cSNAIL)) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ($true = ((cVEG_EATS @ cSNAIL @ sK0)))),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : a] : ((((cVEG_EATS @ X1 @ cGRAIN)) != $true) | (((cMEAT_EATS @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 thf(f23,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : p] : (($true != $true) | ($true = ((cMEAT_EATS @ X0 @ cSNAIL))) | ($true != ((cSMALLER @ cSNAIL @ X0))) | (((cVEG_EATS @ X0 @ X1)) = $true)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f10,f20])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : p] : (($true != ((cSMALLER @ cSNAIL @ X0))) | ($true = ((cMEAT_EATS @ X0 @ cSNAIL))) | (((cVEG_EATS @ X0 @ X1)) = $true)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f25])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X2 : a,X3 : p,X0 : a,X1 : p] : (($true != $true) | ($true = ((cMEAT_EATS @ X2 @ X0))) | ($true != ((cSMALLER @ X0 @ X2))) | (((cVEG_EATS @ X2 @ X3)) = $true) | (((cVEG_EATS @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f10,f23])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ($true != $true) | (((cVEG_EATS @ cWOLF @ cGRAIN)) = $false)),
% 0.19/0.27 inference(constrained_superposition,[],[f16,f23])).
% 0.19/0.27 thf(f36,plain,(
% 0.19/0.27 (((cVEG_EATS @ cWOLF @ cGRAIN)) = $false)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f34])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X2 : a,X3 : p,X0 : a,X1 : p] : (($true != ((cSMALLER @ X0 @ X2))) | ($true = ((cMEAT_EATS @ X2 @ X0))) | (((cVEG_EATS @ X2 @ X3)) = $true) | (((cVEG_EATS @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f33])).
% 0.19/0.27 thf(f66,plain,(
% 0.19/0.27 ( ! [X0 : p] : (($true != $true) | (((cMEAT_EATS @ cBIRD @ cSNAIL)) = $true) | ($true = ((cVEG_EATS @ cBIRD @ X0)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f26,f12])).
% 0.19/0.27 thf(f69,plain,(
% 0.19/0.27 ( ! [X0 : p] : ((((cMEAT_EATS @ cBIRD @ cSNAIL)) = $true) | ($true = ((cVEG_EATS @ cBIRD @ X0)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f66])).
% 0.19/0.27 thf(f70,plain,(
% 0.19/0.27 ( ! [X0 : p] : (($true = ((cVEG_EATS @ cBIRD @ X0)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f69,f18])).
% 0.19/0.27 thf(f71,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($true != $true) | ($true != ((cMEAT_EATS @ X0 @ cBIRD)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f21,f70])).
% 0.19/0.27 thf(f74,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($true != ((cMEAT_EATS @ X0 @ cBIRD)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f71])).
% 0.19/0.27 thf(f83,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : (($true != $true) | ($true = ((cMEAT_EATS @ cFOX @ cBIRD))) | ($true = ((cVEG_EATS @ cFOX @ X0))) | ($false = ((cVEG_EATS @ cBIRD @ X1)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f37,f13])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : (($true != $true) | (((cMEAT_EATS @ cWOLF @ cFOX)) = $true) | ($true = ((cVEG_EATS @ cWOLF @ X0))) | ($false = ((cVEG_EATS @ cFOX @ X1)))) )),
% 0.19/0.27 inference(constrained_superposition,[],[f37,f14])).
% 0.19/0.27 thf(f87,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : ((((cMEAT_EATS @ cWOLF @ cFOX)) = $true) | ($true = ((cVEG_EATS @ cWOLF @ X0))) | ($false = ((cVEG_EATS @ cFOX @ X1)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f84])).
% 0.19/0.27 thf(f88,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : (($true = ((cMEAT_EATS @ cFOX @ cBIRD))) | ($true = ((cVEG_EATS @ cFOX @ X0))) | ($false = ((cVEG_EATS @ cBIRD @ X1)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f83])).
% 0.19/0.27 thf(f91,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : (($true = ((cVEG_EATS @ cWOLF @ X0))) | ($false = ((cVEG_EATS @ cFOX @ X1)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f87,f15])).
% 0.19/0.27 thf(f92,plain,(
% 0.19/0.27 ( ! [X0 : p,X1 : p] : (($true = ((cVEG_EATS @ cFOX @ X0))) | ($false = ((cVEG_EATS @ cBIRD @ X1)))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f88,f74])).
% 0.19/0.27 thf(f94,definition,(
% 0.19/0.27 spl2_1 <=> ! [X1 : p] : ($false = ((cVEG_EATS @ cFOX @ X1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.19/0.27 thf(f95,plain,(
% 0.19/0.27 ( ! [X1 : p] : (($false = ((cVEG_EATS @ cFOX @ X1)))) ) | ~spl2_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f94])).
% 0.19/0.27 thf(f97,definition,(
% 0.19/0.27 spl2_2 <=> ! [X0 : p] : ($true = ((cVEG_EATS @ cWOLF @ X0)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.19/0.27 thf(f98,plain,(
% 0.19/0.27 ( ! [X0 : p] : (($true = ((cVEG_EATS @ cWOLF @ X0)))) ) | ~spl2_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f97])).
% 0.19/0.27 thf(f99,plain,(
% 0.19/0.27 spl2_1 | spl2_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f91,f97,f94])).
% 0.19/0.27 thf(f100,plain,(
% 0.19/0.27 ( ! [X0 : p] : (($true = $false) | ($true = ((cVEG_EATS @ cFOX @ X0)))) )),
% 0.19/0.27 inference(forward_demodulation,[],[f92,f70])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ( ! [X0 : p] : (($true = ((cVEG_EATS @ cFOX @ X0)))) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f100])).
% 0.19/0.27 thf(f102,plain,(
% 0.19/0.27 ($true = $false) | ~spl2_2),
% 0.19/0.27 inference(constrained_superposition,[],[f98,f36])).
% 0.19/0.27 thf(f113,plain,(
% 0.19/0.27 $false | ~spl2_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f102])).
% 0.19/0.27 thf(f114,plain,(
% 0.19/0.27 ~spl2_2),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f113])).
% 0.19/0.27 thf(f119,plain,(
% 0.19/0.27 ($true = $false) | ~spl2_1),
% 0.19/0.27 inference(constrained_superposition,[],[f101,f95])).
% 0.19/0.27 thf(f127,plain,(
% 0.19/0.27 $false | ~spl2_1),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f119])).
% 0.19/0.27 thf(f128,plain,(
% 0.19/0.27 ~spl2_1),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f127])).
% 0.19/0.27 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f99])).
% 0.19/0.27 cnf(s4, plain, ~spl2_2, inference(sat_conversion,[],[f114])).
% 0.19/0.27 cnf(s6, plain, ~spl2_1, inference(sat_conversion,[],[f128])).
% 0.19/0.27 cnf(s7, plain, $false, inference(rat,[],[s1,s4,s6])).
% 0.19/0.27 thf(f129,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s7])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (34590)------------------------------
% 0.19/0.27 % (34590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (34590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (34590)CaDiCaL version: 2.1.3
% 0.19/0.27 % (34590)Termination reason: Refutation
% 0.19/0.27 % (34590)Time elapsed: 0.004 s
% 0.19/0.27 % (34590)Peak memory usage: 13 MB
% 0.19/0.27 % (34590)Instructions burned: 12 (million)
% 0.19/0.27 % (34580)Success in time 0.046 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------