%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV124^5 : 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 : n004.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 08:39:01 AM UTC 2026
% Result : Theorem 0.43s 0.31s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV124^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n004.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:12:08 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 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
% 0.43/0.31 % (1413980)Will run a generic schedule for satisfiability detection.
% 0.43/0.31 % (1413986)% WARNING: option uhcvi not known.
% 0.43/0.31 % (1413985)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1884953785_2999 on theBenchmark for (2999ds/0Mi)
% 0.43/0.31 % (1413986)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3481219933:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.43/0.31 % (1413987)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1454076432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.43/0.31 % (1413989)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3835463675:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.43/0.31 % (1413990)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2943926585:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.31 % (1413991)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=827425751:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.43/0.31 % (1413986)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (1413989)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (1413986)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.31 % Exception at run slice level
% 0.43/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.31 % (1413988)dis+10_1_sil=32000:sp=arity:random_seed=1823101322:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.43/0.31 % (1413998)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4142507763:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.43/0.31 % Exception at run slice level
% 0.43/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.31 % (1413988)Instruction limit reached!
% 0.43/0.31 % (1413988)------------------------------
% 0.43/0.31 % (1413988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (1413988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (1413988)CaDiCaL version: 2.1.3
% 0.43/0.31 % (1413988)Termination reason: Instruction limit
% 0.43/0.31 % (1413988)Termination phase: Saturation
% 0.43/0.31 % (1413988)Time elapsed: 0.027 s
% 0.43/0.31 % (1413988)Peak memory usage: 13 MB
% 0.43/0.31 % (1413988)Instructions burned: 105 (million)
% 0.43/0.31 % (1414001)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3451422300:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.31 % (1414002)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=766236968:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.43/0.31 % (1414002)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (1414002)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.31 % (1413989)Instruction limit reached!
% 0.43/0.31 % (1413989)------------------------------
% 0.43/0.31 % (1413989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (1413989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (1413989)CaDiCaL version: 2.1.3
% 0.43/0.31 % (1413989)Termination reason: Instruction limit
% 0.43/0.31 % (1413989)Termination phase: Saturation
% 0.43/0.31 % (1413989)Time elapsed: 0.054 s
% 0.43/0.31 % (1413989)Peak memory usage: 12 MB
% 0.43/0.31 % (1413989)Instructions burned: 116 (million)
% 0.43/0.31 % (1413990)Instruction limit reached!
% 0.43/0.31 % (1413990)------------------------------
% 0.43/0.31 % (1413990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (1413990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (1413990)CaDiCaL version: 2.1.3
% 0.43/0.31 % (1413990)Termination reason: Instruction limit
% 0.43/0.31 % (1413990)Termination phase: Saturation
% 0.43/0.31 % (1413990)Time elapsed: 0.061 s
% 0.43/0.31 % (1413990)Peak memory usage: 13 MB
% 0.43/0.31 % (1413990)Instructions burned: 131 (million)
% 0.43/0.31 % (1413991) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1413980-1413991"...
% 0.43/0.31 % (1413991)...printing done.
% 0.43/0.31 % (1413991)Refutation found. Thanks to Tanya!
% 0.43/0.31 % SZS status Theorem for theBenchmark
% 0.43/0.31 % SZS output start Proof for theBenchmark
% 0.43/0.31 thf(type_def_5, type, a: $tType).
% 0.43/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.43/0.31 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.43/0.31 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.43/0.31 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.43/0.31 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.43/0.31 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.43/0.31 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.43/0.31 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.43/0.31 thf(func_def_10, type, sK0: ((a > a > $o) > $o)).
% 0.43/0.31 thf(func_def_11, type, sK1: ((a > a > $o) > $o)).
% 0.43/0.31 thf(func_def_12, type, sK2: a).
% 0.43/0.31 thf(func_def_13, type, sK3: a).
% 0.43/0.31 thf(func_def_14, type, sK4: (a > a > $o)).
% 0.43/0.31 thf(func_def_15, type, sK5: ((a > a > $o) > a)).
% 0.43/0.31 thf(func_def_16, type, sK6: ((a > a > $o) > a)).
% 0.43/0.31 thf(func_def_17, type, sK7: ((a > a > $o) > a > a > $o)).
% 0.43/0.31 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.43/0.31 thf(func_def_19, type, sK8: ((a > a > $o) > a > a > a > a > $o)).
% 0.43/0.31 thf(func_def_21, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.43/0.31 thf(func_def_22, type, db3: !>[X0: $tType]:(X0)).
% 0.43/0.31 thf(func_def_23, type, db4: !>[X0: $tType]:(X0)).
% 0.43/0.31 thf(f1,conjecture,(
% 0.43/0.31 ! [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & (X1 @ X7)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : ((X7 = (^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : (((X0 @ X11) & ! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10))))) & (X1 @ X8))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))),
% 0.43/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM254_A_pme)).
% 0.43/0.31 thf(f2,negated_conjecture,(
% 0.43/0.31 ~ ! [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & (X1 @ X7)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & ? [X8 : (a > a > $o)] : ((X7 = (^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : (((X0 @ X11) & ! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13))) => (X11 @ X9 @ X10))))) & (X1 @ X8))) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))),
% 0.43/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.43/0.31 thf(f3,plain,(
% 0.43/0.31 ~ ! [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((X7 @ X5 @ X6) & (X1 @ X7)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X8 : (a > a > $o)] : (((X0 @ X8) & ! [X9 : a,X10 : a] : (? [X11 : (a > a > $o)] : ((X11 @ X9 @ X10) & ? [X12 : (a > a > $o)] : ((X11 = (^[X13 : a, X14 : a] : (! [X15 : (a > a > $o)] : (((X0 @ X15) & ! [X16 : a,X17 : a] : ((X12 @ X16 @ X17) => (X15 @ X16 @ X17))) => (X15 @ X13 @ X14))))) & (X1 @ X12))) => (X8 @ X9 @ X10))) => (X8 @ X2 @ X3)))),
% 0.43/0.31 inference(rectify,[],[f2])).
% 0.43/0.31 thf(f4,plain,(
% 0.43/0.31 ~ ! [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (! [X4 : (a > a > $o)] : (((((X0 @ X4)) = $true) & ! [X5 : a,X6 : a] : (? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & (((X1 @ X7)) = $true)) => (((X4 @ X5 @ X6)) = $true))) => (((X4 @ X2 @ X3)) = $true)) => ! [X8 : (a > a > $o)] : (((((X0 @ X8)) = $true) & ! [X9 : a,X10 : a] : (? [X11 : (a > a > $o)] : ((((X11 @ X9 @ X10)) = $true) & ? [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = X11) & (((X1 @ X12)) = $true))) => (((X8 @ X9 @ X10)) = $true))) => (((X8 @ X2 @ X3)) = $true)))),
% 0.43/0.31 inference(fool_elimination,[],[f3])).
% 0.43/0.31 thf(f5,plain,(
% 0.43/0.31 ? [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (? [X8 : (a > a > $o)] : ((((X8 @ X2 @ X3)) != $true) & ((((X0 @ X8)) = $true) & ! [X9 : a,X10 : a] : ((((X8 @ X9 @ X10)) = $true) | ! [X11 : (a > a > $o)] : ((((X11 @ X9 @ X10)) != $true) | ! [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != X11) | (((X1 @ X12)) != $true)))))) & ! [X4 : (a > a > $o)] : ((((X4 @ X2 @ X3)) = $true) | ((((X0 @ X4)) != $true) | ? [X5 : a,X6 : a] : ((((X4 @ X5 @ X6)) != $true) & ? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & (((X1 @ X7)) = $true))))))),
% 0.43/0.31 inference(ennf_transformation,[],[f4])).
% 0.43/0.31 thf(f6,plain,(
% 0.43/0.31 ? [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (? [X8 : (a > a > $o)] : ((((X8 @ X2 @ X3)) != $true) & (((X0 @ X8)) = $true) & ! [X9 : a,X10 : a] : ((((X8 @ X9 @ X10)) = $true) | ! [X11 : (a > a > $o)] : ((((X11 @ X9 @ X10)) != $true) | ! [X12 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X12 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != X11) | (((X1 @ X12)) != $true))))) & ! [X4 : (a > a > $o)] : ((((X4 @ X2 @ X3)) = $true) | (((X0 @ X4)) != $true) | ? [X5 : a,X6 : a] : ((((X4 @ X5 @ X6)) != $true) & ? [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) = $true) & (((X1 @ X7)) = $true)))))),
% 0.43/0.31 inference(flattening,[],[f5])).
% 0.43/0.31 thf(f7,plain,(
% 0.43/0.31 ? [X0 : ((a > a > $o) > $o),X1 : ((a > a > $o) > $o),X2 : a,X3 : a] : (? [X4 : (a > a > $o)] : ((((X4 @ X2 @ X3)) != $true) & (((X0 @ X4)) = $true) & ! [X5 : a,X6 : a] : ((((X4 @ X5 @ X6)) = $true) | ! [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) != $true) | ! [X8 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (X0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != X7) | (((X1 @ X8)) != $true))))) & ! [X9 : (a > a > $o)] : (($true = ((X9 @ X2 @ X3))) | ($true != ((X0 @ X9))) | ? [X10 : a,X11 : a] : (($true != ((X9 @ X10 @ X11))) & ? [X12 : (a > a > $o)] : (($true = ((X12 @ X10 @ X11))) & (((X1 @ X12)) = $true)))))),
% 0.43/0.31 inference(rectify,[],[f6])).
% 0.43/0.31 thf(f8,plain,(
% 0.43/0.31 (($true != ((sK4 @ sK2 @ sK3))) & ($true = ((sK0 @ sK4))) & ! [X5 : a,X6 : a] : (($true = ((sK4 @ X5 @ X6))) | ! [X7 : (a > a > $o)] : ((((X7 @ X5 @ X6)) != $true) | ! [X8 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != X7) | ($true != ((sK1 @ X8))))))) & ! [X9 : (a > a > $o)] : (($true = ((X9 @ sK2 @ sK3))) | ($true != ((sK0 @ X9))) | (($true != ((X9 @ (sK5 @ X9) @ (sK6 @ X9)))) & (($true = ((sK7 @ X9 @ (sK5 @ X9) @ (sK6 @ X9)))) & ($true = ((sK1 @ (sK7 @ X9)))))))),
% 0.43/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X12,sK7 @ X9),skolemize(X12,sK7 @ X9),skolemize(X12,sK7 @ X9)],[f7])).
% 0.43/0.31 thf(f9,plain,(
% 0.43/0.31 ( ! [X9 : (a > a > $o)] : (($true != ((sK0 @ X9))) | ($true = ((X9 @ sK2 @ sK3))) | ($true = ((sK1 @ (sK7 @ X9))))) )),
% 0.43/0.31 inference(cnf_transformation,[],[f8])).
% 0.43/0.31 thf(f10,plain,(
% 0.43/0.31 ( ! [X9 : (a > a > $o)] : (($true != ((sK0 @ X9))) | ($true = ((X9 @ sK2 @ sK3))) | ($true = ((sK7 @ X9 @ (sK5 @ X9) @ (sK6 @ X9))))) )),
% 0.43/0.31 inference(cnf_transformation,[],[f8])).
% 0.43/0.31 thf(f11,plain,(
% 0.43/0.31 ( ! [X9 : (a > a > $o)] : (($true != ((sK0 @ X9))) | ($true = ((X9 @ sK2 @ sK3))) | ($true != ((X9 @ (sK5 @ X9) @ (sK6 @ X9))))) )),
% 0.43/0.31 inference(cnf_transformation,[],[f8])).
% 0.43/0.31 thf(f12,plain,(
% 0.43/0.31 ( ! [X8 : (a > a > $o),X6 : a,X7 : (a > a > $o),X5 : a] : (($true = ((sK4 @ X5 @ X6))) | (((X7 @ X5 @ X6)) != $true) | ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != X7) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.31 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f13,plain,(
% 0.43/0.32 ($true = ((sK0 @ sK4)))),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f14,plain,(
% 0.43/0.32 ($true != ((sK4 @ sK2 @ sK3)))),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f16,definition,(
% 0.43/0.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.43/0.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.43/0.32 thf(f17,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true != (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X8 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (sK0 @ Y2)) => (Y2 @ Y0 @ Y1))))))) @ X5 @ X6))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(equality_resolution,[],[f12])).
% 0.43/0.32 thf(f18,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true != ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (sK0 @ Y0)) => (Y0 @ X5 @ X6)))))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f17])).
% 0.43/0.32 thf(f19,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($false = (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X8 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (sK0 @ Y0)) => (Y0 @ X5 @ X6))) @ (sK8 @ X8 @ X5 @ X6)))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(sigma_proxy_clausification,[],[f18])).
% 0.43/0.32 thf(f20,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($false = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0)))))) & (sK0 @ (sK8 @ X8 @ X5 @ X6))) => (sK8 @ X8 @ X5 @ X6 @ X5 @ X6)))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f19])).
% 0.43/0.32 thf(f21,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true != ((sK1 @ X8))) | ($false = ((sK8 @ X8 @ X5 @ X6 @ X5 @ X6))) | ($true = ((sK4 @ X5 @ X6)))) )),
% 0.43/0.32 inference(imp_proxy_clausification,[],[f20])).
% 0.43/0.32 thf(f22,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0)))))) & (sK0 @ (sK8 @ X8 @ X5 @ X6))))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(imp_proxy_clausification,[],[f20])).
% 0.43/0.32 thf(f24,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0)))))))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(and_proxy_clausification,[],[f22])).
% 0.43/0.32 thf(f25,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X8 @ Y1 @ Y0) => (sK8 @ X8 @ X5 @ X6 @ Y1 @ Y0))))) @ X9))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(pi_proxy_clausification,[],[f24])).
% 0.43/0.32 thf(f26,plain,(
% 0.43/0.32 ( ! [X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = ((!! @ a @ (^[Y0 : a]: ((X8 @ Y0 @ X9) => (sK8 @ X8 @ X5 @ X6 @ Y0 @ X9)))))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f25])).
% 0.43/0.32 thf(f27,plain,(
% 0.43/0.32 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = (((^[Y0 : a]: ((X8 @ Y0 @ X9) => (sK8 @ X8 @ X5 @ X6 @ Y0 @ X9))) @ X10))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(pi_proxy_clausification,[],[f26])).
% 0.43/0.32 thf(f28,plain,(
% 0.43/0.32 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true = ((sK4 @ X5 @ X6))) | ($true = (((X8 @ X10 @ X9) => (sK8 @ X8 @ X5 @ X6 @ X10 @ X9)))) | ($true != ((sK1 @ X8)))) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f27])).
% 0.43/0.32 thf(f29,plain,(
% 0.43/0.32 ( ! [X10 : a,X8 : (a > a > $o),X6 : a,X9 : a,X5 : a] : (($true != ((sK1 @ X8))) | ($false = ((X8 @ X10 @ X9))) | ($true = ((sK4 @ X5 @ X6))) | ($true = ((sK8 @ X8 @ X5 @ X6 @ X10 @ X9)))) )),
% 0.43/0.32 inference(imp_proxy_clausification,[],[f28])).
% 0.43/0.32 thf(f30,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.43/0.32 inference(constrained_superposition,[],[f9,f13])).
% 0.43/0.32 thf(f31,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f30])).
% 0.43/0.32 thf(f33,definition,(
% 0.43/0.32 spl9_1 <=> ($true = ((sK1 @ (sK7 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.43/0.32 thf(f35,plain,(
% 0.43/0.32 ($true = ((sK1 @ (sK7 @ sK4)))) | ~spl9_1),
% 0.43/0.32 inference(avatar_component_clause,[],[f33])).
% 0.43/0.32 thf(f37,definition,(
% 0.43/0.32 spl9_2 <=> ($true = ((sK4 @ sK2 @ sK3)))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.43/0.32 thf(f39,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2 @ sK3))) | ~spl9_2),
% 0.43/0.32 inference(avatar_component_clause,[],[f37])).
% 0.43/0.32 thf(f40,plain,(
% 0.43/0.32 spl9_1 | spl9_2),
% 0.43/0.32 inference(avatar_split_clause,[],[f31,f37,f33])).
% 0.43/0.32 thf(f41,plain,(
% 0.43/0.32 ($true != $true) | ~spl9_2),
% 0.43/0.32 inference(constrained_superposition,[],[f14,f39])).
% 0.43/0.32 thf(f42,plain,(
% 0.43/0.32 $false | ~spl9_2),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f41])).
% 0.43/0.32 thf(f43,plain,(
% 0.43/0.32 ~spl9_2),
% 0.43/0.32 inference(avatar_contradiction_clause,[],[f42])).
% 0.43/0.32 thf(f44,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 inference(constrained_superposition,[],[f11,f13])).
% 0.43/0.32 thf(f45,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2 @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f44])).
% 0.43/0.32 thf(f47,definition,(
% 0.43/0.32 spl9_3 <=> ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.43/0.32 thf(f50,plain,(
% 0.43/0.32 ~spl9_3 | spl9_2),
% 0.43/0.32 inference(avatar_split_clause,[],[f45,f37,f47])).
% 0.43/0.32 thf(f219,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 inference(constrained_superposition,[],[f10,f13])).
% 0.43/0.32 thf(f224,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f219])).
% 0.43/0.32 thf(f226,definition,(
% 0.43/0.32 spl9_9 <=> ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
% 0.43/0.32 thf(f228,plain,(
% 0.43/0.32 ($true = ((sK7 @ sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ~spl9_9),
% 0.43/0.32 inference(avatar_component_clause,[],[f226])).
% 0.43/0.32 thf(f229,plain,(
% 0.43/0.32 spl9_9 | spl9_2),
% 0.43/0.32 inference(avatar_split_clause,[],[f224,f37,f226])).
% 0.43/0.32 thf(f289,plain,(
% 0.43/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | ($false = ((sK8 @ X0 @ X1 @ X2 @ X1 @ X2))) | ($true = ((sK4 @ X1 @ X2))) | ($false = ((sK1 @ X0)))) )),
% 0.43/0.32 inference(constrained_superposition,[],[f21,f16])).
% 0.43/0.32 thf(f290,plain,(
% 0.43/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($false = ((sK8 @ X0 @ X1 @ X2 @ X1 @ X2))) | ($true = ((sK4 @ X1 @ X2))) | ($false = ((sK1 @ X0)))) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f289])).
% 0.43/0.32 thf(f320,plain,(
% 0.43/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != $true) | ($false = ((X0 @ X1 @ X2))) | ($true = ((sK4 @ X3 @ X4))) | ($true = ((sK8 @ X0 @ X3 @ X4 @ X1 @ X2))) | ($false = ((sK1 @ X0)))) )),
% 0.43/0.32 inference(constrained_superposition,[],[f29,f16])).
% 0.43/0.32 thf(f321,plain,(
% 0.43/0.32 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sK8 @ X0 @ X3 @ X4 @ X1 @ X2))) | ($true = ((sK4 @ X3 @ X4))) | ($false = ((X0 @ X1 @ X2))) | ($false = ((sK1 @ X0)))) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f320])).
% 0.43/0.32 thf(f331,plain,(
% 0.43/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = $false) | ($true = ((sK4 @ X1 @ X2))) | ($false = ((sK1 @ X0))) | ($true = ((sK4 @ X1 @ X2))) | ($false = ((X0 @ X1 @ X2))) | ($false = ((sK1 @ X0)))) )),
% 0.43/0.32 inference(constrained_superposition,[],[f290,f321])).
% 0.43/0.32 thf(f336,plain,(
% 0.43/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = $false) | ($true = ((sK4 @ X1 @ X2))) | ($false = ((sK1 @ X0))) | ($false = ((X0 @ X1 @ X2)))) )),
% 0.43/0.32 inference(duplicate_literal_removal,[],[f331])).
% 0.43/0.32 thf(f337,plain,(
% 0.43/0.32 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sK4 @ X1 @ X2))) | ($false = ((sK1 @ X0))) | ($false = ((X0 @ X1 @ X2)))) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f336])).
% 0.43/0.32 thf(f380,plain,(
% 0.43/0.32 ( ! [X0 : a,X1 : a] : (($true = $false) | ($true = ((sK4 @ X0 @ X1))) | ($false = ((sK7 @ sK4 @ X0 @ X1)))) ) | ~spl9_1),
% 0.43/0.32 inference(constrained_superposition,[],[f35,f337])).
% 0.43/0.32 thf(f476,plain,(
% 0.43/0.32 ( ! [X0 : a,X1 : a] : (($false = ((sK7 @ sK4 @ X0 @ X1))) | ($true = ((sK4 @ X0 @ X1)))) ) | ~spl9_1),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f380])).
% 0.43/0.32 thf(f586,plain,(
% 0.43/0.32 ($true = $false) | ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | (~spl9_1 | ~spl9_9)),
% 0.43/0.32 inference(constrained_superposition,[],[f228,f476])).
% 0.43/0.32 thf(f589,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | (~spl9_1 | ~spl9_9)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f586])).
% 0.43/0.32 thf(f599,plain,(
% 0.43/0.32 spl9_3 | ~spl9_1 | ~spl9_9),
% 0.43/0.32 inference(avatar_split_clause,[],[f589,f226,f33,f47])).
% 0.43/0.32 cnf(s1, plain, spl9_1 | spl9_2, inference(sat_conversion,[],[f40])).
% 0.43/0.32 cnf(s2, plain, ~spl9_2, inference(sat_conversion,[],[f43])).
% 0.43/0.32 cnf(s3, plain, spl9_2 | ~spl9_3, inference(sat_conversion,[],[f50])).
% 0.43/0.32 cnf(s6, plain, spl9_2 | spl9_9, inference(sat_conversion,[],[f229])).
% 0.43/0.32 cnf(s14, plain, ~spl9_1 | spl9_3 | ~spl9_9, inference(sat_conversion,[],[f599])).
% 0.43/0.32 cnf(s17, plain, spl9_9, inference(rat,[],[s6,s2])).
% 0.43/0.32 cnf(s18, plain, ~spl9_3, inference(rat,[],[s3,s2])).
% 0.43/0.32 cnf(s19, plain, ~spl9_1, inference(rat,[],[s14,s17,s18])).
% 0.43/0.32 cnf(s20, plain, $false, inference(rat,[],[s1,s2,s19])).
% 0.43/0.32 thf(f601,plain,(
% 0.43/0.32 $false),
% 0.43/0.32 inference(avatar_sat_refutation,[],[s20])).
% 0.43/0.32 % SZS output end Proof for theBenchmark
% 0.43/0.32 % (1413991)------------------------------
% 0.43/0.32 % (1413991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.32 % (1413991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.32 % (1413991)CaDiCaL version: 2.1.3
% 0.43/0.32 % (1413991)Termination reason: Refutation
% 0.43/0.32 % (1413991)Time elapsed: 0.068 s
% 0.43/0.32 % (1413991)Peak memory usage: 13 MB
% 0.43/0.32 % (1413991)Instructions burned: 140 (million)
% 0.43/0.32 % (1413980)Success in time 0.105 s
% 0.43/0.32 % Vampire exiting
%------------------------------------------------------------------------------