%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:50:23 AM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:14:35 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.19/0.30 % (1338858)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (1338869)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=434820577:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (1338868)% WARNING: option uhcvi not known.
% 0.19/0.30 % (1338869)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338869)------------------------------
% 0.19/0.30 % (1338869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338869)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338869)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338869)Time elapsed: 0.007 s
% 0.19/0.30 % (1338869)Peak memory usage: 12 MB
% 0.19/0.30 % (1338867)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1176425155_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (1338869)Instructions burned: 21 (million)
% 0.19/0.30 % (1338868)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1460014477:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (1338870)dis+10_1_sil=32000:sp=arity:random_seed=1002519097:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (1338871)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3956598736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (1338869)------------------------------
% 0.19/0.30 % (1338869)------------------------------
% 0.19/0.30 % (1338873)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3475887805:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (1338868)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (1338872)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2653512615:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (1338871)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (1338868)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.30 % (1338870)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338870)------------------------------
% 0.19/0.30 % (1338870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338868)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338868)------------------------------
% 0.19/0.30 % (1338868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338870)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338870)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338870)Time elapsed: 0.007 s
% 0.19/0.30 % (1338868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338870)Peak memory usage: 12 MB
% 0.19/0.30 % (1338870)Instructions burned: 12 (million)
% 0.19/0.30 % (1338868)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338868)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338868)Time elapsed: 0.007 s
% 0.19/0.30 % (1338868)Peak memory usage: 12 MB
% 0.19/0.30 % (1338868)Instructions burned: 12 (million)
% 0.19/0.30 % (1338872)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338872)------------------------------
% 0.19/0.30 % (1338872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338872)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338872)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338872)Time elapsed: 0.007 s
% 0.19/0.30 % (1338872)Peak memory usage: 12 MB
% 0.19/0.30 % (1338872)Instructions burned: 11 (million)
% 0.19/0.30 % (1338873)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338873)------------------------------
% 0.19/0.30 % (1338873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338873)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338873)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338873)Time elapsed: 0.007 s
% 0.19/0.30 % (1338873)Peak memory usage: 12 MB
% 0.19/0.30 % (1338873)Instructions burned: 12 (million)
% 0.19/0.30 % (1338870)------------------------------
% 0.19/0.30 % (1338870)------------------------------
% 0.19/0.30 % (1338868)------------------------------
% 0.19/0.30 % (1338868)------------------------------
% 0.19/0.30 % (1338872)------------------------------
% 0.19/0.30 % (1338872)------------------------------
% 0.19/0.30 % (1338873)------------------------------
% 0.19/0.30 % (1338873)------------------------------
% 0.19/0.30 % (1338871)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338871)------------------------------
% 0.19/0.30 % (1338871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338871)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338871)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338871)Time elapsed: 0.012 s
% 0.19/0.30 % (1338871)Peak memory usage: 12 MB
% 0.19/0.30 % (1338871)Instructions burned: 22 (million)
% 0.19/0.30 % (1338871)------------------------------
% 0.19/0.30 % (1338871)------------------------------
% 0.19/0.30 % (1338886)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1211949564:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % (1338888)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=955555341:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (1338888)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338888)------------------------------
% 0.19/0.30 % (1338888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338888)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338888)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338888)Time elapsed: 0.007 s
% 0.19/0.30 % (1338888)Peak memory usage: 12 MB
% 0.19/0.30 % (1338888)Instructions burned: 11 (million)
% 0.19/0.30 % (1338892)ott-21_1_sil=16000:fs=off:random_seed=1135997107:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/0.30 % (1338893)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1127386786:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.19/0.30 % (1338894)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3766697540:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.19/0.30 % (1338891)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=3309935401:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.30 % (1338888)------------------------------
% 0.19/0.30 % (1338888)------------------------------
% 0.19/0.30 % (1338891)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (1338891)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.30 % (1338896)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=759432351:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.19/0.30 % (1338891)Refutation not found, incomplete strategy
% 0.19/0.30 % (1338891)------------------------------
% 0.19/0.30 % (1338891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338891)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338891)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1338891)Time elapsed: 0.007 s
% 0.19/0.30 % (1338891)Peak memory usage: 12 MB
% 0.19/0.30 % (1338891)Instructions burned: 12 (million)
% 0.19/0.30 % (1338891)------------------------------
% 0.19/0.30 % (1338891)------------------------------
% 0.19/0.30 % (1338903)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=480478751:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.19/0.30 % (1338896) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1338858-1338896"...
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (1338896)...printing done.
% 0.19/0.30 % (1338896)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% 0.19/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.30 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.19/0.30 thf(func_def_2, type, if: ($o > $i > $i > $i)).
% 0.19/0.30 thf(func_def_5, type, vOR: ($o > $o > $o)).
% 0.19/0.30 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.19/0.30 thf(func_def_7, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.30 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.19/0.30 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.30 thf(func_def_14, type, sK0: $o).
% 0.19/0.30 thf(f1,axiom,(
% 0.19/0.30 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax)).
% 0.19/0.30 thf(f2,axiom,(
% 0.19/0.30 (if = (^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X2) & ~X0) | ((X3 = X1) & X0)))))))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifd)).
% 0.19/0.30 thf(f3,conjecture,(
% 0.19/0.30 ! [X0 : $o,X1 : $i,X2 : $i] : ((((if @ X0 @ X1 @ X2)) = X2) | (((if @ X0 @ X1 @ X2)) = X1))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.19/0.30 thf(f4,negated_conjecture,(
% 0.19/0.30 ~ ! [X0 : $o,X1 : $i,X2 : $i] : ((((if @ X0 @ X1 @ X2)) = X2) | (((if @ X0 @ X1 @ X2)) = X1))),
% 0.19/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.30 thf(f5,plain,(
% 0.19/0.30 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.19/0.30 inference(rectify,[],[f1])).
% 0.19/0.30 thf(f6,plain,(
% 0.19/0.30 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.19/0.30 inference(fool_elimination,[],[f5])).
% 0.19/0.30 thf(f7,plain,(
% 0.19/0.30 (if = (^[X0 : $o, X1 : $i, X2 : $i] : ((eps @ (^[X3 : $i] : (((X3 = X2) & ~X0) | ((X3 = X1) & X0)))))))),
% 0.19/0.30 inference(rectify,[],[f2])).
% 0.19/0.30 thf(f8,plain,(
% 0.19/0.30 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.19/0.30 inference(fool_elimination,[],[f7])).
% 0.19/0.30 thf(f9,plain,(
% 0.19/0.30 ! [X0 : ($i > $o)] : ((((X0 @ (eps @ X0))) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.19/0.30 inference(ennf_transformation,[],[f6])).
% 0.19/0.30 thf(f10,plain,(
% 0.19/0.30 ? [X0 : $o,X1 : $i,X2 : $i] : ((((if @ X0 @ X1 @ X2)) != X2) & (((if @ X0 @ X1 @ X2)) != X1))),
% 0.19/0.30 inference(ennf_transformation,[],[f4])).
% 0.19/0.30 thf(f11,plain,(
% 0.19/0.30 (sK2 != ((if @ sK0 @ sK1 @ sK2))) & (sK1 != ((if @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10])).
% 0.19/0.30 thf(f12,plain,(
% 0.19/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (eps @ X0))) = $true)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f9])).
% 0.19/0.30 thf(f13,plain,(
% 0.19/0.30 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.19/0.30 inference(cnf_transformation,[],[f8])).
% 0.19/0.30 thf(f14,plain,(
% 0.19/0.30 (sK1 != ((if @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 inference(cnf_transformation,[],[f11])).
% 0.19/0.30 thf(f15,plain,(
% 0.19/0.30 (sK2 != ((if @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 inference(cnf_transformation,[],[f11])).
% 0.19/0.30 thf(f17,definition,(
% 0.19/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.30 thf(f18,plain,(
% 0.19/0.30 (sK2 != (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 inference(definition_unfolding,[],[f15,f13])).
% 0.19/0.30 thf(f19,plain,(
% 0.19/0.30 (sK1 != (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 inference(definition_unfolding,[],[f14,f13])).
% 0.19/0.30 thf(f20,definition,(
% 0.19/0.30 (sF3 = (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK2)))),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.19/0.30 thf(f21,plain,(
% 0.19/0.30 ((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ sK0 @ sK1 @ sK2)) = sF3)),
% 0.19/0.30 inference(reorient_equations,[],[f20])).
% 0.19/0.30 thf(f22,plain,(
% 0.19/0.30 (sK2 != sF3)),
% 0.19/0.30 inference(definition_folding,[],[f18,f21])).
% 0.19/0.30 thf(f23,plain,(
% 0.19/0.30 (sK1 != sF3)),
% 0.19/0.30 inference(definition_folding,[],[f19,f21])).
% 0.19/0.30 thf(f24,plain,(
% 0.19/0.30 (sF3 = ((eps @ (^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK2 = Y0)))))))),
% 0.19/0.30 inference(beta-eta_normalization,[],[f21])).
% 0.19/0.30 thf(f37,plain,(
% 0.19/0.30 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.19/0.30 inference(constrained_superposition,[],[f12,f17])).
% 0.19/0.30 thf(f40,plain,(
% 0.19/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f37])).
% 0.19/0.30 thf(f54,plain,(
% 0.19/0.30 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK2 = Y0)))) @ sF3))) | ($false = (((^[Y0 : $i]: ((sK0 & (sK1 = Y0)) | ((~ sK0) & (sK2 = Y0)))) @ X0)))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f40,f24])).
% 0.19/0.30 thf(f100,plain,(
% 0.19/0.30 ( ! [X0 : $i] : (($true = (((sK0 & (sK1 = sF3)) | ((~ sK0) & (sK2 = sF3))))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK2 = X0)))))) )),
% 0.19/0.30 inference(beta-eta_normalization,[],[f54])).
% 0.19/0.30 thf(f101,plain,(
% 0.19/0.30 ( ! [X0 : $i] : (($true = (((~ sK0) & (sK2 = sF3)))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK2 = X0))))) | ($true = ((sK0 & (sK1 = sF3))))) )),
% 0.19/0.30 inference(or_proxy_clausification,[],[f100])).
% 0.19/0.30 thf(f102,plain,(
% 0.19/0.30 ( ! [X0 : $i] : (($true = ((sK2 = sF3))) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK2 = X0))))) | ($true = ((sK0 & (sK1 = sF3))))) )),
% 0.19/0.30 inference(and_proxy_clausification,[],[f101])).
% 0.19/0.30 thf(f122,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | ($false = (((sK0 & (sK1 = X0)) | ((~ sK0) & (sK2 = X0))))) | ($true = ((sK0 & (sK1 = sF3))))) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f102])).
% 0.19/0.30 thf(f123,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | ($false = (((~ sK0) & (sK2 = X0)))) | ($true = ((sK0 & (sK1 = sF3))))) )),
% 0.19/0.30 inference(or_proxy_clausification,[],[f122])).
% 0.19/0.30 thf(f124,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | ($false = ((sK0 & (sK1 = X0)))) | ($true = ((sK0 & (sK1 = sF3))))) )),
% 0.19/0.30 inference(or_proxy_clausification,[],[f122])).
% 0.19/0.30 thf(f125,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | ($false = ((sK1 = X0))) | ($true = ((sK0 & (sK1 = sF3)))) | (sK0 = $false)) )),
% 0.19/0.30 inference(and_proxy_clausification,[],[f124])).
% 0.19/0.30 thf(f126,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK1 != X0) | ($true = ((sK0 & (sK1 = sF3)))) | (sK0 = $false)) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f125])).
% 0.19/0.30 thf(f127,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK1 != X0) | ($true = ((sK1 = sF3))) | (sK0 = $false)) )),
% 0.19/0.30 inference(and_proxy_clausification,[],[f126])).
% 0.19/0.30 thf(f129,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK1 != X0) | (sK1 = sF3) | (sK0 = $false)) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f127])).
% 0.19/0.30 thf(f130,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | ($false = ((sK2 = X0))) | ($true = ((sK0 & (sK1 = sF3)))) | ($false = ((~ sK0)))) )),
% 0.19/0.30 inference(and_proxy_clausification,[],[f123])).
% 0.19/0.30 thf(f131,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK2 != X0) | ($true = ((sK0 & (sK1 = sF3)))) | ($false = ((~ sK0)))) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f130])).
% 0.19/0.30 thf(f132,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK2 != X0) | ($true = ((sK1 = sF3))) | ($false = ((~ sK0)))) )),
% 0.19/0.30 inference(and_proxy_clausification,[],[f131])).
% 0.19/0.30 thf(f136,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK2 != X0) | (sK1 = sF3) | ($false = ((~ sK0)))) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f132])).
% 0.19/0.30 thf(f137,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 = sF3) | (sK2 != X0) | (sK1 = sF3) | ($true = sK0)) )),
% 0.19/0.30 inference(not_proxy_clausification,[],[f136])).
% 0.19/0.30 thf(f151,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK1 != X0) | (sK1 = sF3) | (sK0 = $false)) )),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f129,f22])).
% 0.19/0.30 thf(f153,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 != X0) | (sK1 = sF3) | ($true = sK0)) )),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f137,f22])).
% 0.19/0.30 thf(f155,definition,(
% 0.19/0.30 spl4_1 <=> ! [X0 : $i] : (sK1 != X0)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.30 thf(f156,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK1 != X0)) ) | ~spl4_1),
% 0.19/0.30 inference(avatar_component_clause,[],[f155])).
% 0.19/0.30 thf(f158,definition,(
% 0.19/0.30 spl4_2 <=> (sK0 = $false)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.30 thf(f160,plain,(
% 0.19/0.30 (sK0 = $false) | ~spl4_2),
% 0.19/0.30 inference(avatar_component_clause,[],[f158])).
% 0.19/0.30 thf(f162,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK1 != X0) | (sK0 = $false)) )),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f151,f23])).
% 0.19/0.30 thf(f164,definition,(
% 0.19/0.30 spl4_3 <=> ($true = sK0)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.19/0.30 thf(f166,plain,(
% 0.19/0.30 ($true = sK0) | ~spl4_3),
% 0.19/0.30 inference(avatar_component_clause,[],[f164])).
% 0.19/0.30 thf(f168,definition,(
% 0.19/0.30 spl4_4 <=> ! [X0 : $i] : (sK2 != X0)),
% 0.19/0.30 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.19/0.30 thf(f169,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 != X0)) ) | ~spl4_4),
% 0.19/0.30 inference(avatar_component_clause,[],[f168])).
% 0.19/0.30 thf(f171,plain,(
% 0.19/0.30 ( ! [X0 : $i] : ((sK2 != X0) | ($true = sK0)) )),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f153,f23])).
% 0.19/0.30 thf(f172,plain,(
% 0.19/0.30 spl4_2 | spl4_1),
% 0.19/0.30 inference(avatar_split_clause,[],[f162,f155,f158])).
% 0.19/0.30 thf(f173,plain,(
% 0.19/0.30 spl4_3 | spl4_4),
% 0.19/0.30 inference(avatar_split_clause,[],[f171,f168,f164])).
% 0.19/0.30 thf(f174,plain,(
% 0.19/0.30 ($true = $false) | (~spl4_2 | ~spl4_3)),
% 0.19/0.30 inference(forward_demodulation,[],[f166,f160])).
% 0.19/0.30 thf(f175,plain,(
% 0.19/0.30 $false | (~spl4_2 | ~spl4_3)),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f174])).
% 0.19/0.30 thf(f176,plain,(
% 0.19/0.30 ~spl4_2 | ~spl4_3),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f175])).
% 0.19/0.30 thf(f177,plain,(
% 0.19/0.30 $false | ~spl4_1),
% 0.19/0.30 inference(equality_resolution,[],[f156])).
% 0.19/0.30 thf(f178,plain,(
% 0.19/0.30 ~spl4_1),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f177])).
% 0.19/0.30 thf(f358,plain,(
% 0.19/0.30 $false | ~spl4_4),
% 0.19/0.30 inference(equality_resolution,[],[f169])).
% 0.19/0.30 thf(f359,plain,(
% 0.19/0.30 ~spl4_4),
% 0.19/0.30 inference(avatar_contradiction_clause,[],[f358])).
% 0.19/0.30 cnf(s3, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f172])).
% 0.19/0.30 cnf(s4, plain, spl4_3 | spl4_4, inference(sat_conversion,[],[f173])).
% 0.19/0.30 cnf(s5, plain, ~spl4_2 | ~spl4_3, inference(sat_conversion,[],[f176])).
% 0.19/0.30 cnf(s6, plain, ~spl4_1, inference(sat_conversion,[],[f178])).
% 0.19/0.30 cnf(s7, plain, ~spl4_4, inference(sat_conversion,[],[f359])).
% 0.19/0.30 cnf(s8, plain, spl4_3, inference(rat,[],[s4,s7])).
% 0.19/0.30 cnf(s9, plain, ~spl4_2, inference(rat,[],[s5,s8])).
% 0.19/0.30 cnf(s10, plain, $false, inference(rat,[],[s3,s9,s6])).
% 0.19/0.30 thf(f360,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(avatar_sat_refutation,[],[s10])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (1338896)------------------------------
% 0.19/0.30 % (1338896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1338896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1338896)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1338896)Termination reason: Refutation
% 0.19/0.30 % (1338896)Time elapsed: 0.008 s
% 0.19/0.30 % (1338896)Peak memory usage: 12 MB
% 0.19/0.30 % (1338896)Instructions burned: 13 (million)
% 0.19/0.30 % (1338858)Success in time 0.085 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------