%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN041^4 : 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 : n017.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 08:41:48 AM UTC 2026
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN041^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:09:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.38 % (522538)Will run a generic schedule for satisfiability detection.
% 0.20/0.38 % (522543)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3273086294_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (522544)% WARNING: option uhcvi not known.
% 0.20/0.38 % (522547)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=148586367:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.38 % (522544)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1919944851:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.38 % (522545)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2167325572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.38 % (522546)dis+10_1_sil=32000:sp=arity:random_seed=3910821962:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.38 % (522547)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.38 % (522544)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.38 % (522548)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4183609401:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.38 % (522544)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.38 % (522549)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3377228195:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.38 % (522546)Instruction limit reached!
% 0.20/0.38 % (522546)------------------------------
% 0.20/0.38 % (522546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.38 % (522546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.38 % (522546)CaDiCaL version: 2.1.3
% 0.20/0.38 % (522546)Termination reason: Instruction limit
% 0.20/0.38 % (522546)Termination phase: Saturation
% 0.20/0.38 % (522546)Time elapsed: 0.027 s
% 0.20/0.38 % (522546)Peak memory usage: 12 MB
% 0.20/0.38 % (522546)Instructions burned: 107 (million)
% 0.20/0.38 % (522551)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1477621572:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (522558)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4015543214:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.38 % (522547)Instruction limit reached!
% 0.20/0.38 % (522547)------------------------------
% 0.20/0.38 % (522547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.38 % (522547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.38 % (522547)CaDiCaL version: 2.1.3
% 0.20/0.38 % (522547)Termination reason: Instruction limit
% 0.20/0.38 % (522547)Termination phase: Saturation
% 0.20/0.38 % (522547)Time elapsed: 0.053 s
% 0.20/0.38 % (522547)Peak memory usage: 12 MB
% 0.20/0.38 % (522547)Instructions burned: 117 (million)
% 0.20/0.38 % (522560)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=128077323:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.38 % (522562)ott-21_1_sil=16000:fs=off:random_seed=578341176:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.38 % (522558)Instruction limit reached!
% 0.20/0.38 % (522558)------------------------------
% 0.20/0.38 % (522558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.38 % (522558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.38 % (522558)CaDiCaL version: 2.1.3
% 0.20/0.38 % (522558)Termination reason: Instruction limit
% 0.20/0.38 % (522558)Termination phase: Saturation
% 0.20/0.38 % (522558)Time elapsed: 0.035 s
% 0.20/0.38 % (522558)Peak memory usage: 12 MB
% 0.20/0.38 % (522558)Instructions burned: 136 (million)
% 0.20/0.38 % (522560)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.38 % (522560)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.38 % (522548)Instruction limit reached!
% 0.20/0.38 % (522548)------------------------------
% 0.20/0.38 % (522548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.38 % (522548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.38 % (522548)CaDiCaL version: 2.1.3
% 0.20/0.38 % (522548)Termination reason: Instruction limit
% 0.20/0.38 % (522548)Termination phase: Saturation
% 0.20/0.38 % (522548)Time elapsed: 0.082 s
% 0.20/0.38 % (522548)Peak memory usage: 12 MB
% 0.20/0.38 % (522548)Instructions burned: 131 (million)
% 0.20/0.38 % (522565)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3998716270:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.20/0.38 % (522545) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-522538-522545"...
% 0.20/0.38 % (522545)...printing done.
% 0.20/0.38 % (522545)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% 0.20/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.38 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.20/0.38 thf(func_def_2, type, mnot: (($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_3, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_4, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_5, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_6, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_7, type, iatom: (($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_8, type, inot: (($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_9, type, itrue: ($i > $o)).
% 0.20/0.38 thf(func_def_10, type, ifalse: ($i > $o)).
% 0.20/0.38 thf(func_def_11, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_12, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_13, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_14, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_15, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_16, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.38 thf(func_def_17, type, ivalid: (($i > $o) > $o)).
% 0.20/0.38 thf(func_def_18, type, isatisfiable: (($i > $o) > $o)).
% 0.20/0.38 thf(func_def_19, type, icountersatisfiable: (($i > $o) > $o)).
% 0.20/0.38 thf(func_def_20, type, iinvalid: (($i > $o) > $o)).
% 0.20/0.38 thf(func_def_21, type, p: ($i > $o)).
% 0.20/0.38 thf(func_def_22, type, q: ($i > $o)).
% 0.20/0.38 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.20/0.38 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.38 thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.38 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.38 thf(func_def_29, type, vOR: ($o > $o > $o)).
% 0.20/0.38 thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.38 thf(func_def_31, type, vAND: ($o > $o > $o)).
% 0.20/0.38 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.38 thf(func_def_33, type, vIMP: ($o > $o > $o)).
% 0.20/0.38 thf(func_def_34, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.38 thf(func_def_36, type, sK1: ($i > $i)).
% 0.20/0.38 thf(func_def_37, type, sK2: ($i > $i)).
% 0.20/0.38 thf(f2,axiom,(
% 0.20/0.38 ! [X0 : $i,X1 : $i,X2 : $i] : (((irel @ X1 @ X2) & (irel @ X0 @ X1)) => (irel @ X0 @ X2))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',trans_axiom)).
% 0.20/0.38 thf(f3,axiom,(
% 0.20/0.38 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot)).
% 0.20/0.38 thf(f4,axiom,(
% 0.20/0.38 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor)).
% 0.20/0.38 thf(f6,axiom,(
% 0.20/0.38 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies)).
% 0.20/0.38 thf(f7,axiom,(
% 0.20/0.38 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4)).
% 0.20/0.38 thf(f8,axiom,(
% 0.20/0.38 (iatom = (^[X0 : ($i > $o)] : (X0)))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom)).
% 0.20/0.38 thf(f9,axiom,(
% 0.20/0.38 (inot = (^[X0 : ($i > $o)] : ((mnot @ (mbox_s4 @ X0)))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',inot)).
% 0.20/0.38 thf(f14,axiom,(
% 0.20/0.38 (iimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies)).
% 0.20/0.38 thf(f18,axiom,(
% 0.20/0.38 (ivalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid)).
% 0.20/0.38 thf(f22,conjecture,(
% 0.20/0.38 (ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel3)).
% 0.20/0.38 thf(f23,negated_conjecture,(
% 0.20/0.38 ~(ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))),
% 0.20/0.38 inference(negated_conjecture,[status(cth)],[f22])).
% 0.20/0.38 thf(f26,plain,(
% 0.20/0.38 ! [X0 : $i,X1 : $i,X2 : $i] : (((irel @ X1 @ X2) & (irel @ X0 @ X1)) => (irel @ X0 @ X2))),
% 0.20/0.38 inference(rectify,[],[f2])).
% 0.20/0.38 thf(f27,plain,(
% 0.20/0.38 ! [X0 : $i,X1 : $i,X2 : $i] : (((((irel @ X1 @ X2)) = $true) & (((irel @ X0 @ X1)) = $true)) => (((irel @ X0 @ X2)) = $true))),
% 0.20/0.38 inference(fool_elimination,[],[f26])).
% 0.20/0.38 thf(f28,plain,(
% 0.20/0.38 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.38 inference(rectify,[],[f3])).
% 0.20/0.38 thf(f29,plain,(
% 0.20/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.38 inference(fool_elimination,[],[f28])).
% 0.20/0.38 thf(f30,plain,(
% 0.20/0.38 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.38 inference(rectify,[],[f4])).
% 0.20/0.38 thf(f31,plain,(
% 0.20/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f30])).
% 0.20/0.38 thf(f34,plain,(
% 0.20/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.38 inference(fool_elimination,[],[f6])).
% 0.20/0.38 thf(f35,plain,(
% 0.20/0.38 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.38 inference(rectify,[],[f7])).
% 0.20/0.38 thf(f36,plain,(
% 0.20/0.38 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f35])).
% 0.20/0.38 thf(f37,plain,(
% 0.20/0.38 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.38 inference(fool_elimination,[],[f8])).
% 0.20/0.38 thf(f38,plain,(
% 0.20/0.38 (inot = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ Y0))))),
% 0.20/0.38 inference(fool_elimination,[],[f9])).
% 0.20/0.38 thf(f42,plain,(
% 0.20/0.38 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.38 inference(fool_elimination,[],[f14])).
% 0.20/0.38 thf(f46,plain,(
% 0.20/0.38 (ivalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.20/0.38 inference(rectify,[],[f18])).
% 0.20/0.38 thf(f47,plain,(
% 0.20/0.38 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.38 inference(fool_elimination,[],[f46])).
% 0.20/0.38 thf(f54,plain,(
% 0.20/0.38 ~(ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))),
% 0.20/0.38 inference(rectify,[],[f23])).
% 0.20/0.38 thf(f55,plain,(
% 0.20/0.38 ~ (((ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))) = $true)),
% 0.20/0.38 inference(fool_elimination,[],[f54])).
% 0.20/0.38 thf(f56,plain,(
% 0.20/0.38 (((ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))) != $true)),
% 0.20/0.38 inference(flattening,[],[f55])).
% 0.20/0.38 thf(f57,plain,(
% 0.20/0.38 ! [X0 : $i,X1 : $i,X2 : $i] : ((((irel @ X0 @ X2)) = $true) | ((((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X1)) != $true)))),
% 0.20/0.38 inference(ennf_transformation,[],[f27])).
% 0.20/0.38 thf(f58,plain,(
% 0.20/0.38 ! [X0 : $i,X1 : $i,X2 : $i] : ((((irel @ X0 @ X2)) = $true) | (((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X1)) != $true))),
% 0.20/0.38 inference(flattening,[],[f57])).
% 0.20/0.38 thf(f60,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X2)) = $true) | (((irel @ X0 @ X1)) != $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f58])).
% 0.20/0.38 thf(f61,plain,(
% 0.20/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f29])).
% 0.20/0.38 thf(f62,plain,(
% 0.20/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f31])).
% 0.20/0.38 thf(f64,plain,(
% 0.20/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.38 inference(cnf_transformation,[],[f34])).
% 0.20/0.38 thf(f65,plain,(
% 0.20/0.38 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f66,plain,(
% 0.20/0.38 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.38 inference(cnf_transformation,[],[f37])).
% 0.20/0.38 thf(f67,plain,(
% 0.20/0.38 (inot = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ Y0))))),
% 0.20/0.38 inference(cnf_transformation,[],[f38])).
% 0.20/0.38 thf(f72,plain,(
% 0.20/0.38 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f42])).
% 0.20/0.38 thf(f76,plain,(
% 0.20/0.38 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.38 inference(cnf_transformation,[],[f47])).
% 0.20/0.38 thf(f80,plain,(
% 0.20/0.38 (((ivalid @ (iimplies @ (inot @ (iimplies @ (iatom @ p) @ (iatom @ q))) @ (iimplies @ (iatom @ q) @ (iatom @ p))))) != $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f56])).
% 0.20/0.38 thf(f82,definition,(
% 0.20/0.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.38 thf(f83,plain,(
% 0.20/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.38 inference(definition_unfolding,[],[f64,f62,f61])).
% 0.20/0.38 thf(f84,plain,(
% 0.20/0.38 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ Y0))))),
% 0.20/0.38 inference(definition_unfolding,[],[f67,f61,f65])).
% 0.20/0.38 thf(f88,plain,(
% 0.20/0.38 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f72,f83,f65,f65])).
% 0.20/0.38 thf(f92,plain,(
% 0.20/0.38 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ Y0))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ p))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f80,f76,f88,f84,f88,f66,f66,f88,f66,f66])).
% 0.20/0.38 thf(f93,plain,(
% 0.20/0.38 ($true != ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (q @ Y3))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))))))))))))),
% 0.20/0.38 inference(beta-eta_normalization,[],[f92])).
% 0.20/0.38 thf(f94,plain,(
% 0.20/0.38 ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (q @ Y3))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))))))))) @ sK0)))),
% 0.20/0.38 inference(sigma_proxy_clausification,[],[f93])).
% 0.20/0.38 thf(f95,plain,(
% 0.20/0.38 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))))))))))),
% 0.20/0.38 inference(beta-eta_normalization,[],[f94])).
% 0.20/0.38 thf(f96,plain,(
% 0.20/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))))))))),
% 0.20/0.38 inference(or_proxy_clausification,[],[f95])).
% 0.20/0.38 thf(f97,plain,(
% 0.20/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2)))))))))))))))),
% 0.20/0.38 inference(or_proxy_clausification,[],[f95])).
% 0.20/0.38 thf(f98,plain,(
% 0.20/0.38 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))))))))))))),
% 0.20/0.38 inference(not_proxy_clausification,[],[f97])).
% 0.20/0.38 thf(f99,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))))))))) @ X1)))) )),
% 0.20/0.38 inference(pi_proxy_clausification,[],[f98])).
% 0.20/0.38 thf(f100,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = (((irel @ sK0 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))))))))) )),
% 0.20/0.38 inference(beta-eta_normalization,[],[f99])).
% 0.20/0.38 thf(f101,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1)))))))))))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f100])).
% 0.20/0.38 thf(f102,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))))))) )),
% 0.20/0.38 inference(not_proxy_clausification,[],[f101])).
% 0.20/0.38 thf(f103,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))))) @ (sK1 @ X1))))) )),
% 0.20/0.38 inference(sigma_proxy_clausification,[],[f102])).
% 0.20/0.38 thf(f104,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = (((irel @ X1 @ (sK1 @ X1)) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (q @ Y0))))))))) )),
% 0.20/0.38 inference(beta-eta_normalization,[],[f103])).
% 0.20/0.38 thf(f105,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (q @ Y0)))))))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f104])).
% 0.20/0.38 thf(f106,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = ((irel @ X1 @ (sK1 @ X1)))) | ($false = ((irel @ sK0 @ X1)))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f104])).
% 0.20/0.38 thf(f107,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (q @ Y0))))))) )),
% 0.20/0.38 inference(or_proxy_clausification,[],[f105])).
% 0.20/0.38 thf(f113,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = (((^[Y0 : $i]: ((irel @ (sK1 @ X1) @ Y0) => (q @ Y0))) @ (sK2 @ X1))))) )),
% 0.20/0.38 inference(sigma_proxy_clausification,[],[f107])).
% 0.20/0.38 thf(f114,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = (((irel @ (sK1 @ X1) @ (sK2 @ X1)) => (q @ (sK2 @ X1)))))) )),
% 0.20/0.38 inference(beta-eta_normalization,[],[f113])).
% 0.20/0.38 thf(f115,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = ((q @ (sK2 @ X1))))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f114])).
% 0.20/0.38 thf(f116,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = ((irel @ (sK1 @ X1) @ (sK2 @ X1)))) | ($false = ((irel @ sK0 @ X1)))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f114])).
% 0.20/0.38 thf(f117,plain,(
% 0.20/0.38 ($false = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1))))))) @ sK3)))),
% 0.20/0.38 inference(sigma_proxy_clausification,[],[f96])).
% 0.20/0.38 thf(f118,plain,(
% 0.20/0.38 ($false = (((irel @ sK0 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))))))))),
% 0.20/0.38 inference(beta-eta_normalization,[],[f117])).
% 0.20/0.38 thf(f119,plain,(
% 0.20/0.38 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))))))),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f118])).
% 0.20/0.38 thf(f120,plain,(
% 0.20/0.38 ($true = ((irel @ sK0 @ sK3)))),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f118])).
% 0.20/0.38 thf(f121,plain,(
% 0.20/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))))))),
% 0.20/0.38 inference(or_proxy_clausification,[],[f119])).
% 0.20/0.38 thf(f122,plain,(
% 0.20/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))))))),
% 0.20/0.38 inference(or_proxy_clausification,[],[f119])).
% 0.20/0.38 thf(f123,plain,(
% 0.20/0.38 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))))),
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% 0.20/0.38 thf(f124,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))) @ X1)))) )),
% 0.20/0.38 inference(pi_proxy_clausification,[],[f123])).
% 0.20/0.38 thf(f125,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true = (((irel @ sK3 @ X1) => (q @ X1))))) )),
% 0.20/0.38 inference(beta-eta_normalization,[],[f124])).
% 0.20/0.38 thf(f126,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((q @ X1)))) )),
% 0.20/0.38 inference(imp_proxy_clausification,[],[f125])).
% 0.20/0.38 thf(f127,plain,(
% 0.20/0.38 ($false = (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))) @ sK4)))),
% 0.20/0.38 inference(sigma_proxy_clausification,[],[f121])).
% 0.20/0.38 thf(f128,plain,(
% 0.20/0.38 ($false = (((irel @ sK3 @ sK4) => (p @ sK4))))),
% 0.20/0.38 inference(beta-eta_normalization,[],[f127])).
% 0.20/0.38 thf(f130,plain,(
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% 0.20/0.38 inference(imp_proxy_clausification,[],[f128])).
% 0.20/0.38 thf(f397,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((irel @ X2 @ X1))) | ($true != ((irel @ X2 @ X0))) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.38 inference(constrained_superposition,[],[f60,f82])).
% 0.20/0.38 thf(f409,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($true != $true) | ($true = ((irel @ X0 @ sK4))) | ($true != ((irel @ X0 @ sK3)))) )),
% 0.20/0.38 inference(constrained_superposition,[],[f60,f130])).
% 0.20/0.38 thf(f410,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($true != ((irel @ X0 @ sK3))) | ($true = ((irel @ X0 @ sK4)))) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f409])).
% 0.20/0.38 thf(f416,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((irel @ X2 @ X0))) | ($true = ((irel @ X2 @ X1))) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f397])).
% 0.20/0.38 thf(f571,plain,(
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% 0.20/0.38 inference(constrained_superposition,[],[f410,f120])).
% 0.20/0.38 thf(f574,plain,(
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% 0.20/0.38 inference(trivial_inequality_removal,[],[f571])).
% 0.20/0.38 thf(f624,plain,(
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% 0.20/0.38 inference(constrained_superposition,[],[f115,f574])).
% 0.20/0.38 thf(f627,plain,(
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% 0.20/0.38 inference(trivial_inequality_removal,[],[f624])).
% 0.20/0.38 thf(f2021,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($true != $true) | ($true = ((irel @ sK3 @ X0))) | ($false = ((irel @ sK4 @ X0)))) )),
% 0.20/0.38 inference(constrained_superposition,[],[f416,f130])).
% 0.20/0.38 thf(f2028,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($false = ((irel @ sK4 @ X0))) | ($true = ((irel @ sK3 @ X0)))) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f2021])).
% 0.20/0.38 thf(f2461,plain,(
% 0.20/0.38 ($true = $false) | ($false = ((irel @ sK0 @ sK4))) | ($true = ((irel @ sK3 @ (sK1 @ sK4))))),
% 0.20/0.38 inference(constrained_superposition,[],[f106,f2028])).
% 0.20/0.38 thf(f2476,plain,(
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% 0.20/0.38 inference(trivial_inequality_removal,[],[f2461])).
% 0.20/0.38 thf(f3051,plain,(
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% 0.20/0.38 inference(forward_demodulation,[],[f2476,f574])).
% 0.20/0.38 thf(f3052,plain,(
% 0.20/0.38 ($true = ((irel @ sK3 @ (sK1 @ sK4))))),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3051])).
% 0.20/0.38 thf(f3059,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($true != $true) | ($true = ((irel @ sK3 @ X0))) | ($false = ((irel @ (sK1 @ sK4) @ X0)))) )),
% 0.20/0.38 inference(constrained_superposition,[],[f416,f3052])).
% 0.20/0.38 thf(f3062,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (($false = ((irel @ (sK1 @ sK4) @ X0))) | ($true = ((irel @ sK3 @ X0)))) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3059])).
% 0.20/0.38 thf(f3101,plain,(
% 0.20/0.38 ($true = $false) | ($false = ((irel @ sK0 @ sK4))) | ($true = ((irel @ sK3 @ (sK2 @ sK4))))),
% 0.20/0.38 inference(constrained_superposition,[],[f116,f3062])).
% 0.20/0.38 thf(f3113,plain,(
% 0.20/0.38 ($false = ((irel @ sK0 @ sK4))) | ($true = ((irel @ sK3 @ (sK2 @ sK4))))),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3101])).
% 0.20/0.38 thf(f3125,plain,(
% 0.20/0.38 ($true = $false) | ($true = ((irel @ sK3 @ (sK2 @ sK4))))),
% 0.20/0.38 inference(forward_demodulation,[],[f3113,f574])).
% 0.20/0.38 thf(f3126,plain,(
% 0.20/0.38 ($true = ((irel @ sK3 @ (sK2 @ sK4))))),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3125])).
% 0.20/0.38 thf(f3136,plain,(
% 0.20/0.38 ($true = $false) | ($true = ((q @ (sK2 @ sK4))))),
% 0.20/0.38 inference(constrained_superposition,[],[f126,f3126])).
% 0.20/0.38 thf(f3141,plain,(
% 0.20/0.38 ($true = ((q @ (sK2 @ sK4))))),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3136])).
% 0.20/0.38 thf(f3145,plain,(
% 0.20/0.38 ($true = $false)),
% 0.20/0.38 inference(forward_demodulation,[],[f3141,f627])).
% 0.20/0.38 thf(f3146,plain,(
% 0.20/0.38 $false),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f3145])).
% 0.20/0.38 % SZS output end Proof for theBenchmark
% 0.20/0.38 % (522545)------------------------------
% 0.20/0.38 % (522545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.38 % (522545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.38 % (522545)CaDiCaL version: 2.1.3
% 0.20/0.38 % (522545)Termination reason: Refutation
% 0.20/0.38 % (522545)Time elapsed: 0.097 s
% 0.20/0.38 % (522545)Peak memory usage: 13 MB
% 0.20/0.38 % (522545)Instructions burned: 182 (million)
% 0.20/0.38 % (522538)Success in time 0.143 s
% 0.20/0.38 % Vampire exiting
%------------------------------------------------------------------------------