%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL878^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:15:13 AM UTC 2026
% Result : Theorem 0.88s 0.42s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL878^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.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 10:23:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.88/0.42 % (1483632)Will run a generic schedule for satisfiability detection.
% 0.88/0.42 % (1483640)dis+10_1_sil=32000:sp=arity:random_seed=3905849749:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.88/0.42 % (1483638)% WARNING: option uhcvi not known.
% 0.88/0.42 % (1483637)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=866804889_2999 on theBenchmark for (2999ds/0Mi)
% 0.88/0.42 % (1483638)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2304931994:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.88/0.42 % (1483639)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1742264040:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.88/0.42 % (1483641)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1906483019:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.88/0.42 % (1483642)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1845314330:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.88/0.42 % (1483643)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1986557852:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.88/0.42 % (1483638)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.42 % (1483641)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.42 % Exception at run slice level
% 0.88/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.42 % (1483638)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.88/0.42 % (1483640)Instruction limit reached!
% 0.88/0.42 % (1483640)------------------------------
% 0.88/0.42 % (1483640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.42 % (1483640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.42 % (1483640)CaDiCaL version: 2.1.3
% 0.88/0.42 % (1483640)Termination reason: Instruction limit
% 0.88/0.42 % (1483640)Termination phase: Saturation
% 0.88/0.42 % (1483640)Time elapsed: 0.028 s
% 0.88/0.42 % (1483640)Peak memory usage: 12 MB
% 0.88/0.42 % (1483640)Instructions burned: 105 (million)
% 0.88/0.42 % (1483651)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3969125708:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.88/0.42 % Exception at run slice level
% 0.88/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.42 % (1483652)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1742193329:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.88/0.42 % (1483654)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=2026352583:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.88/0.42 % (1483654)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.42 % (1483654)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.88/0.42 % (1483641)Instruction limit reached!
% 0.88/0.42 % (1483641)------------------------------
% 0.88/0.42 % (1483641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.42 % (1483641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.42 % (1483641)CaDiCaL version: 2.1.3
% 0.88/0.42 % (1483641)Termination reason: Instruction limit
% 0.88/0.42 % (1483641)Termination phase: Saturation
% 0.88/0.42 % (1483641)Time elapsed: 0.058 s
% 0.88/0.42 % (1483641)Peak memory usage: 13 MB
% 0.88/0.42 % (1483641)Instructions burned: 117 (million)
% 0.88/0.42 % (1483642)Instruction limit reached!
% 0.88/0.42 % (1483642)------------------------------
% 0.88/0.42 % (1483642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.42 % (1483642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.42 % (1483642)CaDiCaL version: 2.1.3
% 0.88/0.42 % (1483642)Termination reason: Instruction limit
% 0.88/0.42 % (1483642)Termination phase: Saturation
% 0.88/0.42 % (1483642)Time elapsed: 0.065 s
% 0.88/0.42 % (1483642)Peak memory usage: 13 MB
% 0.88/0.42 % (1483642)Instructions burned: 132 (million)
% 0.88/0.42 % (1483652)Instruction limit reached!
% 0.88/0.42 % (1483652)------------------------------
% 0.88/0.42 % (1483652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.42 % (1483652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.42 % (1483652)CaDiCaL version: 2.1.3
% 0.88/0.42 % (1483652)Termination reason: Instruction limit
% 0.88/0.42 % (1483652)Termination phase: Saturation
% 0.88/0.42 % (1483652)Time elapsed: 0.036 s
% 0.88/0.42 % (1483652)Peak memory usage: 13 MB
% 0.88/0.42 % (1483652)Instructions burned: 131 (million)
% 0.88/0.42 % (1483659)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=902283377:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.88/0.42 % (1483657)ott-21_1_sil=16000:fs=off:random_seed=157797711:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.88/0.42 % (1483643)Instruction limit reached!
% 0.88/0.42 % (1483643)------------------------------
% 0.88/0.42 % (1483643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.42 % (1483643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.42 % (1483643)CaDiCaL version: 2.1.3
% 0.88/0.42 % (1483643)Termination reason: Instruction limit
% 0.88/0.42 % (1483643)Termination phase: Saturation
% 0.88/0.42 % (1483643)Time elapsed: 0.079 s
% 0.88/0.42 % (1483643)Peak memory usage: 13 MB
% 0.88/0.42 % (1483643)Instructions burned: 159 (million)
% 0.88/0.42 % Exception at run slice level
% 0.88/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.42 % (1483658)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2112563018:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.88/0.42 % (1483663)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1576781982:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.88/0.42 % Exception at run slice level
% 0.88/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.88/0.42 % (1483662)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3919420092:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.88/0.42 % (1483666)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1659462653:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.88/0.42 % (1483666)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.88/0.42 % (1483666) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1483632-1483666"...
% 0.88/0.42 % (1483666)...printing done.
% 0.88/0.42 % (1483666)Refutation found. Thanks to Tanya!
% 0.88/0.42 % SZS status Theorem for theBenchmark
% 0.88/0.42 % SZS output start Proof for theBenchmark
% 0.88/0.42 thf(type_def_5, type, mu: $tType).
% 0.88/0.42 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.88/0.42 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 0.88/0.42 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_14, type, mtrue: ($i > $o)).
% 0.88/0.42 thf(func_def_15, type, mfalse: ($i > $o)).
% 0.88/0.42 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.88/0.42 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 0.88/0.42 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 0.88/0.42 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 0.88/0.42 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 0.88/0.42 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 0.88/0.42 thf(func_def_32, type, db2: !>[X0: $tType]:(X0)).
% 0.88/0.42 thf(func_def_33, type, db1: !>[X0: $tType]:(X0)).
% 0.88/0.42 thf(func_def_34, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.88/0.42 thf(func_def_35, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.88/0.42 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 0.88/0.42 thf(func_def_37, type, vNOT: ($o > $o)).
% 0.88/0.42 thf(func_def_38, type, vOR: ($o > $o > $o)).
% 0.88/0.42 thf(func_def_39, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.88/0.42 thf(func_def_42, type, db3: !>[X0: $tType]:(X0)).
% 0.88/0.42 thf(func_def_43, type, vIMP: ($o > $o > $o)).
% 0.88/0.42 thf(func_def_44, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.88/0.42 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.88/0.42 thf(func_def_46, type, db4: !>[X0: $tType]:(X0)).
% 0.88/0.42 thf(func_def_47, type, sK0: ($i > $i > $o)).
% 0.88/0.42 thf(func_def_48, type, sK1: ($i > $i > $o)).
% 0.88/0.42 thf(func_def_51, type, sK4: (($i > $o) > $i > $i)).
% 0.88/0.42 thf(func_def_53, type, sK6: ($i > $o)).
% 0.88/0.42 thf(func_def_56, type, sK9: ($i > $o)).
% 0.88/0.42 thf(func_def_59, type, sK12: ($i > $i)).
% 0.88/0.42 thf(func_def_60, type, sK13: ($i > $i)).
% 0.88/0.42 thf(func_def_61, type, sK14: ($i > $i)).
% 0.88/0.42 thf(f3,axiom,(
% 0.88/0.42 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot)).
% 0.88/0.42 thf(f4,axiom,(
% 0.88/0.42 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor)).
% 0.88/0.42 thf(f6,axiom,(
% 0.88/0.42 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 0.88/0.42 thf(f11,axiom,(
% 0.88/0.42 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 0.88/0.42 thf(f16,axiom,(
% 0.88/0.42 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox)).
% 0.88/0.42 thf(f28,axiom,(
% 0.88/0.42 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 0.88/0.42 thf(f32,conjecture,(
% 0.88/0.42 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((mvalid @ (mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ X2) @ (mbox @ X1 @ X2)))))) <=> ! [X3 : $i,X4 : $i] : ((X1 @ X3 @ X4) => (X0 @ X3 @ X4)))),
% 0.88/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.88/0.42 thf(f33,negated_conjecture,(
% 0.88/0.42 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((mvalid @ (mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ X2) @ (mbox @ X1 @ X2)))))) <=> ! [X3 : $i,X4 : $i] : ((X1 @ X3 @ X4) => (X0 @ X3 @ X4)))),
% 0.88/0.42 inference(negated_conjecture,[status(cth)],[f32])).
% 0.88/0.42 thf(f36,plain,(
% 0.88/0.42 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.88/0.43 inference(rectify,[],[f3])).
% 0.88/0.43 thf(f37,plain,(
% 0.88/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.88/0.43 inference(fool_elimination,[],[f36])).
% 0.88/0.43 thf(f38,plain,(
% 0.88/0.43 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.88/0.43 inference(rectify,[],[f4])).
% 0.88/0.43 thf(f39,plain,(
% 0.88/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.88/0.43 inference(fool_elimination,[],[f38])).
% 0.88/0.43 thf(f41,plain,(
% 0.88/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.88/0.43 inference(fool_elimination,[],[f6])).
% 0.88/0.43 thf(f47,plain,(
% 0.88/0.43 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 0.88/0.43 inference(rectify,[],[f11])).
% 0.88/0.43 thf(f48,plain,(
% 0.88/0.43 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.88/0.43 inference(fool_elimination,[],[f47])).
% 0.88/0.43 thf(f54,plain,(
% 0.88/0.43 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.88/0.43 inference(rectify,[],[f16])).
% 0.88/0.43 thf(f55,plain,(
% 0.88/0.43 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.88/0.43 inference(fool_elimination,[],[f54])).
% 0.88/0.43 thf(f77,plain,(
% 0.88/0.43 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.88/0.43 inference(rectify,[],[f28])).
% 0.88/0.43 thf(f78,plain,(
% 0.88/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.88/0.43 inference(fool_elimination,[],[f77])).
% 0.88/0.43 thf(f85,plain,(
% 0.88/0.43 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((mvalid @ (mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ X2) @ (mbox @ X1 @ X2)))))) <=> ! [X3 : $i,X4 : $i] : ((X1 @ X3 @ X4) => (X0 @ X3 @ X4)))),
% 0.88/0.43 inference(rectify,[],[f33])).
% 0.88/0.43 thf(f86,plain,(
% 0.88/0.43 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0))))))) <=> ! [X3 : $i,X4 : $i] : ((((X1 @ X3 @ X4)) = $true) => (((X0 @ X3 @ X4)) = $true)))),
% 0.88/0.43 inference(fool_elimination,[],[f85])).
% 0.88/0.43 thf(f87,plain,(
% 0.88/0.43 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0))))))) <=> ! [X2 : $i,X3 : $i] : (($true = ((X1 @ X2 @ X3))) => (((X0 @ X2 @ X3)) = $true)))),
% 0.88/0.43 inference(rectify,[],[f86])).
% 0.88/0.43 thf(f88,plain,(
% 0.88/0.43 ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0))))))) <~> ! [X2 : $i,X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | ($true != ((X1 @ X2 @ X3)))))),
% 0.88/0.43 inference(ennf_transformation,[],[f87])).
% 0.88/0.43 thf(f89,plain,(
% 0.88/0.43 ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((? [X2 : $i,X3 : $i] : ((((X0 @ X2 @ X3)) != $true) & ($true = ((X1 @ X2 @ X3)))) | ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0)))))))) & (! [X2 : $i,X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | ($true != ((X1 @ X2 @ X3)))) | ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0)))))))))),
% 0.88/0.43 inference(nnf_transformation,[],[f88])).
% 0.88/0.43 thf(f90,plain,(
% 0.88/0.43 ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((? [X2 : $i,X3 : $i] : ((((X0 @ X2 @ X3)) != $true) & ($true = ((X1 @ X2 @ X3)))) | ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0)))))))) & (! [X4 : $i,X5 : $i] : (($true = ((X0 @ X4 @ X5))) | ($true != ((X1 @ X4 @ X5)))) | ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mbox @ X1 @ Y0)))))))))),
% 0.88/0.43 inference(rectify,[],[f89])).
% 0.88/0.43 thf(f91,plain,(
% 0.88/0.43 ((($true != ((sK0 @ sK2 @ sK3))) & ($true = ((sK1 @ sK2 @ sK3)))) | ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK1 @ Y0)))))))) & (! [X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5)))) | ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK1 @ Y0))))))))),
% 0.88/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f90])).
% 0.88/0.43 thf(f94,plain,(
% 0.88/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f37])).
% 0.88/0.43 thf(f95,plain,(
% 0.88/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f39])).
% 0.88/0.43 thf(f97,plain,(
% 0.88/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.88/0.43 inference(cnf_transformation,[],[f41])).
% 0.88/0.43 thf(f102,plain,(
% 0.88/0.43 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f48])).
% 0.88/0.43 thf(f107,plain,(
% 0.88/0.43 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f55])).
% 0.88/0.43 thf(f119,plain,(
% 0.88/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.88/0.43 inference(cnf_transformation,[],[f78])).
% 0.88/0.43 thf(f123,plain,(
% 0.88/0.43 ( ! [X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK1 @ Y0)))))))) )),
% 0.88/0.43 inference(cnf_transformation,[],[f91])).
% 0.88/0.43 thf(f124,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK1 @ Y0)))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f91])).
% 0.88/0.43 thf(f125,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mbox @ sK1 @ Y0)))))))),
% 0.88/0.43 inference(cnf_transformation,[],[f91])).
% 0.88/0.43 thf(f127,definition,(
% 0.88/0.43 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.88/0.43 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.88/0.43 thf(f129,plain,(
% 0.88/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.88/0.43 inference(definition_unfolding,[],[f97,f95,f94])).
% 0.88/0.43 thf(f137,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK1 @ Y0)))))))),
% 0.88/0.43 inference(definition_unfolding,[],[f125,f119,f102,f129,f107,f107])).
% 0.88/0.43 thf(f138,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK1 @ Y0)))))))),
% 0.88/0.43 inference(definition_unfolding,[],[f124,f119,f102,f129,f107,f107])).
% 0.88/0.43 thf(f139,plain,(
% 0.88/0.43 ( ! [X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK1 @ Y0)))))))) )),
% 0.88/0.43 inference(definition_unfolding,[],[f123,f119,f102,f129,f107,f107])).
% 0.88/0.43 thf(f140,plain,(
% 0.88/0.43 ( ! [X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f139])).
% 0.88/0.43 thf(f141,plain,(
% 0.88/0.43 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ X6)))) )),
% 0.88/0.43 inference(pi_proxy_clausification,[],[f140])).
% 0.88/0.43 thf(f142,plain,(
% 0.88/0.43 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X6 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ X6 @ Y1)) | (Y0 @ Y1)))))))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f141])).
% 0.88/0.43 thf(f143,plain,(
% 0.88/0.43 ( ! [X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X6 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ X6 @ Y1)) | (Y0 @ Y1)))))) @ X7)))) )),
% 0.88/0.43 inference(pi_proxy_clausification,[],[f142])).
% 0.88/0.43 thf(f144,plain,(
% 0.88/0.43 ( ! [X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X6 @ Y0)) | (X7 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X6 @ Y0)) | (X7 @ Y0)))))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f143])).
% 0.88/0.43 thf(f145,plain,(
% 0.88/0.43 ( ! [X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ X6 @ Y0)) | (X7 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X6 @ Y0)) | (X7 @ Y0)))))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f144])).
% 0.88/0.43 thf(f146,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X6 @ Y0)) | (X7 @ Y0))) @ X8))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X6 @ Y0)) | (X7 @ Y0)))))))) )),
% 0.88/0.43 inference(pi_proxy_clausification,[],[f145])).
% 0.88/0.43 thf(f147,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X6 @ Y0)) | (X7 @ Y0))) @ X8))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X6 @ Y0)) | (X7 @ Y0))))))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f146])).
% 0.88/0.43 thf(f148,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ X6 @ Y0)) | (X7 @ Y0))) @ X8))) | ($false = (((^[Y0 : $i]: ((~ (sK0 @ X6 @ Y0)) | (X7 @ Y0))) @ (sK4 @ X7 @ X6))))) )),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f147])).
% 0.88/0.43 thf(f149,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = (((~ (sK1 @ X6 @ X8)) | (X7 @ X8)))) | ($false = (((~ (sK0 @ X6 @ (sK4 @ X7 @ X6))) | (X7 @ (sK4 @ X7 @ X6)))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f148])).
% 0.88/0.43 thf(f150,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($false = (((~ (sK0 @ X6 @ (sK4 @ X7 @ X6))) | (X7 @ (sK4 @ X7 @ X6))))) | ($true = ((~ (sK1 @ X6 @ X8))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f149])).
% 0.88/0.43 thf(f151,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($false = ((X7 @ (sK4 @ X7 @ X6)))) | ($true = ((~ (sK1 @ X6 @ X8))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f150])).
% 0.88/0.43 thf(f152,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($false = ((~ (sK0 @ X6 @ (sK4 @ X7 @ X6))))) | ($true = ((~ (sK1 @ X6 @ X8))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f150])).
% 0.88/0.43 thf(f153,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($true = ((sK0 @ X6 @ (sK4 @ X7 @ X6)))) | ($true = ((~ (sK1 @ X6 @ X8))))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f152])).
% 0.88/0.43 thf(f154,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($true = ((sK0 @ X6 @ (sK4 @ X7 @ X6)))) | ($false = ((sK1 @ X6 @ X8)))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f153])).
% 0.88/0.43 thf(f155,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))) | ($true = ((X7 @ X8))) | ($false = ((X7 @ (sK4 @ X7 @ X6)))) | ($false = ((sK1 @ X6 @ X8)))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f151])).
% 0.88/0.43 thf(f156,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f138])).
% 0.88/0.43 thf(f157,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ sK5)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f156])).
% 0.88/0.43 thf(f158,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK5 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ sK5 @ Y1)) | (Y0 @ Y1)))))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f157])).
% 0.88/0.43 thf(f159,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK5 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ sK5 @ Y1)) | (Y0 @ Y1)))))) @ sK6)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f158])).
% 0.88/0.43 thf(f160,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK5 @ Y0)) | (sK6 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ sK5 @ Y0)) | (sK6 @ Y0)))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f159])).
% 0.88/0.43 thf(f161,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ sK5 @ Y0)) | (sK6 @ Y0))))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f160])).
% 0.88/0.43 thf(f162,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK5 @ Y0)) | (sK6 @ Y0)))))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f160])).
% 0.88/0.43 thf(f163,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK5 @ Y0)) | (sK6 @ Y0))))))),
% 0.88/0.43 inference(not_proxy_clausification,[],[f162])).
% 0.88/0.43 thf(f164,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true = ((sK1 @ sK2 @ sK3))) | ($true = (((^[Y0 : $i]: ((~ (sK0 @ sK5 @ Y0)) | (sK6 @ Y0))) @ X1)))) )),
% 0.88/0.43 inference(pi_proxy_clausification,[],[f163])).
% 0.88/0.43 thf(f165,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true = ((sK1 @ sK2 @ sK3))) | ($true = (((~ (sK0 @ sK5 @ X1)) | (sK6 @ X1))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f164])).
% 0.88/0.43 thf(f166,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true = ((sK1 @ sK2 @ sK3))) | ($true = ((sK6 @ X1))) | ($true = ((~ (sK0 @ sK5 @ X1))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f165])).
% 0.88/0.43 thf(f167,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true = ((sK1 @ sK2 @ sK3))) | ($true = ((sK6 @ X1))) | ($false = ((sK0 @ sK5 @ X1)))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f166])).
% 0.88/0.43 thf(f168,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ sK5 @ Y0)) | (sK6 @ Y0))) @ sK7)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f161])).
% 0.88/0.43 thf(f169,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = (((~ (sK1 @ sK5 @ sK7)) | (sK6 @ sK7))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f168])).
% 0.88/0.43 thf(f170,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = ((sK6 @ sK7)))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f169])).
% 0.88/0.43 thf(f171,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($false = ((~ (sK1 @ sK5 @ sK7))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f169])).
% 0.88/0.43 thf(f172,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ($true = ((sK1 @ sK5 @ sK7)))),
% 0.88/0.43 inference(not_proxy_clausification,[],[f171])).
% 0.88/0.43 thf(f173,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f137])).
% 0.88/0.43 thf(f174,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ sK8)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f173])).
% 0.88/0.43 thf(f175,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK8 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ sK8 @ Y1)) | (Y0 @ Y1)))))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f174])).
% 0.88/0.43 thf(f176,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ sK8 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ sK8 @ Y1)) | (Y0 @ Y1)))))) @ sK9)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f175])).
% 0.88/0.43 thf(f177,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK8 @ Y0)) | (sK9 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ sK8 @ Y0)) | (sK9 @ Y0)))))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f176])).
% 0.88/0.43 thf(f178,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ sK8 @ Y0)) | (sK9 @ Y0))))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f177])).
% 0.88/0.43 thf(f179,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK8 @ Y0)) | (sK9 @ Y0)))))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f177])).
% 0.88/0.43 thf(f180,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ sK8 @ Y0)) | (sK9 @ Y0))))))),
% 0.88/0.43 inference(not_proxy_clausification,[],[f179])).
% 0.88/0.43 thf(f181,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true != ((sK0 @ sK2 @ sK3))) | ($true = (((^[Y0 : $i]: ((~ (sK0 @ sK8 @ Y0)) | (sK9 @ Y0))) @ X1)))) )),
% 0.88/0.43 inference(pi_proxy_clausification,[],[f180])).
% 0.88/0.43 thf(f182,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true != ((sK0 @ sK2 @ sK3))) | ($true = (((~ (sK0 @ sK8 @ X1)) | (sK9 @ X1))))) )),
% 0.88/0.43 inference(beta-eta_normalization,[],[f181])).
% 0.88/0.43 thf(f183,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true != ((sK0 @ sK2 @ sK3))) | ($true = ((sK9 @ X1))) | ($true = ((~ (sK0 @ sK8 @ X1))))) )),
% 0.88/0.43 inference(or_proxy_clausification,[],[f182])).
% 0.88/0.43 thf(f184,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($true != ((sK0 @ sK2 @ sK3))) | ($true = ((sK9 @ X1))) | ($false = ((sK0 @ sK8 @ X1)))) )),
% 0.88/0.43 inference(not_proxy_clausification,[],[f183])).
% 0.88/0.43 thf(f185,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ sK8 @ Y0)) | (sK9 @ Y0))) @ sK10)))),
% 0.88/0.43 inference(sigma_proxy_clausification,[],[f178])).
% 0.88/0.43 thf(f186,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = (((~ (sK1 @ sK8 @ sK10)) | (sK9 @ sK10))))),
% 0.88/0.43 inference(beta-eta_normalization,[],[f185])).
% 0.88/0.43 thf(f187,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = ((sK9 @ sK10)))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f186])).
% 0.88/0.43 thf(f188,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($false = ((~ (sK1 @ sK8 @ sK10))))),
% 0.88/0.43 inference(or_proxy_clausification,[],[f186])).
% 0.88/0.43 thf(f189,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | ($true = ((sK1 @ sK8 @ sK10)))),
% 0.88/0.43 inference(not_proxy_clausification,[],[f188])).
% 0.88/0.43 thf(f191,definition,(
% 0.88/0.43 spl11_1 <=> ! [X6 : $i,X8 : $i,X7 : ($i > $o)] : (($true = ((X7 @ X8))) | ($false = ((sK1 @ X6 @ X8))) | ($true = ((sK0 @ X6 @ (sK4 @ X7 @ X6)))))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition])).
% 0.88/0.43 thf(f192,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o)] : (($true = ((X7 @ X8))) | ($false = ((sK1 @ X6 @ X8))) | ($true = ((sK0 @ X6 @ (sK4 @ X7 @ X6))))) ) | ~spl11_1),
% 0.88/0.43 inference(avatar_component_clause,[],[f191])).
% 0.88/0.43 thf(f194,definition,(
% 0.88/0.43 spl11_2 <=> ! [X4 : $i,X5 : $i] : (($true = ((sK0 @ X4 @ X5))) | ($true != ((sK1 @ X4 @ X5))))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition])).
% 0.88/0.43 thf(f195,plain,(
% 0.88/0.43 ( ! [X4 : $i,X5 : $i] : (($true != ((sK1 @ X4 @ X5))) | ($true = ((sK0 @ X4 @ X5)))) ) | ~spl11_2),
% 0.88/0.43 inference(avatar_component_clause,[],[f194])).
% 0.88/0.43 thf(f196,plain,(
% 0.88/0.43 spl11_1 | spl11_2),
% 0.88/0.43 inference(avatar_split_clause,[],[f154,f194,f191])).
% 0.88/0.43 thf(f198,definition,(
% 0.88/0.43 spl11_3 <=> ! [X6 : $i,X8 : $i,X7 : ($i > $o)] : (($true = ((X7 @ X8))) | ($false = ((sK1 @ X6 @ X8))) | ($false = ((X7 @ (sK4 @ X7 @ X6)))))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition])).
% 0.88/0.43 thf(f199,plain,(
% 0.88/0.43 ( ! [X8 : $i,X6 : $i,X7 : ($i > $o)] : (($true = ((X7 @ X8))) | ($false = ((sK1 @ X6 @ X8))) | ($false = ((X7 @ (sK4 @ X7 @ X6))))) ) | ~spl11_3),
% 0.88/0.43 inference(avatar_component_clause,[],[f198])).
% 0.88/0.43 thf(f200,plain,(
% 0.88/0.43 spl11_3 | spl11_2),
% 0.88/0.43 inference(avatar_split_clause,[],[f155,f194,f198])).
% 0.88/0.43 thf(f202,definition,(
% 0.88/0.43 spl11_4 <=> ! [X1 : $i] : (($true = ((sK6 @ X1))) | ($false = ((sK0 @ sK5 @ X1))))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])).
% 0.88/0.43 thf(f203,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($false = ((sK0 @ sK5 @ X1))) | ($true = ((sK6 @ X1)))) ) | ~spl11_4),
% 0.88/0.43 inference(avatar_component_clause,[],[f202])).
% 0.88/0.43 thf(f205,definition,(
% 0.88/0.43 spl11_5 <=> ($true = ((sK1 @ sK2 @ sK3)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition])).
% 0.88/0.43 thf(f207,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK2 @ sK3))) | ~spl11_5),
% 0.88/0.43 inference(avatar_component_clause,[],[f205])).
% 0.88/0.43 thf(f208,plain,(
% 0.88/0.43 spl11_4 | spl11_5),
% 0.88/0.43 inference(avatar_split_clause,[],[f167,f205,f202])).
% 0.88/0.43 thf(f210,definition,(
% 0.88/0.43 spl11_6 <=> ($true = ((sK1 @ sK5 @ sK7)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition])).
% 0.88/0.43 thf(f212,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK5 @ sK7))) | ~spl11_6),
% 0.88/0.43 inference(avatar_component_clause,[],[f210])).
% 0.88/0.43 thf(f213,plain,(
% 0.88/0.43 spl11_6 | spl11_5),
% 0.88/0.43 inference(avatar_split_clause,[],[f172,f205,f210])).
% 0.88/0.43 thf(f215,definition,(
% 0.88/0.43 spl11_7 <=> ($false = ((sK6 @ sK7)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition])).
% 0.88/0.43 thf(f217,plain,(
% 0.88/0.43 ($false = ((sK6 @ sK7))) | ~spl11_7),
% 0.88/0.43 inference(avatar_component_clause,[],[f215])).
% 0.88/0.43 thf(f218,plain,(
% 0.88/0.43 spl11_7 | spl11_5),
% 0.88/0.43 inference(avatar_split_clause,[],[f170,f205,f215])).
% 0.88/0.43 thf(f220,definition,(
% 0.88/0.43 spl11_8 <=> ! [X1 : $i] : (($true = ((sK9 @ X1))) | ($false = ((sK0 @ sK8 @ X1))))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 0.88/0.43 thf(f221,plain,(
% 0.88/0.43 ( ! [X1 : $i] : (($false = ((sK0 @ sK8 @ X1))) | ($true = ((sK9 @ X1)))) ) | ~spl11_8),
% 0.88/0.43 inference(avatar_component_clause,[],[f220])).
% 0.88/0.43 thf(f223,definition,(
% 0.88/0.43 spl11_9 <=> ($true = ((sK0 @ sK2 @ sK3)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition])).
% 0.88/0.43 thf(f225,plain,(
% 0.88/0.43 ($true != ((sK0 @ sK2 @ sK3))) | spl11_9),
% 0.88/0.43 inference(avatar_component_clause,[],[f223])).
% 0.88/0.43 thf(f226,plain,(
% 0.88/0.43 spl11_8 | ~spl11_9),
% 0.88/0.43 inference(avatar_split_clause,[],[f184,f223,f220])).
% 0.88/0.43 thf(f228,definition,(
% 0.88/0.43 spl11_10 <=> ($true = ((sK1 @ sK8 @ sK10)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition])).
% 0.88/0.43 thf(f230,plain,(
% 0.88/0.43 ($true = ((sK1 @ sK8 @ sK10))) | ~spl11_10),
% 0.88/0.43 inference(avatar_component_clause,[],[f228])).
% 0.88/0.43 thf(f231,plain,(
% 0.88/0.43 spl11_10 | ~spl11_9),
% 0.88/0.43 inference(avatar_split_clause,[],[f189,f223,f228])).
% 0.88/0.43 thf(f233,definition,(
% 0.88/0.43 spl11_11 <=> ($false = ((sK9 @ sK10)))),
% 0.88/0.43 introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition])).
% 0.88/0.43 thf(f235,plain,(
% 0.88/0.43 ($false = ((sK9 @ sK10))) | ~spl11_11),
% 0.88/0.43 inference(avatar_component_clause,[],[f233])).
% 0.88/0.43 thf(f236,plain,(
% 0.88/0.43 spl11_11 | ~spl11_9),
% 0.88/0.43 inference(avatar_split_clause,[],[f187,f223,f233])).
% 0.88/0.43 thf(f249,plain,(
% 0.88/0.43 ($true != $true) | ($true = ((sK0 @ sK2 @ sK3))) | (~spl11_2 | ~spl11_5)),
% 0.88/0.43 inference(constrained_superposition,[],[f195,f207])).
% 0.88/0.43 thf(f250,plain,(
% 0.88/0.43 ($true != $true) | ($true = ((sK0 @ sK8 @ sK10))) | (~spl11_2 | ~spl11_10)),
% 0.88/0.43 inference(constrained_superposition,[],[f195,f230])).
% 0.88/0.43 thf(f251,plain,(
% 0.88/0.43 ($true = ((sK0 @ sK8 @ sK10))) | (~spl11_2 | ~spl11_10)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f250])).
% 0.88/0.43 thf(f252,plain,(
% 0.88/0.43 ($true = ((sK0 @ sK2 @ sK3))) | (~spl11_2 | ~spl11_5)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f249])).
% 0.88/0.43 thf(f254,plain,(
% 0.88/0.43 spl11_9 | ~spl11_2 | ~spl11_5),
% 0.88/0.43 inference(avatar_split_clause,[],[f252,f205,f194,f223])).
% 0.88/0.43 thf(f255,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK9 @ sK10))) | (~spl11_2 | ~spl11_8 | ~spl11_10)),
% 0.88/0.43 inference(constrained_superposition,[],[f251,f221])).
% 0.88/0.43 thf(f258,plain,(
% 0.88/0.43 ($true = ((sK9 @ sK10))) | (~spl11_2 | ~spl11_8 | ~spl11_10)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f255])).
% 0.88/0.43 thf(f262,plain,(
% 0.88/0.43 ($true = $false) | (~spl11_2 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(forward_demodulation,[],[f258,f235])).
% 0.88/0.43 thf(f263,plain,(
% 0.88/0.43 $false | (~spl11_2 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f262])).
% 0.88/0.43 thf(f264,plain,(
% 0.88/0.43 ~spl11_2 | ~spl11_8 | ~spl11_10 | ~spl11_11),
% 0.88/0.43 inference(avatar_contradiction_clause,[],[f263])).
% 0.88/0.43 thf(f289,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : (($true != $true) | ($false = ((sK1 @ X2 @ X1))) | ($false = (((^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X2)))) | (sK2 != ((X0 @ X1))) | (sK3 != X1)) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(constrained_superposition,[],[f225,f199])).
% 0.88/0.43 thf(f297,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (sK4 @ X0 @ X2)))) | ($false = ((sK1 @ X2 @ X1))) | ($false = ((X0 @ (sK4 @ X0 @ X2)))) | (((X0 @ X1)) != $false)) ) | ~spl11_3),
% 0.88/0.43 inference(equality_factoring,[],[f199])).
% 0.88/0.43 thf(f336,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : (($false = ((sK1 @ X2 @ X1))) | ($false = (((^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X2)))) | (sK2 != ((X0 @ X1))) | (sK3 != X1)) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f289])).
% 0.88/0.43 thf(f337,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((sK2 != ((X0 @ X1))) | ($false = ((sK0 @ (X0 @ (sK4 @ (^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ Y0)) @ X2)) @ (sK4 @ (^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ Y0)) @ X2)))) | ($false = ((sK1 @ X2 @ X1))) | (sK3 != X1)) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f336])).
% 0.88/0.43 thf(f375,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $false) | ($false = ((X0 @ (sK4 @ X0 @ X2)))) | ($false = ((sK1 @ X2 @ X1)))) ) | ~spl11_3),
% 0.88/0.43 inference(forward_subsumption_resolution,[],[f297,f127])).
% 0.88/0.43 thf(f473,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false = ((sK0 @ ((^[Y0 : $i]: (sK2)) @ (sK4 @ (^[Y0 : $i]: (sK0 @ ((^[Y1 : $i]: (sK2)) @ Y0) @ Y0)) @ X0)) @ (sK4 @ (^[Y0 : $i]: (sK0 @ ((^[Y1 : $i]: (sK2)) @ Y0) @ Y0)) @ X0)))) | ($false = ((sK1 @ X0 @ X1))) | (sK3 != X1)) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(equality_resolution,[],[f337])).
% 0.88/0.43 thf(f474,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : ((sK3 != X1) | ($false = ((sK1 @ X0 @ X1))) | ($false = ((sK0 @ sK2 @ (sK4 @ (sK0 @ sK2) @ X0))))) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f473])).
% 0.88/0.43 thf(f486,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($false = ((sK0 @ sK2 @ (sK4 @ (sK0 @ sK2) @ X0)))) | ($false = ((sK1 @ X0 @ sK3)))) ) | (~spl11_3 | spl11_9)),
% 0.88/0.43 inference(equality_resolution,[],[f474])).
% 0.88/0.43 thf(f610,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($true = $false) | (((sK1 @ sK2 @ sK3)) = $false) | ($true = ((sK0 @ sK2 @ X0))) | ($false = ((sK1 @ sK2 @ X0)))) ) | (~spl11_1 | ~spl11_3 | spl11_9)),
% 0.88/0.43 inference(constrained_superposition,[],[f486,f192])).
% 0.88/0.43 thf(f617,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true != ((sK1 @ X2 @ X1))) | ($false = ((sK1 @ X2 @ X1))) | ($true = ((sK0 @ X2 @ (sK4 @ X0 @ X2)))) | (((X0 @ X1)) != $false)) ) | ~spl11_1),
% 0.88/0.43 inference(equality_factoring,[],[f192])).
% 0.88/0.43 thf(f649,plain,(
% 0.88/0.43 ( ! [X0 : $i] : ((((sK1 @ sK2 @ sK3)) = $false) | ($true = ((sK0 @ sK2 @ X0))) | ($false = ((sK1 @ sK2 @ X0)))) ) | (~spl11_1 | ~spl11_3 | spl11_9)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f610])).
% 0.88/0.43 thf(f721,plain,(
% 0.88/0.43 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $false) | ($true = ((sK0 @ X2 @ (sK4 @ X0 @ X2)))) | ($false = ((sK1 @ X2 @ X1)))) ) | ~spl11_1),
% 0.88/0.43 inference(forward_subsumption_resolution,[],[f617,f127])).
% 0.88/0.43 thf(f722,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK0 @ sK2 @ X0))) | ($false = ((sK1 @ sK2 @ X0)))) ) | (~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9)),
% 0.88/0.43 inference(forward_demodulation,[],[f649,f207])).
% 0.88/0.43 thf(f723,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($false = ((sK1 @ sK2 @ X0))) | ($true = ((sK0 @ sK2 @ X0)))) ) | (~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f722])).
% 0.88/0.43 thf(f730,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK0 @ sK2 @ sK3))) | (~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9)),
% 0.88/0.43 inference(constrained_superposition,[],[f723,f207])).
% 0.88/0.43 thf(f765,plain,(
% 0.88/0.43 ($true = ((sK0 @ sK2 @ sK3))) | (~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f730])).
% 0.88/0.43 thf(f769,plain,(
% 0.88/0.43 $false | (~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9)),
% 0.88/0.43 inference(forward_subsumption_resolution,[],[f765,f225])).
% 0.88/0.43 thf(f770,plain,(
% 0.88/0.43 ~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9),
% 0.88/0.43 inference(avatar_contradiction_clause,[],[f769])).
% 0.88/0.43 thf(f776,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((sK1 @ X1 @ X0))) | ($true = ((sK0 @ X1 @ (sK4 @ (^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | (sK10 != X0)) ) | (~spl11_1 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f192,f235])).
% 0.88/0.43 thf(f780,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((sK1 @ X1 @ X0))) | ($false = (((^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | (sK10 != X0)) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f199,f235])).
% 0.88/0.43 thf(f786,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false = ((sK1 @ X1 @ X0))) | ($false = (((^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | (sK10 != X0)) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f780])).
% 0.88/0.43 thf(f787,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : ((sK10 != X0) | ($false = ((sK9 @ (sK4 @ sK9 @ X1)))) | ($false = ((sK1 @ X1 @ X0)))) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f786])).
% 0.88/0.43 thf(f794,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false = ((sK1 @ X1 @ X0))) | ($true = ((sK0 @ X1 @ (sK4 @ (^[Y0 : $i]: (sK9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | (sK10 != X0)) ) | (~spl11_1 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f776])).
% 0.88/0.43 thf(f795,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : ((sK10 != X0) | ($true = ((sK0 @ X1 @ (sK4 @ sK9 @ X1)))) | ($false = ((sK1 @ X1 @ X0)))) ) | (~spl11_1 | ~spl11_11)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f794])).
% 0.88/0.43 thf(f880,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($false = ((sK9 @ (sK4 @ sK9 @ X0)))) | ($false = ((sK1 @ X0 @ sK10)))) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(equality_resolution,[],[f787])).
% 0.88/0.43 thf(f881,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($true = $false) | ($false = ((sK1 @ X0 @ sK10))) | ($false = ((sK9 @ (sK4 @ sK9 @ X0))))) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f880,f127])).
% 0.88/0.43 thf(f1024,plain,(
% 0.88/0.43 ($true != $true) | ($true = ((sK0 @ sK5 @ sK7))) | (~spl11_2 | ~spl11_6)),
% 0.88/0.43 inference(constrained_superposition,[],[f195,f212])).
% 0.88/0.43 thf(f1027,plain,(
% 0.88/0.43 ($true = ((sK0 @ sK5 @ sK7))) | (~spl11_2 | ~spl11_6)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1024])).
% 0.88/0.43 thf(f1029,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK6 @ sK7))) | (~spl11_2 | ~spl11_4 | ~spl11_6)),
% 0.88/0.43 inference(constrained_superposition,[],[f1027,f203])).
% 0.88/0.43 thf(f1032,plain,(
% 0.88/0.43 ($true = ((sK6 @ sK7))) | (~spl11_2 | ~spl11_4 | ~spl11_6)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1029])).
% 0.88/0.43 thf(f1036,plain,(
% 0.88/0.43 ($true = $false) | (~spl11_2 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(forward_demodulation,[],[f1032,f217])).
% 0.88/0.43 thf(f1037,plain,(
% 0.88/0.43 $false | (~spl11_2 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1036])).
% 0.88/0.43 thf(f1038,plain,(
% 0.88/0.43 ~spl11_2 | ~spl11_4 | ~spl11_6 | ~spl11_7),
% 0.88/0.43 inference(avatar_contradiction_clause,[],[f1037])).
% 0.88/0.43 thf(f1067,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($false = ((sK9 @ (sK4 @ sK9 @ X0)))) | ($false = ((sK1 @ X0 @ sK10)))) ) | (~spl11_3 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f881])).
% 0.88/0.43 thf(f1132,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false != $false) | ($false = (((^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | ($false = ((sK1 @ X1 @ X0))) | (sK7 != X0)) ) | (~spl11_3 | ~spl11_7)),
% 0.88/0.43 inference(constrained_superposition,[],[f375,f217])).
% 0.88/0.43 thf(f1154,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | ($false = ((sK1 @ X1 @ X0))) | (sK7 != X0)) ) | (~spl11_3 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1132])).
% 0.88/0.43 thf(f1155,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : ((sK7 != X0) | ($false = ((sK1 @ X1 @ X0))) | ($false = ((sK6 @ (sK4 @ sK6 @ X1))))) ) | (~spl11_3 | ~spl11_7)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f1154])).
% 0.88/0.43 thf(f1175,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($false = ((sK6 @ (sK4 @ sK6 @ X0)))) | ($false = ((sK1 @ X0 @ sK7)))) ) | (~spl11_3 | ~spl11_7)),
% 0.88/0.43 inference(equality_resolution,[],[f1155])).
% 0.88/0.43 thf(f1203,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($false != $false) | ($true = ((sK0 @ X1 @ (sK4 @ (^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | ($false = ((sK1 @ X1 @ X0))) | (sK7 != X0)) ) | (~spl11_1 | ~spl11_7)),
% 0.88/0.43 inference(constrained_superposition,[],[f721,f217])).
% 0.88/0.43 thf(f1230,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : (($true = ((sK0 @ X1 @ (sK4 @ (^[Y0 : $i]: (sK6 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1)))) | ($false = ((sK1 @ X1 @ X0))) | (sK7 != X0)) ) | (~spl11_1 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1203])).
% 0.88/0.43 thf(f1231,plain,(
% 0.88/0.43 ( ! [X0 : $i,X1 : $i] : ((sK7 != X0) | ($false = ((sK1 @ X1 @ X0))) | ($true = ((sK0 @ X1 @ (sK4 @ sK6 @ X1))))) ) | (~spl11_1 | ~spl11_7)),
% 0.88/0.43 inference(beta-eta_normalization,[],[f1230])).
% 0.88/0.43 thf(f1251,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($true = ((sK0 @ X0 @ (sK4 @ sK9 @ X0)))) | ($false = ((sK1 @ X0 @ sK10)))) ) | (~spl11_1 | ~spl11_11)),
% 0.88/0.43 inference(equality_resolution,[],[f795])).
% 0.88/0.43 thf(f1259,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK9 @ (sK4 @ sK9 @ sK8)))) | ($false = ((sK1 @ sK8 @ sK10))) | (~spl11_1 | ~spl11_8 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f221,f1251])).
% 0.88/0.43 thf(f1262,plain,(
% 0.88/0.43 ($true = ((sK9 @ (sK4 @ sK9 @ sK8)))) | ($false = ((sK1 @ sK8 @ sK10))) | (~spl11_1 | ~spl11_8 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1259])).
% 0.88/0.43 thf(f1280,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK9 @ (sK4 @ sK9 @ sK8)))) | (~spl11_1 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(forward_demodulation,[],[f1262,f230])).
% 0.88/0.43 thf(f1281,plain,(
% 0.88/0.43 ($true = ((sK9 @ (sK4 @ sK9 @ sK8)))) | (~spl11_1 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1280])).
% 0.88/0.43 thf(f1301,plain,(
% 0.88/0.43 ( ! [X0 : $i] : (($true = ((sK0 @ X0 @ (sK4 @ sK6 @ X0)))) | ($false = ((sK1 @ X0 @ sK7)))) ) | (~spl11_1 | ~spl11_7)),
% 0.88/0.43 inference(equality_resolution,[],[f1231])).
% 0.88/0.43 thf(f1309,plain,(
% 0.88/0.43 ($true = $false) | ($false = ((sK1 @ sK8 @ sK10))) | (~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f1067,f1281])).
% 0.88/0.43 thf(f1310,plain,(
% 0.88/0.43 ($false = ((sK1 @ sK8 @ sK10))) | (~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1309])).
% 0.88/0.43 thf(f1321,plain,(
% 0.88/0.43 ($true = $false) | (~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(constrained_superposition,[],[f1310,f230])).
% 0.88/0.43 thf(f1339,plain,(
% 0.88/0.43 $false | (~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1321])).
% 0.88/0.43 thf(f1340,plain,(
% 0.88/0.43 ~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11),
% 0.88/0.43 inference(avatar_contradiction_clause,[],[f1339])).
% 0.88/0.43 thf(f1758,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK6 @ (sK4 @ sK6 @ sK5)))) | ($false = ((sK1 @ sK5 @ sK7))) | (~spl11_1 | ~spl11_4 | ~spl11_7)),
% 0.88/0.43 inference(constrained_superposition,[],[f203,f1301])).
% 0.88/0.43 thf(f1759,plain,(
% 0.88/0.43 ($true = ((sK6 @ (sK4 @ sK6 @ sK5)))) | ($false = ((sK1 @ sK5 @ sK7))) | (~spl11_1 | ~spl11_4 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1758])).
% 0.88/0.43 thf(f1771,plain,(
% 0.88/0.43 ($true = $false) | ($true = ((sK6 @ (sK4 @ sK6 @ sK5)))) | (~spl11_1 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(forward_demodulation,[],[f1759,f212])).
% 0.88/0.43 thf(f1772,plain,(
% 0.88/0.43 ($true = ((sK6 @ (sK4 @ sK6 @ sK5)))) | (~spl11_1 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1771])).
% 0.88/0.43 thf(f1786,plain,(
% 0.88/0.43 ($true = $false) | ($false = ((sK1 @ sK5 @ sK7))) | (~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(constrained_superposition,[],[f1175,f1772])).
% 0.88/0.43 thf(f1787,plain,(
% 0.88/0.43 ($false = ((sK1 @ sK5 @ sK7))) | (~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1786])).
% 0.88/0.43 thf(f1808,plain,(
% 0.88/0.43 ($true = $false) | (~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(constrained_superposition,[],[f1787,f212])).
% 0.88/0.43 thf(f1832,plain,(
% 0.88/0.43 $false | (~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7)),
% 0.88/0.43 inference(trivial_inequality_removal,[],[f1808])).
% 0.88/0.43 thf(f1833,plain,(
% 0.88/0.43 ~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7),
% 0.88/0.43 inference(avatar_contradiction_clause,[],[f1832])).
% 0.88/0.43 cnf(s1, plain, spl11_1 | spl11_2, inference(sat_conversion,[],[f196])).
% 0.88/0.43 cnf(s2, plain, spl11_2 | spl11_3, inference(sat_conversion,[],[f200])).
% 0.88/0.43 cnf(s3, plain, spl11_4 | spl11_5, inference(sat_conversion,[],[f208])).
% 0.88/0.43 cnf(s4, plain, spl11_5 | spl11_6, inference(sat_conversion,[],[f213])).
% 0.88/0.43 cnf(s5, plain, spl11_5 | spl11_7, inference(sat_conversion,[],[f218])).
% 0.88/0.43 cnf(s6, plain, spl11_8 | ~spl11_9, inference(sat_conversion,[],[f226])).
% 0.88/0.43 cnf(s7, plain, ~spl11_9 | spl11_10, inference(sat_conversion,[],[f231])).
% 0.88/0.43 cnf(s8, plain, ~spl11_9 | spl11_11, inference(sat_conversion,[],[f236])).
% 0.88/0.43 cnf(s9, plain, ~spl11_2 | ~spl11_5 | spl11_9, inference(sat_conversion,[],[f254])).
% 0.88/0.43 cnf(s11, plain, ~spl11_2 | ~spl11_8 | ~spl11_10 | ~spl11_11, inference(sat_conversion,[],[f264])).
% 0.88/0.43 cnf(s14, plain, ~spl11_1 | ~spl11_3 | ~spl11_5 | spl11_9, inference(sat_conversion,[],[f770])).
% 0.88/0.43 cnf(s20, plain, ~spl11_2 | ~spl11_4 | ~spl11_6 | ~spl11_7, inference(sat_conversion,[],[f1038])).
% 0.88/0.43 cnf(s28, plain, ~spl11_1 | ~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11, inference(sat_conversion,[],[f1340])).
% 0.88/0.43 cnf(s35, plain, ~spl11_1 | ~spl11_3 | ~spl11_4 | ~spl11_6 | ~spl11_7, inference(sat_conversion,[],[f1833])).
% 0.88/0.43 cnf(s36, plain, ~spl11_9 | ~spl11_2, inference(rat,[],[s11,s6,s7,s8])).
% 0.88/0.43 cnf(s37, plain, spl11_9 | ~spl11_2, inference(rat,[],[s20,s3,s4,s5,s9])).
% 0.88/0.43 cnf(s38, plain, ~spl11_2, inference(rat,[],[s37,s36])).
% 0.88/0.43 cnf(s39, plain, spl11_3, inference(rat,[],[s2,s38])).
% 0.88/0.43 cnf(s40, plain, spl11_1, inference(rat,[],[s1,s38])).
% 0.88/0.43 cnf(s41, plain, ~spl11_9, inference(rat,[],[s28,s6,s7,s8,s40,s39])).
% 0.88/0.43 cnf(s42, plain, ~spl11_5, inference(rat,[],[s14,s40,s39,s41])).
% 0.88/0.43 cnf(s43, plain, spl11_7, inference(rat,[],[s5,s42])).
% 0.88/0.43 cnf(s44, plain, spl11_6, inference(rat,[],[s4,s42])).
% 0.88/0.43 cnf(s45, plain, spl11_4, inference(rat,[],[s3,s42])).
% 0.88/0.43 cnf(s46, plain, $false, inference(rat,[],[s35,s43,s39,s40,s44,s45])).
% 0.88/0.43 thf(f1839,plain,(
% 0.88/0.43 $false),
% 0.88/0.43 inference(avatar_sat_refutation,[],[s46])).
% 0.88/0.43 % SZS output end Proof for theBenchmark
% 0.88/0.43 % (1483666)------------------------------
% 0.88/0.43 % (1483666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.43 % (1483666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.43 % (1483666)CaDiCaL version: 2.1.3
% 0.88/0.43 % (1483666)Termination reason: Refutation
% 0.88/0.43 % (1483666)Time elapsed: 0.050 s
% 0.88/0.43 % (1483666)Peak memory usage: 14 MB
% 0.88/0.43 % (1483666)Instructions burned: 180 (million)
% 0.88/0.43 % (1483632)Success in time 0.191 s
% 0.88/0.43 % Vampire exiting
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