0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.36 % Computer : n023.cluster.edu 0.11/0.36 % Model : x86_64 x86_64 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.36 % Memory : 8046.5625MB 0.11/0.36 % OS : Linux 6.8.0-71-generic 0.11/0.36 % CPULimit : 1440 0.11/0.36 % WCLimit : 180 0.11/0.36 % DateTime : Mon Jul 27 09:27:36 UTC 2026 0.11/0.36 % CPUTime : 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.40 Running higher-order theorem proving 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p 0.18/0.49 % (703008)Detected a higher-order problem, will run a greedy HOL sequence. 0.18/0.49 % (703015)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2425191838:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.18/0.49 % (703015)Instruction limit reached! 0.18/0.49 % (703015)------------------------------ 0.18/0.49 % (703015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.18/0.49 % (703015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.18/0.49 % (703015)CaDiCaL version: 2.1.3 0.18/0.49 % (703015)Termination reason: Instruction limit 0.18/0.49 % (703015)Termination phase: Saturation 0.18/0.49 % (703015)Time elapsed: 0.001 s 0.18/0.49 % (703015)Peak memory usage: 11 MB 0.18/0.49 % (703015)Instructions burned: 5 (million) 0.18/0.49 % (703014)lrs+10_16_si=on:nwc=1.5:random_seed=24862572:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.18/0.49 % (703013)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=811836510:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.18/0.49 % (703016)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3929148457:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 0.18/0.49 % (703021)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3215377660:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.18/0.49 % (703021)Instruction limit reached! 0.18/0.49 % (703021)------------------------------ 0.18/0.49 % (703021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.18/0.49 % (703021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.18/0.49 % (703021)CaDiCaL version: 2.1.3 0.18/0.49 % (703021)Termination reason: Instruction limit 0.18/0.49 % (703021)Termination phase: Property scanning 0.18/0.49 % (703021)Time elapsed: 0.001 s 0.18/0.49 % (703021)Peak memory usage: 10 MB 0.18/0.49 % (703021)Instructions burned: 4 (million) 0.18/0.49 % (703014)Instruction limit reached! 0.18/0.49 % (703014)------------------------------ 0.18/0.49 % (703014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.18/0.49 % (703014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.18/0.49 % (703014)CaDiCaL version: 2.1.3 0.18/0.49 % (703014)Termination reason: Instruction limit 0.18/0.49 % (703014)Termination phase: Saturation 0.18/0.49 % (703014)Time elapsed: 0.009 s 0.18/0.49 % (703014)Peak memory usage: 12 MB 0.18/0.49 % (703014)Instructions burned: 18 (million) 0.18/0.49 % (703019)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.18/0.49 % (703019)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.18/0.49 % (703017)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1018717557:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.18/0.49 % (703026)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=528654820:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.18/0.49 % (703016) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-703008-703016"... 0.18/0.49 % (703019)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2734276428:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.18/0.49 % (703026)Instruction limit reached! 0.18/0.49 % (703026)------------------------------ 0.18/0.49 % (703026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.18/0.49 % (703026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.18/0.49 % (703026)CaDiCaL version: 2.1.3 0.18/0.49 % (703026)Termination reason: Instruction limit 0.18/0.49 % (703026)Termination phase: Saturation 0.18/0.49 % (703026)Time elapsed: 0.002 s 0.18/0.49 % (703026)Peak memory usage: 11 MB 0.18/0.49 % (703026)Instructions burned: 7 (million) 0.18/0.49 % (703018)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1617938642:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.18/0.49 % (703027)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.18/0.49 % (703016)...printing done. 0.18/0.49 % (703016)Refutation found. Thanks to Tanya! 0.18/0.49 % SZS status Theorem for theBenchmark 0.18/0.49 % SZS output start Proof for theBenchmark 0.18/0.49 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 0.18/0.49 thf(func_def_0, type, cQ_6: ($i > $i > $i > $o)). 0.18/0.49 thf(func_def_1, type, f: ($i > $i)). 0.18/0.49 thf(func_def_2, type, cP_5: ($i > $i > $o)). 0.18/0.49 thf(func_def_3, type, cQ_5: ($i > $i > $i > $o)). 0.18/0.49 thf(func_def_8, type, cP_4: ($i > $i > $o)). 0.18/0.49 thf(func_def_9, type, cQ_4: ($i > $i > $i > $o)). 0.18/0.49 thf(func_def_10, type, cP_3: ($i > $i > $o)). 0.18/0.49 thf(func_def_11, type, cQ_3: ($i > $i > $i > $o)). 0.18/0.49 thf(func_def_12, type, cP_2: ($i > $i > $o)). 0.18/0.49 thf(func_def_13, type, cQ_2: ($i > $i > $i > $o)). 0.18/0.49 thf(func_def_14, type, cP_1: ($i > $i > $o)). 0.18/0.49 thf(func_def_15, type, cQ_1: ($i > $i > $i > $o)). 0.18/0.49 thf(f1,conjecture,( 0.18/0.49 ~(! [X0 : $i] : (cP_5 @ d @ X0) & ! [X0 : $i,X1 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & ! [X0 : $i,X2 : $i,X3 : $i,X5 : $i,X1 : $i,X4 : $i] : (~(cP_3 @ (f @ X1) @ X4) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X0) @ X3) | (cQ_4 @ X3 @ X4 @ X5)) & (cP_5 @ c @ c) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_2 @ c @ c) & ! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X4 : $i,X5 : $i,X0 : $i,X2 : $i,X1 : $i,X3 : $i] : (~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X1) @ X4) | (cQ_5 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X1 : $i,X0 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cQ_1 @ a @ b @ c) & (cP_5 @ b @ b) & (cP_1 @ a @ a) & (cP_4 @ a @ a) & ! [X5 : $i,X4 : $i,X0 : $i,X1 : $i,X3 : $i,X2 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_4 @ d @ X0) & ! [X1 : $i,X0 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ b @ b) & (cP_1 @ b @ b) & (cP_4 @ c @ c) & (cP_2 @ a @ a) & ! [X3 : $i,X5 : $i,X4 : $i,X2 : $i,X1 : $i,X0 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5)) & ! [X1 : $i,X0 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_1 @ c @ c) & (cP_5 @ a @ a) & ! [X1 : $i,X0 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & (cP_4 @ b @ b) & ! [X1 : $i,X5 : $i,X3 : $i,X0 : $i,X2 : $i,X4 : $i] : (~(cP_5 @ (f @ X1) @ X4) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X0) @ X3) | ~(cP_5 @ (f @ X2) @ X5) | ~(cQ_5 @ X0 @ X1 @ X2)) & (cP_3 @ a @ a))), 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_5)). 0.18/0.49 thf(f2,negated_conjecture,( 0.18/0.49 ~ ~(! [X0 : $i] : (cP_5 @ d @ X0) & ! [X0 : $i,X1 : $i] : (~(cP_5 @ X0 @ X1) | (cP_5 @ (f @ X0) @ X1)) & ! [X0 : $i,X2 : $i,X3 : $i,X5 : $i,X1 : $i,X4 : $i] : (~(cP_3 @ (f @ X1) @ X4) | ~(cQ_3 @ X0 @ X1 @ X2) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X0) @ X3) | (cQ_4 @ X3 @ X4 @ X5)) & (cP_5 @ c @ c) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_2 @ c @ c) & ! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X4 : $i,X5 : $i,X0 : $i,X2 : $i,X1 : $i,X3 : $i] : (~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2) | ~(cP_4 @ (f @ X1) @ X4) | (cQ_5 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_3 @ d @ X0) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X1 : $i,X0 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & (cQ_1 @ a @ b @ c) & (cP_5 @ b @ b) & (cP_1 @ a @ a) & (cP_4 @ a @ a) & ! [X5 : $i,X4 : $i,X0 : $i,X1 : $i,X3 : $i,X2 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X0 : $i] : (cP_4 @ d @ X0) & ! [X1 : $i,X0 : $i] : (~(cP_1 @ X0 @ X1) | (cP_1 @ (f @ X0) @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ b @ b) & (cP_1 @ b @ b) & (cP_4 @ c @ c) & (cP_2 @ a @ a) & ! [X3 : $i,X5 : $i,X4 : $i,X2 : $i,X1 : $i,X0 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2) | ~(cP_2 @ (f @ X2) @ X5)) & ! [X1 : $i,X0 : $i] : (~(cP_2 @ X0 @ X1) | (cP_2 @ (f @ X0) @ X1)) & (cP_1 @ c @ c) & (cP_5 @ a @ a) & ! [X1 : $i,X0 : $i] : (~(cP_4 @ X0 @ X1) | (cP_4 @ (f @ X0) @ X1)) & (cP_4 @ b @ b) & ! [X1 : $i,X5 : $i,X3 : $i,X0 : $i,X2 : $i,X4 : $i] : (~(cP_5 @ (f @ X1) @ X4) | (cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X0) @ X3) | ~(cP_5 @ (f @ X2) @ X5) | ~(cQ_5 @ X0 @ X1 @ X2)) & (cP_3 @ a @ a))), 0.18/0.49 inference(negated_conjecture,[status(cth)],[f1])). 0.18/0.49 thf(f3,plain,( 0.18/0.49 ~ ~(! [X0 : $i] : (cP_5 @ d @ X0) & ! [X1 : $i,X2 : $i] : (~(cP_5 @ X1 @ X2) | (cP_5 @ (f @ X1) @ X2)) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : (~(cP_3 @ (f @ X7) @ X8) | ~(cQ_3 @ X3 @ X7 @ X4) | ~(cP_3 @ (f @ X4) @ X6) | ~(cP_3 @ (f @ X3) @ X5) | (cQ_4 @ X5 @ X8 @ X6)) & (cP_5 @ c @ c) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_2 @ c @ c) & ! [X9 : $i,X10 : $i,X11 : $i] : ~(cQ_6 @ X9 @ X10 @ X11) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : (~(cP_4 @ (f @ X15) @ X13) | ~(cP_4 @ (f @ X14) @ X17) | ~(cQ_4 @ X14 @ X16 @ X15) | ~(cP_4 @ (f @ X16) @ X12) | (cQ_5 @ X17 @ X12 @ X13)) & ! [X18 : $i] : (cP_3 @ d @ X18) & ! [X19 : $i] : (cP_1 @ d @ X19) & ! [X20 : $i,X21 : $i] : ((cP_3 @ (f @ X21) @ X20) | ~(cP_3 @ X21 @ X20)) & (cQ_1 @ a @ b @ c) & (cP_5 @ b @ b) & (cP_1 @ a @ a) & (cP_4 @ a @ a) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (~(cP_1 @ (f @ X25) @ X23) | ~(cP_1 @ (f @ X27) @ X22) | ~(cQ_1 @ X24 @ X25 @ X27) | ~(cP_1 @ (f @ X24) @ X26) | (cQ_2 @ X26 @ X23 @ X22)) & ! [X28 : $i] : (cP_4 @ d @ X28) & ! [X29 : $i,X30 : $i] : (~(cP_1 @ X30 @ X29) | (cP_1 @ (f @ X30) @ X29)) & ! [X31 : $i] : (cP_2 @ d @ X31) & (cP_2 @ b @ b) & (cP_1 @ b @ b) & (cP_4 @ c @ c) & (cP_2 @ a @ a) & ! [X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i] : ((cQ_3 @ X32 @ X34 @ X33) | ~(cP_2 @ (f @ X36) @ X34) | ~(cP_2 @ (f @ X37) @ X32) | ~(cQ_2 @ X37 @ X36 @ X35) | ~(cP_2 @ (f @ X35) @ X33)) & ! [X38 : $i,X39 : $i] : (~(cP_2 @ X39 @ X38) | (cP_2 @ (f @ X39) @ X38)) & (cP_1 @ c @ c) & (cP_5 @ a @ a) & ! [X40 : $i,X41 : $i] : (~(cP_4 @ X41 @ X40) | (cP_4 @ (f @ X41) @ X40)) & (cP_4 @ b @ b) & ! [X42 : $i,X43 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i] : (~(cP_5 @ (f @ X42) @ X47) | (cQ_6 @ X44 @ X47 @ X43) | ~(cP_5 @ (f @ X45) @ X44) | ~(cP_5 @ (f @ X46) @ X43) | ~(cQ_5 @ X45 @ X42 @ X46)) & (cP_3 @ a @ a))), 0.18/0.49 inference(rectify,[],[f2])). 0.18/0.49 thf(f4,plain,( 0.18/0.49 ~ ~(! [X0 : $i] : (((cP_5 @ d @ X0)) = $true) & ! [X1 : $i,X2 : $i] : (~ (((cP_5 @ X1 @ X2)) = $true) | (((cP_5 @ (f @ X1) @ X2)) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : (~ (((cP_3 @ (f @ X7) @ X8)) = $true) | ~ ($true = ((cQ_3 @ X3 @ X7 @ X4))) | ~ (((cP_3 @ (f @ X4) @ X6)) = $true) | ~ (((cP_3 @ (f @ X3) @ X5)) = $true) | ($true = ((cQ_4 @ X5 @ X8 @ X6)))) & (((cP_5 @ c @ c)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_2 @ c @ c)) = $true) & ! [X9 : $i,X10 : $i,X11 : $i] : ~ ($true = ((cQ_6 @ X9 @ X10 @ X11))) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : (~ ($true = ((cP_4 @ (f @ X15) @ X13))) | ~ (((cP_4 @ (f @ X14) @ X17)) = $true) | ~ (((cQ_4 @ X14 @ X16 @ X15)) = $true) | ~ ($true = ((cP_4 @ (f @ X16) @ X12))) | ($true = ((cQ_5 @ X17 @ X12 @ X13)))) & ! [X18 : $i] : (((cP_3 @ d @ X18)) = $true) & ! [X19 : $i] : (((cP_1 @ d @ X19)) = $true) & ! [X20 : $i,X21 : $i] : (($true = ((cP_3 @ (f @ X21) @ X20))) | ~ ($true = ((cP_3 @ X21 @ X20)))) & (((cQ_1 @ a @ b @ c)) = $true) & (((cP_5 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i,X27 : $i] : (~ ($true = ((cP_1 @ (f @ X25) @ X23))) | ~ (((cP_1 @ (f @ X27) @ X22)) = $true) | ~ (((cQ_1 @ X24 @ X25 @ X27)) = $true) | ~ ($true = ((cP_1 @ (f @ X24) @ X26))) | (((cQ_2 @ X26 @ X23 @ X22)) = $true)) & ! [X28 : $i] : ($true = ((cP_4 @ d @ X28))) & ! [X29 : $i,X30 : $i] : (~ (((cP_1 @ X30 @ X29)) = $true) | ($true = ((cP_1 @ (f @ X30) @ X29)))) & ! [X31 : $i] : ($true = ((cP_2 @ d @ X31))) & (((cP_2 @ b @ b)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_4 @ c @ c)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X32 : $i,X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i] : ((((cQ_3 @ X32 @ X34 @ X33)) = $true) | ~ ($true = ((cP_2 @ (f @ X36) @ X34))) | ~ ($true = ((cP_2 @ (f @ X37) @ X32))) | ~ (((cQ_2 @ X37 @ X36 @ X35)) = $true) | ~ ($true = ((cP_2 @ (f @ X35) @ X33)))) & ! [X38 : $i,X39 : $i] : (~ ($true = ((cP_2 @ X39 @ X38))) | (((cP_2 @ (f @ X39) @ X38)) = $true)) & (((cP_1 @ c @ c)) = $true) & (((cP_5 @ a @ a)) = $true) & ! [X40 : $i,X41 : $i] : (~ ($true = ((cP_4 @ X41 @ X40))) | (((cP_4 @ (f @ X41) @ X40)) = $true)) & (((cP_4 @ b @ b)) = $true) & ! [X42 : $i,X43 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i] : (~ (((cP_5 @ (f @ X42) @ X47)) = $true) | ($true = ((cQ_6 @ X44 @ X47 @ X43))) | ~ ($true = ((cP_5 @ (f @ X45) @ X44))) | ~ (((cP_5 @ (f @ X46) @ X43)) = $true) | ~ ($true = ((cQ_5 @ X45 @ X42 @ X46)))) & (((cP_3 @ a @ a)) = $true))), 0.18/0.49 inference(fool_elimination,[],[f3])). 0.18/0.49 thf(f5,plain,( 0.18/0.49 ! [X21 : $i,X20 : $i] : (($true = ((cP_3 @ (f @ X21) @ X20))) | ($true != ((cP_3 @ X21 @ X20)))) & (((cP_2 @ a @ a)) = $true) & ! [X0 : $i] : (((cP_5 @ d @ X0)) = $true) & (((cP_5 @ a @ a)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ c @ c)) = $true) & ! [X16 : $i,X12 : $i,X14 : $i,X17 : $i,X15 : $i,X13 : $i] : (($true = ((cQ_5 @ X17 @ X12 @ X13))) | ($true != ((cP_4 @ (f @ X15) @ X13))) | (((cQ_4 @ X14 @ X16 @ X15)) != $true) | ($true != ((cP_4 @ (f @ X16) @ X12))) | (((cP_4 @ (f @ X14) @ X17)) != $true)) & (((cP_5 @ c @ c)) = $true) & ! [X40 : $i,X41 : $i] : (($true != ((cP_4 @ X41 @ X40))) | (((cP_4 @ (f @ X41) @ X40)) = $true)) & (((cP_3 @ a @ a)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X37 : $i,X34 : $i,X35 : $i,X33 : $i,X32 : $i,X36 : $i] : (($true != ((cP_2 @ (f @ X37) @ X32))) | ($true != ((cP_2 @ (f @ X36) @ X34))) | (((cQ_2 @ X37 @ X36 @ X35)) != $true) | ($true != ((cP_2 @ (f @ X35) @ X33))) | (((cQ_3 @ X32 @ X34 @ X33)) = $true)) & ! [X6 : $i,X4 : $i,X5 : $i,X8 : $i,X7 : $i,X3 : $i] : (($true != ((cQ_3 @ X3 @ X7 @ X4))) | (((cP_3 @ (f @ X7) @ X8)) != $true) | (((cP_3 @ (f @ X3) @ X5)) != $true) | ($true = ((cQ_4 @ X5 @ X8 @ X6))) | (((cP_3 @ (f @ X4) @ X6)) != $true)) & (((cP_3 @ c @ c)) = $true) & ! [X10 : $i,X11 : $i,X9 : $i] : ($true != ((cQ_6 @ X9 @ X10 @ X11))) & (((cP_4 @ c @ c)) = $true) & ! [X22 : $i,X24 : $i,X25 : $i,X27 : $i,X23 : $i,X26 : $i] : (($true != ((cP_1 @ (f @ X25) @ X23))) | (((cQ_2 @ X26 @ X23 @ X22)) = $true) | ($true != ((cP_1 @ (f @ X24) @ X26))) | (((cQ_1 @ X24 @ X25 @ X27)) != $true) | (((cP_1 @ (f @ X27) @ X22)) != $true)) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ c @ c)) = $true) & ! [X31 : $i] : ($true = ((cP_2 @ d @ X31))) & ! [X42 : $i,X44 : $i,X45 : $i,X46 : $i,X47 : $i,X43 : $i] : (($true = ((cQ_6 @ X44 @ X47 @ X43))) | ($true != ((cP_5 @ (f @ X45) @ X44))) | (((cP_5 @ (f @ X42) @ X47)) != $true) | ($true != ((cQ_5 @ X45 @ X42 @ X46))) | (((cP_5 @ (f @ X46) @ X43)) != $true)) & (((cP_4 @ b @ b)) = $true) & (((cQ_1 @ a @ b @ c)) = $true) & ! [X39 : $i,X38 : $i] : (($true != ((cP_2 @ X39 @ X38))) | (((cP_2 @ (f @ X39) @ X38)) = $true)) & ! [X19 : $i] : (((cP_1 @ d @ X19)) = $true) & ! [X18 : $i] : (((cP_3 @ d @ X18)) = $true) & (((cP_3 @ b @ b)) = $true) & ! [X28 : $i] : ($true = ((cP_4 @ d @ X28))) & ! [X29 : $i,X30 : $i] : ((((cP_1 @ X30 @ X29)) != $true) | ($true = ((cP_1 @ (f @ X30) @ X29)))) & (((cP_1 @ a @ a)) = $true) & (((cP_5 @ b @ b)) = $true) & ! [X1 : $i,X2 : $i] : ((((cP_5 @ (f @ X1) @ X2)) = $true) | (((cP_5 @ X1 @ X2)) != $true))), 0.18/0.49 inference(flattening,[],[f4])). 0.18/0.49 thf(f6,plain,( 0.18/0.49 ! [X0 : $i,X1 : $i] : ((((cP_3 @ (f @ X0) @ X1)) = $true) | (((cP_3 @ X0 @ X1)) != $true)) & (((cP_2 @ a @ a)) = $true) & ! [X2 : $i] : ($true = ((cP_5 @ d @ X2))) & (((cP_5 @ a @ a)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ c @ c)) = $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : (($true = ((cQ_5 @ X6 @ X4 @ X8))) | ($true != ((cP_4 @ (f @ X7) @ X8))) | ($true != ((cQ_4 @ X5 @ X3 @ X7))) | (((cP_4 @ (f @ X3) @ X4)) != $true) | (((cP_4 @ (f @ X5) @ X6)) != $true)) & (((cP_5 @ c @ c)) = $true) & ! [X9 : $i,X10 : $i] : (($true != ((cP_4 @ X10 @ X9))) | ($true = ((cP_4 @ (f @ X10) @ X9)))) & (((cP_3 @ a @ a)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X11 : $i,X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i] : ((((cP_2 @ (f @ X11) @ X15)) != $true) | (((cP_2 @ (f @ X16) @ X12)) != $true) | (((cQ_2 @ X11 @ X16 @ X13)) != $true) | ($true != ((cP_2 @ (f @ X13) @ X14))) | ($true = ((cQ_3 @ X15 @ X12 @ X14)))) & ! [X17 : $i,X18 : $i,X19 : $i,X20 : $i,X21 : $i,X22 : $i] : (($true != ((cQ_3 @ X22 @ X21 @ X18))) | ($true != ((cP_3 @ (f @ X21) @ X20))) | ($true != ((cP_3 @ (f @ X22) @ X19))) | ($true = ((cQ_4 @ X19 @ X20 @ X17))) | ($true != ((cP_3 @ (f @ X18) @ X17)))) & (((cP_3 @ c @ c)) = $true) & ! [X23 : $i,X24 : $i,X25 : $i] : ($true != ((cQ_6 @ X25 @ X23 @ X24))) & (((cP_4 @ c @ c)) = $true) & ! [X26 : $i,X27 : $i,X28 : $i,X29 : $i,X30 : $i,X31 : $i] : (($true != ((cP_1 @ (f @ X28) @ X30))) | ($true = ((cQ_2 @ X31 @ X30 @ X26))) | ($true != ((cP_1 @ (f @ X27) @ X31))) | (((cQ_1 @ X27 @ X28 @ X29)) != $true) | (((cP_1 @ (f @ X29) @ X26)) != $true)) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ c @ c)) = $true) & ! [X32 : $i] : ($true = ((cP_2 @ d @ X32))) & ! [X33 : $i,X34 : $i,X35 : $i,X36 : $i,X37 : $i,X38 : $i] : ((((cQ_6 @ X34 @ X37 @ X38)) = $true) | (((cP_5 @ (f @ X35) @ X34)) != $true) | ($true != ((cP_5 @ (f @ X33) @ X37))) | ($true != ((cQ_5 @ X35 @ X33 @ X36))) | ($true != ((cP_5 @ (f @ X36) @ X38)))) & (((cP_4 @ b @ b)) = $true) & (((cQ_1 @ a @ b @ c)) = $true) & ! [X39 : $i,X40 : $i] : (($true != ((cP_2 @ X39 @ X40))) | (((cP_2 @ (f @ X39) @ X40)) = $true)) & ! [X41 : $i] : ($true = ((cP_1 @ d @ X41))) & ! [X42 : $i] : ($true = ((cP_3 @ d @ X42))) & (((cP_3 @ b @ b)) = $true) & ! [X43 : $i] : ($true = ((cP_4 @ d @ X43))) & ! [X44 : $i,X45 : $i] : ((((cP_1 @ X45 @ X44)) != $true) | ($true = ((cP_1 @ (f @ X45) @ X44)))) & (((cP_1 @ a @ a)) = $true) & (((cP_5 @ b @ b)) = $true) & ! [X46 : $i,X47 : $i] : (($true = ((cP_5 @ (f @ X46) @ X47))) | (((cP_5 @ X46 @ X47)) != $true))), 0.18/0.49 inference(rectify,[],[f5])). 0.18/0.49 thf(f7,plain,( 0.18/0.49 ( ! [X46 : $i,X47 : $i] : (($true = ((cP_5 @ (f @ X46) @ X47))) | (((cP_5 @ X46 @ X47)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f8,plain,( 0.18/0.49 (((cP_5 @ b @ b)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f9,plain,( 0.18/0.49 (((cP_1 @ a @ a)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f10,plain,( 0.18/0.49 ( ! [X44 : $i,X45 : $i] : (($true = ((cP_1 @ (f @ X45) @ X44))) | (((cP_1 @ X45 @ X44)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f12,plain,( 0.18/0.49 (((cP_3 @ b @ b)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f15,plain,( 0.18/0.49 ( ! [X40 : $i,X39 : $i] : ((((cP_2 @ (f @ X39) @ X40)) = $true) | ($true != ((cP_2 @ X39 @ X40)))) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f16,plain,( 0.18/0.49 (((cQ_1 @ a @ b @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f17,plain,( 0.18/0.49 (((cP_4 @ b @ b)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f18,plain,( 0.18/0.49 ( ! [X38 : $i,X36 : $i,X37 : $i,X34 : $i,X35 : $i,X33 : $i] : ((((cQ_6 @ X34 @ X37 @ X38)) = $true) | (((cP_5 @ (f @ X35) @ X34)) != $true) | ($true != ((cP_5 @ (f @ X33) @ X37))) | ($true != ((cQ_5 @ X35 @ X33 @ X36))) | ($true != ((cP_5 @ (f @ X36) @ X38)))) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f20,plain,( 0.18/0.49 (((cP_1 @ c @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f21,plain,( 0.18/0.49 (((cP_1 @ b @ b)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f22,plain,( 0.18/0.49 ( ! [X31 : $i,X28 : $i,X29 : $i,X26 : $i,X27 : $i,X30 : $i] : (($true = ((cQ_2 @ X31 @ X30 @ X26))) | ($true != ((cP_1 @ (f @ X28) @ X30))) | ($true != ((cP_1 @ (f @ X27) @ X31))) | (((cP_1 @ (f @ X29) @ X26)) != $true) | (((cQ_1 @ X27 @ X28 @ X29)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f23,plain,( 0.18/0.49 (((cP_4 @ c @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f24,plain,( 0.18/0.49 ( ! [X24 : $i,X25 : $i,X23 : $i] : (($true != ((cQ_6 @ X25 @ X23 @ X24)))) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f25,plain,( 0.18/0.49 (((cP_3 @ c @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f26,plain,( 0.18/0.49 ( ! [X21 : $i,X18 : $i,X19 : $i,X17 : $i,X22 : $i,X20 : $i] : (($true = ((cQ_4 @ X19 @ X20 @ X17))) | ($true != ((cP_3 @ (f @ X21) @ X20))) | ($true != ((cQ_3 @ X22 @ X21 @ X18))) | ($true != ((cP_3 @ (f @ X22) @ X19))) | ($true != ((cP_3 @ (f @ X18) @ X17)))) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f27,plain,( 0.18/0.49 ( ! [X11 : $i,X16 : $i,X14 : $i,X15 : $i,X12 : $i,X13 : $i] : (($true = ((cQ_3 @ X15 @ X12 @ X14))) | (((cP_2 @ (f @ X16) @ X12)) != $true) | ($true != ((cP_2 @ (f @ X13) @ X14))) | (((cQ_2 @ X11 @ X16 @ X13)) != $true) | (((cP_2 @ (f @ X11) @ X15)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f28,plain,( 0.18/0.49 (((cP_4 @ a @ a)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f29,plain,( 0.18/0.49 (((cP_3 @ a @ a)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f30,plain,( 0.18/0.49 ( ! [X10 : $i,X9 : $i] : (($true = ((cP_4 @ (f @ X10) @ X9))) | ($true != ((cP_4 @ X10 @ X9)))) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f31,plain,( 0.18/0.49 (((cP_5 @ c @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f32,plain,( 0.18/0.49 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((cQ_5 @ X6 @ X4 @ X8))) | (((cP_4 @ (f @ X3) @ X4)) != $true) | ($true != ((cP_4 @ (f @ X7) @ X8))) | ($true != ((cQ_4 @ X5 @ X3 @ X7))) | (((cP_4 @ (f @ X5) @ X6)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f33,plain,( 0.18/0.49 (((cP_2 @ c @ c)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f34,plain,( 0.18/0.49 (((cP_2 @ b @ b)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f35,plain,( 0.18/0.49 (((cP_5 @ a @ a)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f37,plain,( 0.18/0.49 (((cP_2 @ a @ a)) = $true)), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f38,plain,( 0.18/0.49 ( ! [X0 : $i,X1 : $i] : ((((cP_3 @ (f @ X0) @ X1)) = $true) | (((cP_3 @ X0 @ X1)) != $true)) )), 0.18/0.49 inference(cnf_transformation,[],[f6])). 0.18/0.49 thf(f41,definition,( 0.18/0.49 spl0_1 <=> (((cP_5 @ a @ a)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])). 0.18/0.49 thf(f43,plain,( 0.18/0.49 (((cP_5 @ a @ a)) = $true) | ~spl0_1), 0.18/0.49 inference(avatar_component_clause,[],[f41])). 0.18/0.49 thf(f44,plain,( 0.18/0.49 spl0_1), 0.18/0.49 inference(avatar_split_clause,[],[f35,f41])). 0.18/0.49 thf(f46,definition,( 0.18/0.49 spl0_2 <=> (((cP_2 @ c @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])). 0.18/0.49 thf(f48,plain,( 0.18/0.49 (((cP_2 @ c @ c)) = $true) | ~spl0_2), 0.18/0.49 inference(avatar_component_clause,[],[f46])). 0.18/0.49 thf(f49,plain,( 0.18/0.49 spl0_2), 0.18/0.49 inference(avatar_split_clause,[],[f33,f46])). 0.18/0.49 thf(f51,definition,( 0.18/0.49 spl0_3 <=> (((cQ_1 @ a @ b @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])). 0.18/0.49 thf(f53,plain,( 0.18/0.49 (((cQ_1 @ a @ b @ c)) = $true) | ~spl0_3), 0.18/0.49 inference(avatar_component_clause,[],[f51])). 0.18/0.49 thf(f54,plain,( 0.18/0.49 spl0_3), 0.18/0.49 inference(avatar_split_clause,[],[f16,f51])). 0.18/0.49 thf(f56,definition,( 0.18/0.49 spl0_4 <=> (((cP_5 @ c @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])). 0.18/0.49 thf(f58,plain,( 0.18/0.49 (((cP_5 @ c @ c)) = $true) | ~spl0_4), 0.18/0.49 inference(avatar_component_clause,[],[f56])). 0.18/0.49 thf(f59,plain,( 0.18/0.49 spl0_4), 0.18/0.49 inference(avatar_split_clause,[],[f31,f56])). 0.18/0.49 thf(f61,definition,( 0.18/0.49 spl0_5 <=> (((cP_4 @ b @ b)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])). 0.18/0.49 thf(f63,plain,( 0.18/0.49 (((cP_4 @ b @ b)) = $true) | ~spl0_5), 0.18/0.49 inference(avatar_component_clause,[],[f61])). 0.18/0.49 thf(f64,plain,( 0.18/0.49 spl0_5), 0.18/0.49 inference(avatar_split_clause,[],[f17,f61])). 0.18/0.49 thf(f66,definition,( 0.18/0.49 spl0_6 <=> (((cP_4 @ a @ a)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])). 0.18/0.49 thf(f68,plain,( 0.18/0.49 (((cP_4 @ a @ a)) = $true) | ~spl0_6), 0.18/0.49 inference(avatar_component_clause,[],[f66])). 0.18/0.49 thf(f69,plain,( 0.18/0.49 spl0_6), 0.18/0.49 inference(avatar_split_clause,[],[f28,f66])). 0.18/0.49 thf(f71,definition,( 0.18/0.49 spl0_7 <=> (((cP_1 @ c @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])). 0.18/0.49 thf(f73,plain,( 0.18/0.49 (((cP_1 @ c @ c)) = $true) | ~spl0_7), 0.18/0.49 inference(avatar_component_clause,[],[f71])). 0.18/0.49 thf(f74,plain,( 0.18/0.49 spl0_7), 0.18/0.49 inference(avatar_split_clause,[],[f20,f71])). 0.18/0.49 thf(f76,definition,( 0.18/0.49 spl0_8 <=> (((cP_3 @ a @ a)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])). 0.18/0.49 thf(f78,plain,( 0.18/0.49 (((cP_3 @ a @ a)) = $true) | ~spl0_8), 0.18/0.49 inference(avatar_component_clause,[],[f76])). 0.18/0.49 thf(f79,plain,( 0.18/0.49 spl0_8), 0.18/0.49 inference(avatar_split_clause,[],[f29,f76])). 0.18/0.49 thf(f81,definition,( 0.18/0.49 spl0_9 <=> (((cP_1 @ a @ a)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])). 0.18/0.49 thf(f83,plain,( 0.18/0.49 (((cP_1 @ a @ a)) = $true) | ~spl0_9), 0.18/0.49 inference(avatar_component_clause,[],[f81])). 0.18/0.49 thf(f84,plain,( 0.18/0.49 spl0_9), 0.18/0.49 inference(avatar_split_clause,[],[f9,f81])). 0.18/0.49 thf(f86,definition,( 0.18/0.49 spl0_10 <=> (((cP_4 @ c @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])). 0.18/0.49 thf(f88,plain,( 0.18/0.49 (((cP_4 @ c @ c)) = $true) | ~spl0_10), 0.18/0.49 inference(avatar_component_clause,[],[f86])). 0.18/0.49 thf(f89,plain,( 0.18/0.49 spl0_10), 0.18/0.49 inference(avatar_split_clause,[],[f23,f86])). 0.18/0.49 thf(f91,definition,( 0.18/0.49 spl0_11 <=> (((cP_3 @ c @ c)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])). 0.18/0.49 thf(f93,plain,( 0.18/0.49 (((cP_3 @ c @ c)) = $true) | ~spl0_11), 0.18/0.49 inference(avatar_component_clause,[],[f91])). 0.18/0.49 thf(f94,plain,( 0.18/0.49 spl0_11), 0.18/0.49 inference(avatar_split_clause,[],[f25,f91])). 0.18/0.49 thf(f96,definition,( 0.18/0.49 spl0_12 <=> (((cP_2 @ a @ a)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])). 0.18/0.49 thf(f98,plain,( 0.18/0.49 (((cP_2 @ a @ a)) = $true) | ~spl0_12), 0.18/0.49 inference(avatar_component_clause,[],[f96])). 0.18/0.49 thf(f99,plain,( 0.18/0.49 spl0_12), 0.18/0.49 inference(avatar_split_clause,[],[f37,f96])). 0.18/0.49 thf(f101,definition,( 0.18/0.49 spl0_13 <=> (((cP_1 @ b @ b)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])). 0.18/0.49 thf(f103,plain,( 0.18/0.49 (((cP_1 @ b @ b)) = $true) | ~spl0_13), 0.18/0.49 inference(avatar_component_clause,[],[f101])). 0.18/0.49 thf(f104,plain,( 0.18/0.49 spl0_13), 0.18/0.49 inference(avatar_split_clause,[],[f21,f101])). 0.18/0.49 thf(f106,definition,( 0.18/0.49 spl0_14 <=> (((cP_5 @ b @ b)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])). 0.18/0.49 thf(f108,plain,( 0.18/0.49 (((cP_5 @ b @ b)) = $true) | ~spl0_14), 0.18/0.49 inference(avatar_component_clause,[],[f106])). 0.18/0.49 thf(f109,plain,( 0.18/0.49 spl0_14), 0.18/0.49 inference(avatar_split_clause,[],[f8,f106])). 0.18/0.49 thf(f111,definition,( 0.18/0.49 spl0_15 <=> (((cP_2 @ b @ b)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])). 0.18/0.49 thf(f113,plain,( 0.18/0.49 (((cP_2 @ b @ b)) = $true) | ~spl0_15), 0.18/0.49 inference(avatar_component_clause,[],[f111])). 0.18/0.49 thf(f114,plain,( 0.18/0.49 spl0_15), 0.18/0.49 inference(avatar_split_clause,[],[f34,f111])). 0.18/0.49 thf(f116,definition,( 0.18/0.49 spl0_16 <=> (((cP_3 @ b @ b)) = $true)), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition])). 0.18/0.49 thf(f118,plain,( 0.18/0.49 (((cP_3 @ b @ b)) = $true) | ~spl0_16), 0.18/0.49 inference(avatar_component_clause,[],[f116])). 0.18/0.49 thf(f119,plain,( 0.18/0.49 spl0_16), 0.18/0.49 inference(avatar_split_clause,[],[f12,f116])). 0.18/0.49 thf(f120,plain,( 0.18/0.49 ( ! [X38 : $i,X36 : $i,X37 : $i,X34 : $i,X35 : $i,X33 : $i] : (($true != ((cQ_5 @ X35 @ X33 @ X36))) | ($true != ((cP_5 @ (f @ X36) @ X38))) | (((cP_5 @ (f @ X35) @ X34)) != $true) | ($true != ((cP_5 @ (f @ X33) @ X37)))) )), 0.18/0.49 inference(forward_subsumption_resolution,[],[f18,f24])). 0.18/0.49 thf(f121,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != ((cP_4 @ (f @ X7) @ X2))) | ($true != ((cP_5 @ (f @ X2) @ X3))) | ($true != ((cP_4 @ (f @ X8) @ X0))) | ($true != ((cP_5 @ (f @ X1) @ X5))) | (((cQ_4 @ X8 @ X6 @ X7)) != $true) | ($true != $true) | ($true != ((cP_4 @ (f @ X6) @ X1))) | ($true != ((cP_5 @ (f @ X0) @ X4)))) )), 0.18/0.49 inference(superposition,[],[f120,f32])). 0.18/0.49 thf(f122,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cQ_4 @ X8 @ X6 @ X7)) != $true) | ($true != ((cP_5 @ (f @ X2) @ X3))) | ($true != ((cP_4 @ (f @ X8) @ X0))) | ($true != ((cP_4 @ (f @ X6) @ X1))) | ($true != ((cP_5 @ (f @ X0) @ X4))) | ($true != ((cP_5 @ (f @ X1) @ X5))) | ($true != ((cP_4 @ (f @ X7) @ X2)))) )), 0.18/0.49 inference(trivial_inequality_removal,[],[f121])). 0.18/0.49 thf(f123,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cP_5 @ (f @ X5) @ X7)) != $true) | ($true != ((cP_3 @ (f @ X9) @ X1))) | ($true != ((cP_4 @ (f @ X1) @ X6))) | ($true != ((cP_4 @ (f @ X2) @ X3))) | ($true != ((cP_3 @ (f @ X10) @ X0))) | ($true != ((cQ_3 @ X10 @ X9 @ X11))) | ($true != ((cP_5 @ (f @ X6) @ X8))) | (((cP_5 @ (f @ X3) @ X4)) != $true) | (((cP_4 @ (f @ X0) @ X5)) != $true) | ($true != $true) | ($true != ((cP_3 @ (f @ X11) @ X2)))) )), 0.18/0.49 inference(superposition,[],[f122,f26])). 0.18/0.49 thf(f124,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != ((cQ_3 @ X10 @ X9 @ X11))) | ($true != ((cP_4 @ (f @ X1) @ X6))) | ($true != ((cP_5 @ (f @ X6) @ X8))) | ($true != ((cP_3 @ (f @ X11) @ X2))) | (((cP_5 @ (f @ X3) @ X4)) != $true) | (((cP_4 @ (f @ X0) @ X5)) != $true) | ($true != ((cP_3 @ (f @ X9) @ X1))) | ($true != ((cP_3 @ (f @ X10) @ X0))) | ($true != ((cP_4 @ (f @ X2) @ X3))) | (((cP_5 @ (f @ X5) @ X7)) != $true)) )), 0.18/0.49 inference(trivial_inequality_removal,[],[f123])). 0.18/0.49 thf(f125,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : ((((cP_4 @ (f @ X3) @ X4)) != $true) | ($true != ((cP_4 @ (f @ X9) @ X10))) | ($true != $true) | ($true != ((cP_3 @ (f @ X2) @ X6))) | ($true != ((cP_5 @ (f @ X10) @ X11))) | ($true != ((cP_5 @ (f @ X7) @ X8))) | (((cP_2 @ (f @ X13) @ X2)) != $true) | (((cQ_2 @ X14 @ X12 @ X13)) != $true) | (((cP_3 @ (f @ X1) @ X3)) != $true) | ($true != ((cP_2 @ (f @ X14) @ X0))) | ($true != ((cP_5 @ (f @ X4) @ X5))) | (((cP_3 @ (f @ X0) @ X9)) != $true) | ($true != ((cP_4 @ (f @ X6) @ X7))) | ($true != ((cP_2 @ (f @ X12) @ X1)))) )), 0.18/0.49 inference(superposition,[],[f124,f27])). 0.18/0.49 thf(f126,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : ((((cQ_2 @ X14 @ X12 @ X13)) != $true) | ($true != ((cP_5 @ (f @ X7) @ X8))) | (((cP_2 @ (f @ X13) @ X2)) != $true) | ($true != ((cP_2 @ (f @ X12) @ X1))) | (((cP_3 @ (f @ X0) @ X9)) != $true) | (((cP_4 @ (f @ X3) @ X4)) != $true) | (((cP_3 @ (f @ X1) @ X3)) != $true) | ($true != ((cP_5 @ (f @ X4) @ X5))) | ($true != ((cP_2 @ (f @ X14) @ X0))) | ($true != ((cP_5 @ (f @ X10) @ X11))) | ($true != ((cP_4 @ (f @ X6) @ X7))) | ($true != ((cP_3 @ (f @ X2) @ X6))) | ($true != ((cP_4 @ (f @ X9) @ X10)))) )), 0.18/0.49 inference(trivial_inequality_removal,[],[f125])). 0.18/0.49 thf(f127,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X16 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : ((((cP_2 @ (f @ X2) @ X5)) != $true) | ($true != ((cP_2 @ (f @ X1) @ X6))) | ($true != ((cP_2 @ (f @ X0) @ X7))) | ($true != ((cP_3 @ (f @ X5) @ X14))) | ($true != ((cP_1 @ (f @ X15) @ X1))) | (((cP_3 @ (f @ X6) @ X9)) != $true) | (((cP_1 @ (f @ X16) @ X0)) != $true) | ($true != ((cP_5 @ (f @ X10) @ X11))) | ($true != ((cQ_1 @ X16 @ X15 @ X17))) | (((cP_3 @ (f @ X7) @ X8)) != $true) | ($true != ((cP_1 @ (f @ X17) @ X2))) | ($true != ((cP_5 @ (f @ X12) @ X13))) | ($true != ((cP_4 @ (f @ X9) @ X10))) | (((cP_5 @ (f @ X3) @ X4)) != $true) | ($true != ((cP_4 @ (f @ X14) @ X3))) | ($true != ((cP_4 @ (f @ X8) @ X12))) | ($true != $true)) )), 0.18/0.49 inference(superposition,[],[f126,f22])). 0.18/0.49 thf(f128,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X16 : $i,X14 : $i,X7 : $i,X4 : $i,X17 : $i,X15 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != ((cQ_1 @ X16 @ X15 @ X17))) | ($true != ((cP_5 @ (f @ X12) @ X13))) | ($true != ((cP_3 @ (f @ X5) @ X14))) | (((cP_3 @ (f @ X6) @ X9)) != $true) | ($true != ((cP_2 @ (f @ X1) @ X6))) | ($true != ((cP_4 @ (f @ X8) @ X12))) | ($true != ((cP_2 @ (f @ X0) @ X7))) | ($true != ((cP_4 @ (f @ X9) @ X10))) | (((cP_1 @ (f @ X16) @ X0)) != $true) | ($true != ((cP_5 @ (f @ X10) @ X11))) | (((cP_2 @ (f @ X2) @ X5)) != $true) | ($true != ((cP_4 @ (f @ X14) @ X3))) | (((cP_3 @ (f @ X7) @ X8)) != $true) | (((cP_5 @ (f @ X3) @ X4)) != $true) | ($true != ((cP_1 @ (f @ X17) @ X2))) | ($true != ((cP_1 @ (f @ X15) @ X1)))) )), 0.18/0.49 inference(trivial_inequality_removal,[],[f127])). 0.18/0.49 thf(f129,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : ((((cP_4 @ (f @ X3) @ X13)) != $true) | ($true != ((cP_2 @ (f @ X8) @ X9))) | (((cP_4 @ (f @ X5) @ X10)) != $true) | ($true != ((cP_3 @ (f @ X4) @ X5))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | ($true != ((cP_1 @ (f @ a) @ X8))) | ($true != ((cP_2 @ (f @ X12) @ X2))) | ($true != ((cP_5 @ (f @ X10) @ X11))) | ($true != ((cP_4 @ (f @ X7) @ X0))) | ($true != $true) | ($true != ((cP_1 @ (f @ b) @ X6))) | ($true != ((cP_5 @ (f @ X13) @ X14))) | ($true != ((cP_3 @ (f @ X9) @ X7))) | (((cP_1 @ (f @ c) @ X12)) != $true) | (((cP_2 @ (f @ X6) @ X4)) != $true) | (((cP_5 @ (f @ X0) @ X1)) != $true)) ) | ~spl0_3), 0.18/0.49 inference(superposition,[],[f128,f53])). 0.18/0.49 thf(f130,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X10 : $i,X0 : $i,X11 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X14 : $i,X4 : $i,X5 : $i,X12 : $i,X13 : $i] : (($true != ((cP_1 @ (f @ b) @ X6))) | ($true != ((cP_5 @ (f @ X13) @ X14))) | ($true != ((cP_2 @ (f @ X12) @ X2))) | ($true != ((cP_3 @ (f @ X4) @ X5))) | ($true != ((cP_3 @ (f @ X9) @ X7))) | (((cP_4 @ (f @ X3) @ X13)) != $true) | ($true != ((cP_1 @ (f @ a) @ X8))) | (((cP_2 @ (f @ X6) @ X4)) != $true) | (((cP_5 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_2 @ (f @ X8) @ X9))) | (((cP_1 @ (f @ c) @ X12)) != $true) | ($true != ((cP_4 @ (f @ X7) @ X0))) | ($true != ((cP_5 @ (f @ X10) @ X11))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_4 @ (f @ X5) @ X10)) != $true)) ) | ~spl0_3), 0.18/0.49 inference(trivial_inequality_removal,[],[f129])). 0.18/0.49 thf(f132,definition,( 0.18/0.49 spl0_17 <=> ! [X0 : $i,X8 : $i,X9 : $i,X1 : $i,X7 : $i] : (($true != ((cP_3 @ (f @ X9) @ X7))) | ($true != ((cP_4 @ (f @ X7) @ X0))) | (((cP_5 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_1 @ (f @ a) @ X8))) | ($true != ((cP_2 @ (f @ X8) @ X9))))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])). 0.18/0.49 thf(f133,plain,( 0.18/0.49 ( ! [X0 : $i,X1 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != ((cP_1 @ (f @ a) @ X8))) | ($true != ((cP_4 @ (f @ X7) @ X0))) | (((cP_5 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_2 @ (f @ X8) @ X9))) | ($true != ((cP_3 @ (f @ X9) @ X7)))) ) | ~spl0_17), 0.18/0.49 inference(avatar_component_clause,[],[f132])). 0.18/0.49 thf(f135,definition,( 0.18/0.49 spl0_18 <=> ! [X5 : $i,X10 : $i,X11 : $i,X4 : $i,X6 : $i] : (($true != ((cP_1 @ (f @ b) @ X6))) | (((cP_4 @ (f @ X5) @ X10)) != $true) | ($true != ((cP_5 @ (f @ X10) @ X11))) | (((cP_2 @ (f @ X6) @ X4)) != $true) | ($true != ((cP_3 @ (f @ X4) @ X5))))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])). 0.18/0.49 thf(f136,plain,( 0.18/0.49 ( ! [X10 : $i,X11 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true != ((cP_1 @ (f @ b) @ X6))) | ($true != ((cP_3 @ (f @ X4) @ X5))) | (((cP_4 @ (f @ X5) @ X10)) != $true) | ($true != ((cP_5 @ (f @ X10) @ X11))) | (((cP_2 @ (f @ X6) @ X4)) != $true)) ) | ~spl0_18), 0.18/0.49 inference(avatar_component_clause,[],[f135])). 0.18/0.49 thf(f138,definition,( 0.18/0.49 spl0_19 <=> ! [X13 : $i,X14 : $i,X12 : $i,X3 : $i,X2 : $i] : (($true != ((cP_5 @ (f @ X13) @ X14))) | (((cP_4 @ (f @ X3) @ X13)) != $true) | ($true != ((cP_2 @ (f @ X12) @ X2))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_1 @ (f @ c) @ X12)) != $true))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])). 0.18/0.49 thf(f139,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X14 : $i,X12 : $i,X13 : $i] : (($true != ((cP_2 @ (f @ X12) @ X2))) | ($true != ((cP_5 @ (f @ X13) @ X14))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_1 @ (f @ c) @ X12)) != $true) | (((cP_4 @ (f @ X3) @ X13)) != $true)) ) | ~spl0_19), 0.18/0.49 inference(avatar_component_clause,[],[f138])). 0.18/0.49 thf(f140,plain,( 0.18/0.49 spl0_17 | spl0_18 | spl0_19 | ~spl0_3), 0.18/0.49 inference(avatar_split_clause,[],[f130,f51,f138,f135,f132])). 0.18/0.49 thf(f141,plain,( 0.18/0.49 ( ! 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[X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((cP_3 @ (f @ X3) @ X0)) != $true) | (((cP_4 @ X0 @ X1)) != $true) | (((cP_5 @ (f @ X1) @ X4)) != $true) | ($true != $true) | ($true != ((cP_2 @ (f @ X2) @ X3))) | ($true != ((cP_1 @ b @ X2)))) ) | ~spl0_18), 0.18/0.49 inference(superposition,[],[f142,f30])). 0.18/0.49 thf(f144,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_2 @ (f @ X2) @ X3))) | (((cP_5 @ (f @ X1) @ X4)) != $true) | (((cP_4 @ X0 @ X1)) != $true) | (((cP_3 @ (f @ X3) @ X0)) != $true) | ($true != ((cP_1 @ b @ X2)))) ) | ~spl0_18), 0.18/0.49 inference(trivial_inequality_removal,[],[f143])). 0.18/0.49 thf(f145,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_5 @ (f @ X2) @ X3))) | ($true != $true) | (((cP_2 @ X0 @ X1)) != $true) | ($true != ((cP_1 @ b @ X0))) | ($true != ((cP_4 @ X4 @ X2))) | (((cP_3 @ (f @ X1) @ X4)) != $true)) ) | ~spl0_18), 0.18/0.49 inference(superposition,[],[f144,f15])). 0.18/0.49 thf(f146,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_5 @ (f @ X2) @ X3))) | (((cP_2 @ X0 @ X1)) != $true) | (((cP_3 @ (f @ X1) @ X4)) != $true) | ($true != ((cP_1 @ b @ X0))) | ($true != ((cP_4 @ X4 @ X2)))) ) | ~spl0_18), 0.18/0.49 inference(trivial_inequality_removal,[],[f145])). 0.18/0.49 thf(f147,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_1 @ b @ X2))) | ($true != $true) | (((cP_4 @ X4 @ X0)) != $true) | (((cP_5 @ X0 @ X1)) != $true) | ($true != ((cP_3 @ (f @ X3) @ X4))) | ($true != ((cP_2 @ X2 @ X3)))) ) | ~spl0_18), 0.18/0.49 inference(superposition,[],[f146,f7])). 0.18/0.49 thf(f148,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_3 @ (f @ X3) @ X4))) | (((cP_4 @ X4 @ X0)) != $true) | ($true != ((cP_2 @ X2 @ X3))) | ($true != ((cP_1 @ b @ X2))) | (((cP_5 @ X0 @ X1)) != $true)) ) | ~spl0_18), 0.18/0.49 inference(trivial_inequality_removal,[],[f147])). 0.18/0.49 thf(f149,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_4 @ X1 @ X2))) | ($true != $true) | ($true != ((cP_2 @ X3 @ X0))) | (((cP_5 @ X2 @ X4)) != $true) | (((cP_3 @ X0 @ X1)) != $true) | (((cP_1 @ b @ X3)) != $true)) ) | ~spl0_18), 0.18/0.49 inference(superposition,[],[f148,f38])). 0.18/0.49 thf(f150,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_2 @ X3 @ X0))) | (((cP_3 @ X0 @ X1)) != $true) | (((cP_5 @ X2 @ X4)) != $true) | (((cP_1 @ b @ X3)) != $true) | ($true != ((cP_4 @ X1 @ X2)))) ) | ~spl0_18), 0.18/0.49 inference(trivial_inequality_removal,[],[f149])). 0.18/0.49 thf(f153,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cP_1 @ b @ b)) != $true) | (((cP_5 @ X1 @ X2)) != $true) | ($true != ((cP_3 @ b @ X0))) | (((cP_4 @ X0 @ X1)) != $true) | ($true != $true)) ) | (~spl0_15 | ~spl0_18)), 0.18/0.49 inference(superposition,[],[f150,f113])). 0.18/0.49 thf(f156,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cP_4 @ X0 @ X1)) != $true) | (((cP_5 @ X1 @ X2)) != $true) | ($true != ((cP_3 @ b @ X0))) | (((cP_1 @ b @ b)) != $true)) ) | (~spl0_15 | ~spl0_18)), 0.18/0.49 inference(trivial_inequality_removal,[],[f153])). 0.18/0.49 thf(f161,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((cP_3 @ b @ X0))) | (((cP_4 @ X0 @ X1)) != $true) | (((cP_5 @ X1 @ X2)) != $true)) ) | (~spl0_13 | ~spl0_15 | ~spl0_18)), 0.18/0.49 inference(forward_subsumption_resolution,[],[f156,f103])). 0.18/0.49 thf(f171,definition,( 0.18/0.49 spl0_22 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((cP_5 @ X1 @ X2)) != $true) | ($true != ((cP_3 @ c @ X0))) | (((cP_4 @ X0 @ X1)) != $true))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition])). 0.18/0.49 thf(f172,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((cP_3 @ c @ X0))) | (((cP_5 @ X1 @ X2)) != $true) | (((cP_4 @ X0 @ X1)) != $true)) ) | ~spl0_22), 0.18/0.49 inference(avatar_component_clause,[],[f171])). 0.18/0.49 thf(f186,plain,( 0.18/0.49 ( ! 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[X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_5 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X4) @ X1)) != $true) | ($true != ((cP_1 @ a @ X0))) | (((cP_2 @ (f @ X0) @ X4)) != $true) | (((cP_4 @ (f @ X1) @ X2)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(trivial_inequality_removal,[],[f215])). 0.18/0.49 thf(f217,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_1 @ a @ X4))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | ($true != ((cP_2 @ (f @ X4) @ X2))) | (((cP_4 @ (f @ X3) @ X0)) != $true) | ($true != $true) | (((cP_5 @ X0 @ X1)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(superposition,[],[f216,f7])). 0.18/0.49 thf(f218,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_2 @ (f @ X4) @ X2))) | ($true != ((cP_3 @ (f @ X2) @ X3))) | ($true != ((cP_1 @ a @ X4))) | (((cP_5 @ X0 @ X1)) != $true) | (((cP_4 @ (f @ X3) @ X0)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(trivial_inequality_removal,[],[f217])). 0.18/0.49 thf(f219,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((cP_3 @ (f @ X1) @ X2)) != $true) | ($true != ((cP_5 @ X3 @ X4))) | ($true != ((cP_4 @ (f @ X2) @ X3))) | ($true != $true) | ($true != ((cP_1 @ a @ X0))) | (((cP_2 @ X0 @ X1)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(superposition,[],[f218,f15])). 0.18/0.49 thf(f220,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_4 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X1) @ X2)) != $true) | ($true != ((cP_1 @ a @ X0))) | (((cP_2 @ X0 @ X1)) != $true) | ($true != ((cP_5 @ X3 @ X4)))) ) | ~spl0_17), 0.18/0.49 inference(trivial_inequality_removal,[],[f219])). 0.18/0.49 thf(f221,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_5 @ X1 @ X4))) | ($true != $true) | (((cP_2 @ X3 @ X2)) != $true) | ($true != ((cP_1 @ a @ X3))) | (((cP_4 @ X0 @ X1)) != $true) | ($true != ((cP_3 @ (f @ X2) @ X0)))) ) | ~spl0_17), 0.18/0.49 inference(superposition,[],[f220,f30])). 0.18/0.49 thf(f222,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_3 @ (f @ X2) @ X0))) | ($true != ((cP_1 @ a @ X3))) | ($true != ((cP_5 @ X1 @ X4))) | (((cP_2 @ X3 @ X2)) != $true) | (((cP_4 @ X0 @ X1)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(trivial_inequality_removal,[],[f221])). 0.18/0.49 thf(f223,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((cP_2 @ X2 @ X0)) != $true) | ($true != ((cP_4 @ X1 @ X3))) | ($true != ((cP_5 @ X3 @ X4))) | ($true != $true) | (((cP_1 @ a @ X2)) != $true) | (((cP_3 @ X0 @ X1)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(superposition,[],[f222,f38])). 0.18/0.49 thf(f224,plain,( 0.18/0.49 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((cP_4 @ X1 @ X3))) | ($true != ((cP_5 @ X3 @ X4))) | (((cP_3 @ X0 @ X1)) != $true) | (((cP_1 @ a @ X2)) != $true) | (((cP_2 @ X2 @ X0)) != $true)) ) | ~spl0_17), 0.18/0.49 inference(trivial_inequality_removal,[],[f223])). 0.18/0.49 thf(f228,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((cP_5 @ a @ X0))) | ($true != ((cP_2 @ X2 @ X1))) | (((cP_1 @ a @ X2)) != $true) | ($true != ((cP_3 @ X1 @ a)))) ) | (~spl0_6 | ~spl0_17)), 0.18/0.49 inference(superposition,[],[f224,f68])). 0.18/0.49 thf(f234,plain,( 0.18/0.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cP_1 @ a @ X2)) != $true) | ($true != ((cP_5 @ a @ X0))) | ($true != ((cP_2 @ X2 @ X1))) | ($true != ((cP_3 @ X1 @ a)))) ) | (~spl0_6 | ~spl0_17)), 0.18/0.49 inference(trivial_inequality_removal,[],[f228])). 0.18/0.49 thf(f257,definition,( 0.18/0.49 spl0_32 <=> ! [X0 : $i] : ($true != ((cP_5 @ a @ X0)))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition])). 0.18/0.49 thf(f258,plain,( 0.18/0.49 ( ! [X0 : $i] : (($true != ((cP_5 @ a @ X0)))) ) | ~spl0_32), 0.18/0.49 inference(avatar_component_clause,[],[f257])). 0.18/0.49 thf(f260,definition,( 0.18/0.49 spl0_33 <=> ! [X2 : $i,X1 : $i] : ((((cP_1 @ a @ X2)) != $true) | ($true != ((cP_3 @ X1 @ a))) | ($true != ((cP_2 @ X2 @ X1))))), 0.18/0.49 introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition])). 0.18/0.49 thf(f261,plain,( 0.18/0.49 ( ! [X2 : $i,X1 : $i] : (($true != ((cP_2 @ X2 @ X1))) | ($true != ((cP_3 @ X1 @ a))) | (((cP_1 @ a @ X2)) != $true)) ) | ~spl0_33), 0.18/0.49 inference(avatar_component_clause,[],[f260])). 0.18/0.49 thf(f262,plain,( 0.18/0.49 spl0_32 | spl0_33 | ~spl0_6 | ~spl0_17), 0.18/0.49 inference(avatar_split_clause,[],[f234,f132,f66,f260,f257])). 0.18/0.49 thf(f280,plain,( 0.18/0.49 ($true != $true) | (~spl0_1 | ~spl0_32)), 0.18/0.49 inference(superposition,[],[f258,f43])). 0.18/0.49 thf(f281,plain,( 0.18/0.49 $false | (~spl0_1 | ~spl0_32)), 0.18/0.49 inference(trivial_inequality_removal,[],[f280])). 0.18/0.49 thf(f282,plain,( 0.18/0.49 ~spl0_1 | ~spl0_32), 0.18/0.49 inference(avatar_contradiction_clause,[],[f281])). 0.18/0.49 thf(f350,plain,( 0.18/0.49 (((cP_1 @ a @ a)) != $true) | ($true != $true) | (((cP_3 @ a @ a)) != $true) | (~spl0_12 | ~spl0_33)), 0.18/0.49 inference(superposition,[],[f261,f98])). 0.18/0.49 thf(f354,plain,( 0.18/0.49 (((cP_1 @ a @ a)) != $true) | (((cP_3 @ a @ a)) != $true) | (~spl0_12 | ~spl0_33)), 0.18/0.49 inference(trivial_inequality_removal,[],[f350])). 0.18/0.49 thf(f362,plain,( 0.18/0.49 (((cP_3 @ a @ a)) != $true) | (~spl0_9 | ~spl0_12 | ~spl0_33)), 0.18/0.49 inference(forward_subsumption_resolution,[],[f354,f83])). 0.18/0.49 thf(f368,plain,( 0.18/0.49 $false | (~spl0_8 | ~spl0_9 | ~spl0_12 | ~spl0_33)), 0.18/0.49 inference(forward_subsumption_resolution,[],[f362,f78])). 0.18/0.49 thf(f369,plain,( 0.18/0.49 ~spl0_8 | ~spl0_9 | ~spl0_12 | ~spl0_33), 0.18/0.49 inference(avatar_contradiction_clause,[],[f368])). 0.18/0.49 cnf(s1, plain, spl0_1, inference(sat_conversion,[],[f44])). 0.18/0.49 cnf(s2, plain, spl0_2, inference(sat_conversion,[],[f49])). 0.18/0.49 cnf(s3, plain, spl0_3, inference(sat_conversion,[],[f54])). 0.18/0.49 cnf(s4, plain, spl0_4, inference(sat_conversion,[],[f59])). 0.18/0.49 cnf(s5, plain, spl0_5, inference(sat_conversion,[],[f64])). 0.18/0.49 cnf(s6, plain, spl0_6, inference(sat_conversion,[],[f69])). 0.18/0.49 cnf(s7, plain, spl0_7, inference(sat_conversion,[],[f74])). 0.18/0.49 cnf(s8, plain, spl0_8, inference(sat_conversion,[],[f79])). 0.18/0.49 cnf(s9, plain, spl0_9, inference(sat_conversion,[],[f84])). 0.18/0.49 cnf(s10, plain, spl0_10, inference(sat_conversion,[],[f89])). 0.18/0.49 cnf(s11, plain, spl0_11, inference(sat_conversion,[],[f94])). 0.18/0.49 cnf(s12, plain, spl0_12, inference(sat_conversion,[],[f99])). 0.18/0.49 cnf(s13, plain, spl0_13, inference(sat_conversion,[],[f104])). 0.18/0.49 cnf(s14, plain, spl0_14, inference(sat_conversion,[],[f109])). 0.18/0.49 cnf(s15, plain, spl0_15, inference(sat_conversion,[],[f114])). 0.18/0.49 cnf(s16, plain, spl0_16, inference(sat_conversion,[],[f119])). 0.18/0.49 cnf(s17, plain, ~spl0_3 | spl0_17 | spl0_18 | spl0_19, inference(sat_conversion,[],[f140])). 0.18/0.49 cnf(s21, plain, ~spl0_5 | ~spl0_13 | ~spl0_14 | ~spl0_15 | ~spl0_16 | ~spl0_18, inference(sat_conversion,[],[f192])). 0.18/0.49 cnf(s22, plain, ~spl0_2 | ~spl0_7 | ~spl0_19 | spl0_22, inference(sat_conversion,[],[f207])). 0.18/0.49 cnf(s23, plain, ~spl0_4 | ~spl0_10 | ~spl0_11 | ~spl0_22, inference(sat_conversion,[],[f214])). 0.18/0.49 cnf(s27, plain, ~spl0_6 | ~spl0_17 | spl0_32 | spl0_33, inference(sat_conversion,[],[f262])). 0.18/0.49 cnf(s33, plain, ~spl0_1 | ~spl0_32, inference(sat_conversion,[],[f282])). 0.18/0.49 cnf(s43, plain, ~spl0_8 | ~spl0_9 | ~spl0_12 | ~spl0_33, inference(sat_conversion,[],[f369])). 0.18/0.49 cnf(s46, plain, ~spl0_33, inference(rat,[],[s43,s9,s12,s8])). 0.18/0.49 cnf(s47, plain, ~spl0_18, inference(rat,[],[s21,s13,s16,s15,s14,s5])). 0.18/0.49 cnf(s48, plain, ~spl0_22, inference(rat,[],[s23,s10,s11,s4])). 0.18/0.49 cnf(s49, plain, ~spl0_19, inference(rat,[],[s22,s48,s7,s2])). 0.18/0.49 cnf(s50, plain, spl0_17, inference(rat,[],[s17,s3,s47,s49])). 0.18/0.49 cnf(s51, plain, spl0_32, inference(rat,[],[s27,s46,s6,s50])). 0.18/0.49 cnf(s54, plain, ~spl0_1, inference(rat,[],[s33,s51])). 0.18/0.49 cnf(s57, plain, $false, inference(rat,[],[s1,s54])). 0.18/0.49 thf(f370,plain,( 0.18/0.49 $false), 0.18/0.49 inference(avatar_sat_refutation,[],[s57])). 0.18/0.49 % SZS output end Proof for theBenchmark 0.18/0.49 % (703016)------------------------------ 0.18/0.49 % (703016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.18/0.49 % (703016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.18/0.49 % (703016)CaDiCaL version: 2.1.3 0.18/0.49 % (703016)Termination reason: Refutation 0.18/0.49 % (703016)Time elapsed: 0.026 s 0.18/0.49 % (703016)Peak memory usage: 13 MB 0.18/0.49 % (703016)Instructions burned: 47 (million) 0.18/0.49 % (703008)Success in time 0.067 s 0.18/0.49 % Vampire exiting 0.18/0.49 EOF