%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO245^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:47:16 AM UTC 2026
% Result : Theorem 0.59s 0.42s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO245^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n010.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 16:41:04 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.42 % (3113408)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.59/0.42 % (3113416)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=89276949:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.59/0.42 % (3113416)Instruction limit reached!
% 0.59/0.42 % (3113416)------------------------------
% 0.59/0.42 % (3113416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113416)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113416)Termination reason: Instruction limit
% 0.59/0.42 % (3113416)Termination phase: Saturation
% 0.59/0.42 % (3113416)Time elapsed: 0.003 s
% 0.59/0.42 % (3113416)Peak memory usage: 12 MB
% 0.59/0.42 % (3113416)Instructions burned: 4 (million)
% 0.59/0.42 % (3113414)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2471697203:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.59/0.42 % (3113415)lrs+10_16_si=on:nwc=1.5:random_seed=1919008433:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.59/0.42 % (3113420)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.59/0.42 % (3113420)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
% 0.59/0.42 % (3113418)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2409220441:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.59/0.42 % (3113417)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=1419546808: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.59/0.42 % (3113419)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1141275707:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.59/0.42 % (3113420)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=1599089814:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.59/0.42 % (3113422)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=7758702:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.42 % (3113422)Instruction limit reached!
% 0.59/0.42 % (3113422)------------------------------
% 0.59/0.42 % (3113422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113422)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113422)Termination reason: Instruction limit
% 0.59/0.42 % (3113422)Termination phase: Saturation
% 0.59/0.42 % (3113422)Time elapsed: 0.002 s
% 0.59/0.42 % (3113422)Peak memory usage: 12 MB
% 0.59/0.42 % (3113422)Instructions burned: 2 (million)
% 0.59/0.42 % (3113415)Instruction limit reached!
% 0.59/0.42 % (3113415)------------------------------
% 0.59/0.42 % (3113415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113415)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113415)Termination reason: Instruction limit
% 0.59/0.42 % (3113415)Termination phase: Saturation
% 0.59/0.42 % (3113415)Time elapsed: 0.016 s
% 0.59/0.42 % (3113415)Peak memory usage: 12 MB
% 0.59/0.42 % (3113415)Instructions burned: 18 (million)
% 0.59/0.42 % (3113418)Instruction limit reached!
% 0.59/0.42 % (3113418)------------------------------
% 0.59/0.42 % (3113418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113418)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113418)Termination reason: Instruction limit
% 0.59/0.42 % (3113418)Termination phase: Saturation
% 0.59/0.42 % (3113418)Time elapsed: 0.022 s
% 0.59/0.42 % (3113418)Peak memory usage: 12 MB
% 0.59/0.42 % (3113418)Instructions burned: 25 (million)
% 0.59/0.42 % (3113430)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=704691361:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.59/0.42 % (3113430)Instruction limit reached!
% 0.59/0.42 % (3113430)------------------------------
% 0.59/0.42 % (3113430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113430)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113430)Termination reason: Instruction limit
% 0.59/0.42 % (3113430)Termination phase: Saturation
% 0.59/0.42 % (3113430)Time elapsed: 0.003 s
% 0.59/0.42 % (3113430)Peak memory usage: 12 MB
% 0.59/0.42 % (3113430)Instructions burned: 5 (million)
% 0.59/0.42 % (3113417) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3113408-3113417"...
% 0.59/0.42 % (3113414) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3113408-3113414"...
% 0.59/0.42 % (3113431)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.42 % (3113434)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
% 0.59/0.42 % (3113434)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.42 % (3113417)...printing done.
% 0.59/0.42 % (3113434)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2059941049:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.59/0.42 % (3113431)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2752371737:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.59/0.42 % (3113417)Refutation found. Thanks to Tanya!
% 0.59/0.42 % SZS status Theorem for theBenchmark
% 0.59/0.42 % SZS output start Proof for theBenchmark
% 0.59/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.59/0.42 thf(func_def_1, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.59/0.42 thf(func_def_2, type, vAND: ($o > $o > $o)).
% 0.59/0.42 thf(func_def_3, type, vNOT: ($o > $o)).
% 0.59/0.42 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.59/0.42 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.59/0.42 thf(func_def_6, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.59/0.42 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.59/0.42 thf(func_def_10, type, sK0: ((($i > $o) > $i) > $i > $o)).
% 0.59/0.42 thf(func_def_11, type, sK1: (($i > $o) > $i)).
% 0.59/0.42 thf(func_def_12, type, inv_sK1_2: ($i > $i > $o)).
% 0.59/0.42 thf(func_def_13, type, sK3: ($i > $i > $o)).
% 0.59/0.42 thf(func_def_15, type, sK5: ($i > $i > $o)).
% 0.59/0.42 thf(func_def_16, type, sK6: ($i > $i > $o)).
% 0.59/0.42 thf(func_def_17, type, sK7: ($i > $o)).
% 0.59/0.42 thf(func_def_18, type, sK8: ($i > $o)).
% 0.59/0.42 thf(func_def_19, type, sK9: ($i > $o)).
% 0.59/0.42 thf(func_def_20, type, sK10: ($i > $o)).
% 0.59/0.42 thf(func_def_21, type, sK11: ($i > $i > $o)).
% 0.59/0.42 thf(func_def_22, type, sK12: ($i > $o)).
% 0.59/0.42 thf(func_def_23, type, sK13: ($i > $i > $o)).
% 0.59/0.42 thf(f1,conjecture,(
% 0.59/0.42 ! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : (~(X1 @ (X0 @ X1)) & (((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X2 = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))))) = ((X0 @ X1)))) => ? [X1 : ($i > $o)] : (~(X1 @ (X0 @ X1)) & (((X0 @ X1)) = ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (~(X3 @ (X0 @ X3)) & (X2 = ((X0 @ X3))))))))))) => ~ ? [X0 : (($i > $o) > $i)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X4)) = ((X0 @ X5))) => (X4 = X5))),
% 0.59/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM193A)).
% 0.59/0.42 thf(f2,negated_conjecture,(
% 0.59/0.42 ~(! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : (~(X1 @ (X0 @ X1)) & (((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X2 = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))))) = ((X0 @ X1)))) => ? [X1 : ($i > $o)] : (~(X1 @ (X0 @ X1)) & (((X0 @ X1)) = ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : (~(X3 @ (X0 @ X3)) & (X2 = ((X0 @ X3))))))))))) => ~ ? [X0 : (($i > $o) > $i)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X4)) = ((X0 @ X5))) => (X4 = X5)))),
% 0.59/0.42 inference(negated_conjecture,[status(cth)],[f1])).
% 0.59/0.42 thf(f3,plain,(
% 0.59/0.42 ~(! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : (~(X1 @ (X0 @ X1)) & (((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X2 = ((X0 @ X3))) & ~(X3 @ (X0 @ X3))))))) = ((X0 @ X1)))) => ? [X4 : ($i > $o)] : (~(X4 @ (X0 @ X4)) & (((X0 @ X4)) = ((X0 @ (^[X5 : $i] : (? [X6 : ($i > $o)] : (~(X6 @ (X0 @ X6)) & (((X0 @ X6)) = X5))))))))) => ~ ? [X7 : (($i > $o) > $i)] : ! [X8 : ($i > $o),X9 : ($i > $o)] : ((((X7 @ X8)) = ((X7 @ X9))) => (X8 = X9)))),
% 0.59/0.42 inference(rectify,[],[f2])).
% 0.59/0.42 thf(f4,plain,(
% 0.59/0.42 ~(! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : (~ (((X1 @ (X0 @ X1))) = $true) & (((X0 @ X1)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) => ? [X4 : ($i > $o)] : (~ (((X4 @ (X0 @ X4))) = $true) & (((X0 @ X4)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))))) => ~ ? [X7 : (($i > $o) > $i)] : ! [X8 : ($i > $o),X9 : ($i > $o)] : ((((X7 @ X8)) = ((X7 @ X9))) => (X8 = X9)))),
% 0.59/0.42 inference(fool_elimination,[],[f3])).
% 0.59/0.42 thf(f5,plain,(
% 0.59/0.42 ~(! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : (~ (((X1 @ (X0 @ X1))) = $true) & (((X0 @ X1)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) => ? [X2 : ($i > $o)] : (~ ($true = ((X2 @ (X0 @ X2)))) & (((X0 @ X2)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))))) => ~ ? [X3 : (($i > $o) > $i)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : ((((X3 @ X4)) = ((X3 @ X5))) => (X4 = X5)))),
% 0.59/0.42 inference(rectify,[],[f4])).
% 0.59/0.42 thf(f6,plain,(
% 0.59/0.42 ~(! [X0 : (($i > $o) > $i)] : (? [X1 : ($i > $o)] : ((((X1 @ (X0 @ X1))) != $true) & (((X0 @ X1)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) => ? [X2 : ($i > $o)] : ((((X0 @ X2)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))) & ($true != ((X2 @ (X0 @ X2)))))) => ~ ? [X3 : (($i > $o) > $i)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : ((((X3 @ X4)) = ((X3 @ X5))) => (X4 = X5)))),
% 0.59/0.42 inference(flattening,[],[f5])).
% 0.59/0.42 thf(f7,plain,(
% 0.59/0.42 ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o)] : ((((X1 @ (X0 @ X1))) = $true) | (((X0 @ X1)) != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) | ? [X2 : ($i > $o)] : ((((X0 @ X2)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))) & ($true != ((X2 @ (X0 @ X2)))))) & ? [X3 : (($i > $o) > $i)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : ((X4 = X5) | (((X3 @ X4)) != ((X3 @ X5))))),
% 0.59/0.42 inference(ennf_transformation,[],[f6])).
% 0.59/0.42 thf(f8,plain,(
% 0.59/0.42 ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o)] : ((((X1 @ (X0 @ X1))) = $true) | (((X0 @ X1)) != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) | ? [X2 : ($i > $o)] : ((((X0 @ X2)) = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))) & ($true != ((X2 @ (X0 @ X2)))))) & ? [X3 : (($i > $o) > $i)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : ((X4 = X5) | (((X3 @ X4)) != ((X3 @ X5))))),
% 0.59/0.42 inference(rectify,[],[f7])).
% 0.59/0.42 thf(f9,plain,(
% 0.59/0.42 ! [X0 : (($i > $o) > $i)] : (! [X1 : ($i > $o)] : ((((X1 @ (X0 @ X1))) = $true) | (((X0 @ X1)) != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) | ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) = ((X0 @ (sK0 @ X0)))) & ($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))))) & ! [X4 : ($i > $o),X5 : ($i > $o)] : ((X4 = X5) | (((sK1 @ X4)) != ((sK1 @ X5))))),
% 0.59/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X2,sK0 @ X0),skolemize(X3,sK1)],[f8])).
% 0.59/0.42 thf(f10,plain,(
% 0.59/0.42 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sK1 @ X4)) != ((sK1 @ X5))) | (X4 = X5)) )),
% 0.59/0.42 inference(cnf_transformation,[],[f9])).
% 0.59/0.42 thf(f11,plain,(
% 0.59/0.42 ( ! [X0 : (($i > $o) > $i),X1 : ($i > $o)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))) | (((X1 @ (X0 @ X1))) = $true) | (((X0 @ X1)) != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) )),
% 0.59/0.42 inference(cnf_transformation,[],[f9])).
% 0.59/0.42 thf(f12,plain,(
% 0.59/0.42 ( ! [X0 : (($i > $o) > $i),X1 : ($i > $o)] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) = ((X0 @ (sK0 @ X0)))) | (((X1 @ (X0 @ X1))) = $true) | (((X0 @ X1)) != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))) )),
% 0.59/0.42 inference(cnf_transformation,[],[f9])).
% 0.59/0.42 thf(f14,plain,(
% 0.59/0.42 ( ! [X4 : ($i > $o)] : ((((inv_sK1_2 @ (sK1 @ X4))) = X4)) )),
% 0.59/0.42 inference(injectivity,[],[f10])).
% 0.59/0.42 thf(f16,plain,(
% 0.59/0.42 ( ! [X4 : ($i > $o),X5 : $i] : ((((X4 @ X5)) = ((inv_sK1_2 @ (sK1 @ X4) @ X5)))) )),
% 0.59/0.42 inference(argument_congruence,[],[f14])).
% 0.59/0.42 thf(f17,plain,(
% 0.59/0.42 ( ! [X4 : ($i > $o),X5 : $i] : (($false = ((inv_sK1_2 @ (sK1 @ X4) @ X5))) | ($true = ((X4 @ X5)))) )),
% 0.59/0.42 inference(iff_proxy_clausification,[],[f16])).
% 0.59/0.42 thf(f18,plain,(
% 0.59/0.42 ( ! [X4 : ($i > $o),X5 : $i] : (($true = ((inv_sK1_2 @ (sK1 @ X4) @ X5))) | ($false = ((X4 @ X5)))) )),
% 0.59/0.42 inference(iff_proxy_clausification,[],[f16])).
% 0.59/0.42 thf(f20,plain,(
% 0.59/0.42 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK1 @ X0)))) | (((inv_sK1_2 @ (sK1 @ (sK0 @ sK1)))) = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1)))))))) | (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X0)))) )),
% 0.59/0.42 inference(superposition,[],[f14,f12])).
% 0.59/0.42 thf(f31,definition,(
% 0.59/0.42 spl4_1 <=> ! [X1 : ($i > $o)] : ((((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X1))) | ($true = ((X1 @ (sK1 @ X1)))))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.59/0.42 thf(f32,plain,(
% 0.59/0.42 ( ! [X1 : ($i > $o)] : ((((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X1))) | ($true = ((X1 @ (sK1 @ X1))))) ) | ~spl4_1),
% 0.59/0.42 inference(avatar_component_clause,[],[f31])).
% 0.59/0.42 thf(f37,plain,(
% 0.59/0.42 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK1 @ X0)))) | (((sK0 @ sK1)) = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1)))))))) | (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X0)))) )),
% 0.59/0.42 inference(forward_demodulation,[],[f20,f14])).
% 0.59/0.42 thf(f48,definition,(
% 0.59/0.42 spl4_5 <=> (((sK0 @ sK1)) = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1))))))))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.59/0.42 thf(f50,plain,(
% 0.59/0.42 (((sK0 @ sK1)) = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1)))))))) | ~spl4_5),
% 0.59/0.42 inference(avatar_component_clause,[],[f48])).
% 0.59/0.42 thf(f51,plain,(
% 0.59/0.42 spl4_1 | spl4_5),
% 0.59/0.42 inference(avatar_split_clause,[],[f37,f48,f31])).
% 0.59/0.42 thf(f72,plain,(
% 0.59/0.42 ( ! [X1 : $i] : ((((sK0 @ sK1 @ X1)) = (((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1))))))) @ X1)))) ) | ~spl4_5),
% 0.59/0.42 inference(argument_congruence,[],[f50])).
% 0.59/0.42 thf(f74,plain,(
% 0.59/0.42 ( ! [X1 : $i] : (((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK1 @ Y1) = Y0) & (~ (Y1 @ (sK1 @ Y1))))))) @ X1)) = $false) | (((sK0 @ sK1 @ X1)) = $true)) ) | ~spl4_5),
% 0.59/0.42 inference(iff_proxy_clausification,[],[f72])).
% 0.59/0.42 thf(f83,plain,(
% 0.59/0.42 ( ! [X1 : $i] : ((((sK0 @ sK1 @ X1)) = $true) | (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: (((sK1 @ Y0) = X1) & (~ (Y0 @ (sK1 @ Y0))))))) = $false)) ) | ~spl4_5),
% 0.59/0.42 inference(beta-eta_normalization,[],[f74])).
% 0.59/0.42 thf(f84,plain,(
% 0.59/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (((((^[Y0 : $i > $o]: (((sK1 @ Y0) = X1) & (~ (Y0 @ (sK1 @ Y0))))) @ X2)) = $false) | (((sK0 @ sK1 @ X1)) = $true)) ) | ~spl4_5),
% 0.59/0.42 inference(pi_proxy_clausification,[],[f83])).
% 0.59/0.42 thf(f85,plain,(
% 0.59/0.42 ( ! [X2 : ($i > $o),X1 : $i] : ((((sK0 @ sK1 @ X1)) = $true) | ($false = ((((sK1 @ X2) = X1) & (~ (X2 @ (sK1 @ X2))))))) ) | ~spl4_5),
% 0.59/0.42 inference(beta-eta_normalization,[],[f84])).
% 0.59/0.42 thf(f86,plain,(
% 0.59/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((~ (X2 @ (sK1 @ X2))))) | ($false = (((sK1 @ X2) = X1))) | (((sK0 @ sK1 @ X1)) = $true)) ) | ~spl4_5),
% 0.59/0.42 inference(and_proxy_clausification,[],[f85])).
% 0.59/0.42 thf(f87,plain,(
% 0.59/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($false = (((sK1 @ X2) = X1))) | (((sK0 @ sK1 @ X1)) = $true) | ($true = ((X2 @ (sK1 @ X2))))) ) | ~spl4_5),
% 0.59/0.42 inference(not_proxy_clausification,[],[f86])).
% 0.59/0.42 thf(f88,plain,(
% 0.59/0.42 ( ! [X2 : ($i > $o),X1 : $i] : ((((sK0 @ sK1 @ X1)) = $true) | (((sK1 @ X2)) != X1) | ($true = ((X2 @ (sK1 @ X2))))) ) | ~spl4_5),
% 0.59/0.42 inference(equality_proxy_clausification,[],[f87])).
% 0.59/0.42 thf(f117,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true) | ($true != $true) | (((sK1 @ (sK0 @ sK1))) != ((sK1 @ (sK0 @ sK1)))) | ~spl4_5),
% 0.59/0.42 inference(equality_factoring,[],[f88])).
% 0.59/0.42 thf(f120,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true) | ~spl4_5),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f117])).
% 0.59/0.42 thf(f125,definition,(
% 0.59/0.42 spl4_7 <=> (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true)),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.59/0.42 thf(f126,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) != $true) | spl4_7),
% 0.59/0.42 inference(avatar_component_clause,[],[f125])).
% 0.59/0.42 thf(f127,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true) | ~spl4_7),
% 0.59/0.42 inference(avatar_component_clause,[],[f125])).
% 0.59/0.42 thf(f128,plain,(
% 0.59/0.42 spl4_7 | ~spl4_5),
% 0.59/0.42 inference(avatar_split_clause,[],[f120,f48,f125])).
% 0.59/0.42 thf(f134,plain,(
% 0.59/0.42 ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))) @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))) = $true) | ~spl4_1),
% 0.59/0.42 inference(equality_resolution,[],[f32])).
% 0.59/0.42 thf(f142,plain,(
% 0.59/0.42 (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))))) = $true) | ~spl4_1),
% 0.59/0.42 inference(beta-eta_normalization,[],[f134])).
% 0.59/0.42 thf(f143,plain,(
% 0.59/0.42 ($true = (((^[Y0 : $i > $o]: ((~ (Y0 @ (sK1 @ Y0))) & ((sK1 @ Y0) = (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK1 @ Y2))) & ((sK1 @ Y2) = Y1))))))))) @ sK8))) | ~spl4_1),
% 0.59/0.42 inference(sigma_proxy_clausification,[],[f142])).
% 0.59/0.42 thf(f144,plain,(
% 0.59/0.42 ((((~ (sK8 @ (sK1 @ sK8))) & ((sK1 @ sK8) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) = $true) | ~spl4_1),
% 0.59/0.42 inference(beta-eta_normalization,[],[f143])).
% 0.59/0.42 thf(f145,plain,(
% 0.59/0.42 ((((sK1 @ sK8) = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))) = $true) | ~spl4_1),
% 0.59/0.42 inference(and_proxy_clausification,[],[f144])).
% 0.59/0.42 thf(f146,plain,(
% 0.59/0.42 ($true = ((~ (sK8 @ (sK1 @ sK8))))) | ~spl4_1),
% 0.59/0.42 inference(and_proxy_clausification,[],[f144])).
% 0.59/0.42 thf(f147,plain,(
% 0.59/0.42 ($false = ((sK8 @ (sK1 @ sK8)))) | ~spl4_1),
% 0.59/0.42 inference(not_proxy_clausification,[],[f146])).
% 0.59/0.42 thf(f148,plain,(
% 0.59/0.42 (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = ((sK1 @ sK8))) | ~spl4_1),
% 0.59/0.42 inference(equality_proxy_clausification,[],[f145])).
% 0.59/0.42 thf(f150,definition,(
% 0.59/0.42 spl4_9 <=> ($false = ((sK8 @ (sK1 @ sK8))))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition])).
% 0.59/0.42 thf(f153,plain,(
% 0.59/0.42 spl4_9 | ~spl4_1),
% 0.59/0.42 inference(avatar_split_clause,[],[f147,f31,f150])).
% 0.59/0.42 thf(f155,definition,(
% 0.59/0.42 spl4_10 <=> (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = ((sK1 @ sK8)))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.59/0.42 thf(f157,plain,(
% 0.59/0.42 (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) = ((sK1 @ sK8))) | ~spl4_10),
% 0.59/0.42 inference(avatar_component_clause,[],[f155])).
% 0.59/0.42 thf(f158,plain,(
% 0.59/0.42 spl4_10 | ~spl4_1),
% 0.59/0.42 inference(avatar_split_clause,[],[f148,f31,f155])).
% 0.59/0.42 thf(f160,plain,(
% 0.59/0.42 ( ! [X0 : ($i > $o)] : ((((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X0))) | ($true = ((X0 @ (sK1 @ X0)))) | ($true != $true)) ) | ~spl4_7),
% 0.59/0.42 inference(superposition,[],[f11,f127])).
% 0.59/0.42 thf(f164,plain,(
% 0.59/0.42 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK1 @ X0)))) | (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ X0)))) ) | ~spl4_7),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f160])).
% 0.59/0.42 thf(f170,plain,(
% 0.59/0.42 spl4_1 | ~spl4_7),
% 0.59/0.42 inference(avatar_split_clause,[],[f164,f125,f31])).
% 0.59/0.42 thf(f301,definition,(
% 0.59/0.42 spl4_21 <=> (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $false)),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_21])],[avatar_definition])).
% 0.59/0.42 thf(f303,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $false) | ~spl4_21),
% 0.59/0.42 inference(avatar_component_clause,[],[f301])).
% 0.59/0.42 thf(f317,definition,(
% 0.59/0.42 spl4_22 <=> ($false = ((inv_sK1_2 @ (sK1 @ (sK0 @ sK1)) @ (sK1 @ (sK0 @ sK1)))))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition])).
% 0.59/0.42 thf(f318,plain,(
% 0.59/0.42 ($false != ((inv_sK1_2 @ (sK1 @ (sK0 @ sK1)) @ (sK1 @ (sK0 @ sK1))))) | spl4_22),
% 0.59/0.42 inference(avatar_component_clause,[],[f317])).
% 0.59/0.42 thf(f319,plain,(
% 0.59/0.42 ($false = ((inv_sK1_2 @ (sK1 @ (sK0 @ sK1)) @ (sK1 @ (sK0 @ sK1))))) | ~spl4_22),
% 0.59/0.42 inference(avatar_component_clause,[],[f317])).
% 0.59/0.42 thf(f331,plain,(
% 0.59/0.42 ($true = $false) | (~spl4_7 | ~spl4_21)),
% 0.59/0.42 inference(superposition,[],[f127,f303])).
% 0.59/0.42 thf(f335,plain,(
% 0.59/0.42 $false | (~spl4_7 | ~spl4_21)),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f331])).
% 0.59/0.42 thf(f336,plain,(
% 0.59/0.42 ~spl4_7 | ~spl4_21),
% 0.59/0.42 inference(avatar_contradiction_clause,[],[f335])).
% 0.59/0.42 thf(f339,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $false) | ($true = $false) | ~spl4_22),
% 0.59/0.42 inference(superposition,[],[f18,f319])).
% 0.59/0.42 thf(f340,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $false) | ~spl4_22),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f339])).
% 0.59/0.42 thf(f342,plain,(
% 0.59/0.42 spl4_21 | ~spl4_22),
% 0.59/0.42 inference(avatar_split_clause,[],[f340,f317,f301])).
% 0.59/0.42 thf(f451,plain,(
% 0.59/0.42 (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))) | ($true = ((sK8 @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) | (~spl4_1 | ~spl4_10)),
% 0.59/0.42 inference(superposition,[],[f32,f157])).
% 0.59/0.42 thf(f455,plain,(
% 0.59/0.42 ($true = ((sK8 @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) | (~spl4_1 | ~spl4_10)),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f451])).
% 0.59/0.42 thf(f457,definition,(
% 0.59/0.42 spl4_25 <=> ($true = ((sK8 @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0)))))))))),
% 0.59/0.42 introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition])).
% 0.59/0.42 thf(f460,plain,(
% 0.59/0.42 spl4_25 | ~spl4_1 | ~spl4_10),
% 0.59/0.42 inference(avatar_split_clause,[],[f455,f155,f31,f457])).
% 0.59/0.42 thf(f472,definition,(
% 0.59/0.42 (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ sK8))) | (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) != $true) | ($true != ((sK8 @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) | ($false != ((sK8 @ (sK1 @ sK8)))) | (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $false)),
% 0.59/0.42 introduced(theory,[theory_tautology_sat_conflict])).
% 0.59/0.42 thf(f527,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true) | ($false != $false) | spl4_22),
% 0.59/0.42 inference(superposition,[],[f318,f17])).
% 0.59/0.42 thf(f530,plain,(
% 0.59/0.42 (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true) | spl4_22),
% 0.59/0.42 inference(trivial_inequality_removal,[],[f527])).
% 0.59/0.42 thf(f531,plain,(
% 0.59/0.42 $false | (spl4_7 | spl4_22)),
% 0.59/0.42 inference(forward_subsumption_resolution,[],[f530,f126])).
% 0.59/0.42 thf(f532,plain,(
% 0.59/0.42 spl4_7 | spl4_22),
% 0.59/0.42 inference(avatar_contradiction_clause,[],[f531])).
% 0.59/0.42 thf(f533,definition,(
% 0.59/0.42 (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))) != ((sK1 @ sK8))) | (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) != $false) | ($true != ((sK8 @ (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK1 @ Y1))) & ((sK1 @ Y1) = Y0))))))))) | ($false != ((sK8 @ (sK1 @ sK8)))) | (((sK0 @ sK1 @ (sK1 @ (sK0 @ sK1)))) = $true)),
% 0.59/0.42 introduced(theory,[theory_tautology_sat_conflict])).
% 0.59/0.42 cnf(s5, plain, spl4_1 | spl4_5, inference(sat_conversion,[],[f51])).
% 0.59/0.42 cnf(s7, plain, ~spl4_5 | spl4_7, inference(sat_conversion,[],[f128])).
% 0.59/0.42 cnf(s9, plain, ~spl4_1 | spl4_9, inference(sat_conversion,[],[f153])).
% 0.59/0.42 cnf(s10, plain, ~spl4_1 | spl4_10, inference(sat_conversion,[],[f158])).
% 0.59/0.42 cnf(s13, plain, spl4_1 | ~spl4_7, inference(sat_conversion,[],[f170])).
% 0.59/0.42 cnf(s29, plain, ~spl4_7 | ~spl4_21, inference(sat_conversion,[],[f336])).
% 0.59/0.42 cnf(s30, plain, spl4_21 | ~spl4_22, inference(sat_conversion,[],[f342])).
% 0.59/0.42 cnf(s36, plain, ~spl4_1 | ~spl4_10 | spl4_25, inference(sat_conversion,[],[f460])).
% 0.59/0.42 cnf(s39, plain, ~spl4_7 | ~spl4_9 | ~spl4_10 | spl4_21 | ~spl4_25, inference(sat_conversion,[],[f472])).
% 0.59/0.42 cnf(s45, plain, spl4_7 | spl4_22, inference(sat_conversion,[],[f532])).
% 0.59/0.42 cnf(s46, plain, spl4_7 | ~spl4_9 | ~spl4_10 | ~spl4_21 | ~spl4_25, inference(sat_conversion,[],[f533])).
% 0.59/0.42 cnf(s47, plain, spl4_1, inference(rat,[],[s7,s5,s13])).
% 0.59/0.42 cnf(s50, plain, spl4_10, inference(rat,[],[s10,s47])).
% 0.59/0.42 cnf(s51, plain, spl4_9, inference(rat,[],[s9,s47])).
% 0.59/0.42 cnf(s56, plain, spl4_25, inference(rat,[],[s36,s47,s50])).
% 0.59/0.42 cnf(s58, plain, ~spl4_7, inference(rat,[],[s39,s29,s50,s56,s51])).
% 0.59/0.42 cnf(s59, plain, spl4_22, inference(rat,[],[s45,s58])).
% 0.59/0.42 cnf(s63, plain, ~spl4_21, inference(rat,[],[s46,s56,s51,s50,s58])).
% 0.59/0.42 cnf(s64, plain, $false, inference(rat,[],[s30,s59,s63])).
% 0.59/0.42 thf(f534,plain,(
% 0.59/0.42 $false),
% 0.59/0.42 inference(avatar_sat_refutation,[],[s64])).
% 0.59/0.42 % SZS output end Proof for theBenchmark
% 0.59/0.42 % (3113417)------------------------------
% 0.59/0.42 % (3113417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (3113417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (3113417)CaDiCaL version: 2.1.3
% 0.59/0.42 % (3113417)Termination reason: Refutation
% 0.59/0.42 % (3113417)Time elapsed: 0.045 s
% 0.59/0.42 % (3113417)Peak memory usage: 13 MB
% 0.59/0.42 % (3113417)Instructions burned: 43 (million)
% 0.59/0.42 % (3113408)Success in time 0.084 s
% 0.59/0.42 % Vampire exiting
%------------------------------------------------------------------------------