%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN023^1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:19:53 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN023^1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n013.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:05:36 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.33 % (2071415)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (2071424)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=981080044:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (2071423)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=1779325539: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)
% 0.22/0.33 % (2071420)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1473431144:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (2071421)lrs+10_16_si=on:nwc=1.5:random_seed=905594176:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (2071422)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1838296130:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (2071424)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071424)------------------------------
% 0.22/0.33 % (2071424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071424)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071424)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071424)Time elapsed: 0.001 s
% 0.22/0.33 % (2071424)Peak memory usage: 12 MB
% 0.22/0.33 % (2071424)Instructions burned: 1 (million)
% 0.22/0.33 % (2071424)------------------------------
% 0.22/0.33 % (2071424)------------------------------
% 0.22/0.33 % (2071420)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071420)------------------------------
% 0.22/0.33 % (2071420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071420)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071420)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071420)Time elapsed: 0.002 s
% 0.22/0.33 % (2071420)Peak memory usage: 12 MB
% 0.22/0.33 % (2071420)Instructions burned: 2 (million)
% 0.22/0.33 % (2071423)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071423)------------------------------
% 0.22/0.33 % (2071423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071423)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071423)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071423)Time elapsed: 0.002 s
% 0.22/0.33 % (2071423)Peak memory usage: 12 MB
% 0.22/0.33 % (2071423)Instructions burned: 2 (million)
% 0.22/0.33 % (2071422)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071422)------------------------------
% 0.22/0.33 % (2071422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071422)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071422)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071422)Time elapsed: 0.002 s
% 0.22/0.33 % (2071422)Peak memory usage: 12 MB
% 0.22/0.33 % (2071422)Instructions burned: 2 (million)
% 0.22/0.33 % (2071420)------------------------------
% 0.22/0.33 % (2071420)------------------------------
% 0.22/0.33 % (2071423)------------------------------
% 0.22/0.33 % (2071423)------------------------------
% 0.22/0.33 % (2071422)------------------------------
% 0.22/0.33 % (2071422)------------------------------
% 0.22/0.33 % (2071421)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071421)------------------------------
% 0.22/0.33 % (2071421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071421)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071421)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071421)Time elapsed: 0.006 s
% 0.22/0.33 % (2071421)Peak memory usage: 12 MB
% 0.22/0.33 % (2071421)Instructions burned: 9 (million)
% 0.22/0.33 % (2071421)------------------------------
% 0.22/0.33 % (2071421)------------------------------
% 0.22/0.33 % (2071426)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (2071426)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
% 0.22/0.33 % (2071425)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2937005147:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (2071434)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (2071433)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3880057166:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (2071434)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1771366566:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.33 % (2071435)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2540826929:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.33 % (2071426)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=4159646384:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (2071436)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
% 0.22/0.33 % (2071436)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (2071433)Instruction limit reached!
% 0.22/0.33 % (2071433)------------------------------
% 0.22/0.33 % (2071433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071433)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071433)Termination reason: Instruction limit
% 0.22/0.33 % (2071433)Termination phase: Saturation
% 0.22/0.33 % (2071433)Time elapsed: 0.004 s
% 0.22/0.33 % (2071433)Peak memory usage: 11 MB
% 0.22/0.33 % (2071433)Instructions burned: 5 (million)
% 0.22/0.33 % (2071436)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=565846533:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.33 % (2071426)Refutation not found, incomplete strategy
% 0.22/0.33 % (2071426)------------------------------
% 0.22/0.33 % (2071426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071426)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071426)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2071426)Time elapsed: 0.004 s
% 0.22/0.33 % (2071426)Peak memory usage: 12 MB
% 0.22/0.33 % (2071426)Instructions burned: 5 (million)
% 0.22/0.33 % (2071434)Instruction limit reached!
% 0.22/0.33 % (2071434)------------------------------
% 0.22/0.33 % (2071434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071434)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071434)Termination reason: Instruction limit
% 0.22/0.33 % (2071434)Termination phase: Saturation
% 0.22/0.33 % (2071434)Time elapsed: 0.005 s
% 0.22/0.33 % (2071434)Peak memory usage: 12 MB
% 0.22/0.33 % (2071434)Instructions burned: 8 (million)
% 0.22/0.33 % (2071426)------------------------------
% 0.22/0.33 % (2071426)------------------------------
% 0.22/0.33 % (2071435)Instruction limit reached!
% 0.22/0.33 % (2071435)------------------------------
% 0.22/0.33 % (2071435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2071435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2071435)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2071435)Termination reason: Instruction limit
% 0.22/0.33 % (2071435)Termination phase: Saturation
% 0.22/0.33 % (2071435)Time elapsed: 0.009 s
% 0.22/0.33 % (2071435)Peak memory usage: 12 MB
% 0.22/0.33 % (2071435)Instructions burned: 14 (million)
% 0.22/0.33 % (2071436) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2071415-2071436"...
% 0.22/0.33 % (2071436)...printing done.
% 0.22/0.33 % (2071432)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2250215653:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (2071436)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% 0.22/0.33 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.33 thf(func_def_1, type, s: ($i > $i)).
% 0.22/0.33 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.22/0.33 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.22/0.33 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 0.22/0.33 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.22/0.33 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.33 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.33 thf(func_def_13, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_16, type, sF0: $o).
% 0.22/0.33 thf(func_def_17, type, sF1: $o).
% 0.22/0.33 thf(func_def_18, type, sF2: $o).
% 0.22/0.33 thf(func_def_20, type, sF4: $o).
% 0.22/0.33 thf(func_def_21, type, sF5: $o).
% 0.22/0.33 thf(func_def_22, type, sF6: $o).
% 0.22/0.33 thf(func_def_25, type, sK9: ($i > $i)).
% 0.22/0.33 thf(func_def_28, type, sK12: $o).
% 0.22/0.33 thf(func_def_29, type, sK13: $o).
% 0.22/0.33 thf(f1,conjecture,(
% 0.22/0.33 (! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1)) & ! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2))) => ? [X3 : ($i > $i)] : ((((X3 @ zero)) = ((s @ zero))) & (((X3 @ (s @ zero))) = zero))),
% 0.22/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n8)).
% 0.22/0.33 thf(f2,negated_conjecture,(
% 0.22/0.33 ~((! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1)) & ! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2))) => ? [X3 : ($i > $i)] : ((((X3 @ zero)) = ((s @ zero))) & (((X3 @ (s @ zero))) = zero)))),
% 0.22/0.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.33 thf(f3,plain,(
% 0.22/0.33 ~((! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1)) & ! [X3 : $o,X4 : $i,X5 : $i] : (~X3 => (((ite @ X3 @ X4 @ X5)) = X5))) => ? [X6 : ($i > $i)] : ((((s @ zero)) = ((X6 @ zero))) & (zero = ((X6 @ (s @ zero))))))),
% 0.22/0.33 inference(rectify,[],[f2])).
% 0.22/0.33 thf(f4,plain,(
% 0.22/0.33 ($true = ((~ (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ zero)))))))))),
% 0.22/0.33 inference(fool_elimination,[],[f3])).
% 0.22/0.33 thf(f5,plain,(
% 0.22/0.33 ($true = ((~ (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))) => (?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((zero = (Y0 @ (s @ zero))) & ((s @ zero) = (Y0 @ zero)))))))))),
% 0.22/0.33 inference(cnf_transformation,[],[f4])).
% 0.22/0.33 thf(f6,definition,(
% 0.22/0.33 ($true != $false)),
% 0.22/0.33 introduced(theory,[fool_distinctness_axiom])).
% 0.22/0.33 thf(f8,definition,(
% 0.22/0.33 (sF0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0))))))))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 0.22/0.33 thf(f9,plain,(
% 0.22/0.33 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0))))))))) = sF0)),
% 0.22/0.33 inference(reorient_equations,[],[f8])).
% 0.22/0.33 thf(f10,definition,(
% 0.22/0.33 (sF1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.22/0.33 thf(f11,definition,(
% 0.22/0.33 (sF2 = ((sF0 & sF1)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.22/0.33 thf(f12,definition,(
% 0.22/0.33 (sF3 = ((s @ zero)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.22/0.34 thf(f13,plain,(
% 0.22/0.34 (((s @ zero)) = sF3)),
% 0.22/0.34 inference(reorient_equations,[],[f12])).
% 0.22/0.34 thf(f14,definition,(
% 0.22/0.34 (sF4 = ((?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((zero = (Y0 @ sF3)) & (sF3 = (Y0 @ zero)))))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.22/0.34 thf(f15,definition,(
% 0.22/0.34 (sF5 = ((sF2 => sF4)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.22/0.34 thf(f16,definition,(
% 0.22/0.34 (sF6 = ((~ sF5)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.22/0.34 thf(f17,plain,(
% 0.22/0.34 (((~ sF5)) = sF6)),
% 0.22/0.34 inference(reorient_equations,[],[f16])).
% 0.22/0.34 thf(f18,plain,(
% 0.22/0.34 ($true = sF6)),
% 0.22/0.34 inference(definition_folding,[],[f5,f17,f15,f14,f13,f13,f11,f10,f9])).
% 0.22/0.34 thf(f20,plain,(
% 0.22/0.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1)))))))))) | (sF1 = $false)),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f10])).
% 0.22/0.34 thf(f21,plain,(
% 0.22/0.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0)))))))))) | ($false = sF0)),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f9])).
% 0.22/0.34 thf(f23,plain,(
% 0.22/0.34 (sF5 = $true) | (((sF2 => sF4)) = $false)),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f15])).
% 0.22/0.34 thf(f25,plain,(
% 0.22/0.34 ($false = sF6) | (((~ sF5)) = $true)),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f17])).
% 0.22/0.34 thf(f27,plain,(
% 0.22/0.34 ($true = sF4) | ($false = ((?? @ ($i > $i) @ (^[Y0 : $i > $i]: ((zero = (Y0 @ sF3)) & (sF3 = (Y0 @ zero)))))))),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f14])).
% 0.22/0.34 thf(f30,plain,(
% 0.22/0.34 (sF2 = $false) | ($true = ((sF0 & sF1)))),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f11])).
% 0.22/0.34 thf(f33,plain,(
% 0.22/0.34 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (Y2 => ((ite @ Y2 @ Y1 @ Y0) = Y1))))))) @ X1))) | (sF1 = $false)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f20])).
% 0.22/0.34 thf(f34,plain,(
% 0.22/0.34 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0)))))))) | (sF1 = $false)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f33])).
% 0.22/0.34 thf(f35,plain,(
% 0.22/0.34 ( ! [X1 : $i] : (($false = sF0) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((~ Y2) => ((ite @ Y2 @ Y1 @ Y0) = Y0))))))) @ X1)) = $true)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f21])).
% 0.22/0.34 thf(f36,plain,(
% 0.22/0.34 ( ! [X1 : $i] : (($false = sF0) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ Y0 @ X1) = X1))))))))) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f35])).
% 0.22/0.34 thf(f39,plain,(
% 0.22/0.34 ($false = sF4) | (sF5 = $true)),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f23])).
% 0.22/0.34 thf(f40,plain,(
% 0.22/0.34 (sF5 = $true) | (sF2 = $true)),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f23])).
% 0.22/0.34 thf(f42,plain,(
% 0.22/0.34 ($true = $false) | (((~ sF5)) = $true)),
% 0.22/0.34 inference(forward_demodulation,[],[f25,f18])).
% 0.22/0.34 thf(f43,plain,(
% 0.22/0.34 (((~ sF5)) = $true)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f42])).
% 0.22/0.34 thf(f44,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : (($true = sF4) | ((((^[Y0 : $i > $i]: ((zero = (Y0 @ sF3)) & (sF3 = (Y0 @ zero)))) @ X1)) = $false)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f27])).
% 0.22/0.34 thf(f45,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : (((((zero = (X1 @ sF3)) & (sF3 = (X1 @ zero)))) = $false) | ($true = sF4)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f44])).
% 0.22/0.34 thf(f48,plain,(
% 0.22/0.34 (sF2 = $false) | (sF1 = $true)),
% 0.22/0.34 inference(and_proxy_clausification,[],[f30])).
% 0.22/0.34 thf(f49,plain,(
% 0.22/0.34 ($true = sF0) | (sF2 = $false)),
% 0.22/0.34 inference(and_proxy_clausification,[],[f30])).
% 0.22/0.34 thf(f53,plain,(
% 0.22/0.34 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (Y1 => ((ite @ Y1 @ Y0 @ X1) = Y0))))) @ X2))) | (sF1 = $false)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f34])).
% 0.22/0.34 thf(f54,plain,(
% 0.22/0.34 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2)))))) | (sF1 = $false)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f53])).
% 0.22/0.34 thf(f55,plain,(
% 0.22/0.34 ( ! [X2 : $i,X1 : $i] : (($false = sF0) | ((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((~ Y1) => ((ite @ Y1 @ Y0 @ X1) = X1))))) @ X2)) = $true)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f36])).
% 0.22/0.34 thf(f56,plain,(
% 0.22/0.34 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X2 @ X1) = X1)))))) | ($false = sF0)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f55])).
% 0.22/0.34 thf(f59,plain,(
% 0.22/0.34 (sF5 = $false)),
% 0.22/0.34 inference(not_proxy_clausification,[],[f43])).
% 0.22/0.34 thf(f60,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : ((((sF3 = (X1 @ zero))) = $false) | (((zero = (X1 @ sF3))) = $false) | ($true = sF4)) )),
% 0.22/0.34 inference(and_proxy_clausification,[],[f45])).
% 0.22/0.34 thf(f65,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((sF1 = $false) | ($true = (((^[Y0 : $o]: (Y0 => ((ite @ Y0 @ X2 @ X1) = X2))) @ X3)))) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f54])).
% 0.22/0.34 thf(f66,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = ((X3 => ((ite @ X3 @ X2 @ X1) = X2)))) | (sF1 = $false)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f65])).
% 0.22/0.34 thf(f67,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (((^[Y0 : $o]: ((~ Y0) => ((ite @ Y0 @ X2 @ X1) = X1))) @ X3))) | ($false = sF0)) )),
% 0.22/0.34 inference(pi_proxy_clausification,[],[f56])).
% 0.22/0.34 thf(f68,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($false = sF0) | ((((~ X3) => ((ite @ X3 @ X2 @ X1) = X1))) = $true)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f67])).
% 0.22/0.34 thf(f71,plain,(
% 0.22/0.34 ($true = $false) | ($false = sF4)),
% 0.22/0.34 inference(backward_demodulation,[],[f39,f59])).
% 0.22/0.34 thf(f72,plain,(
% 0.22/0.34 (sF2 = $true) | ($true = $false)),
% 0.22/0.34 inference(backward_demodulation,[],[f40,f59])).
% 0.22/0.34 thf(f73,plain,(
% 0.22/0.34 ($false = sF4)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f71])).
% 0.22/0.34 thf(f74,plain,(
% 0.22/0.34 (sF2 = $true)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f72])).
% 0.22/0.34 thf(f75,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : ((sF3 != ((X1 @ zero))) | (((zero = (X1 @ sF3))) = $false) | ($true = sF4)) )),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f60])).
% 0.22/0.34 thf(f80,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($true = (((ite @ X3 @ X2 @ X1) = X2))) | (sF1 = $false) | ($false = X3)) )),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f66])).
% 0.22/0.34 thf(f81,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((((ite @ X3 @ X2 @ X1) = X1)) = $true) | ($false = sF0) | (((~ X3)) = $false)) )),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f68])).
% 0.22/0.34 thf(f84,plain,(
% 0.22/0.34 ($true = $false) | ($true = sF0)),
% 0.22/0.34 inference(backward_demodulation,[],[f49,f74])).
% 0.22/0.34 thf(f85,plain,(
% 0.22/0.34 (sF1 = $true) | ($true = $false)),
% 0.22/0.34 inference(backward_demodulation,[],[f48,f74])).
% 0.22/0.34 thf(f86,plain,(
% 0.22/0.34 ($true = sF0)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.34 thf(f87,plain,(
% 0.22/0.34 (sF1 = $true)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.34 thf(f88,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : ((sF3 != ((X1 @ zero))) | ($true = $false) | (((zero = (X1 @ sF3))) = $false)) )),
% 0.22/0.34 inference(forward_demodulation,[],[f75,f73])).
% 0.22/0.34 thf(f89,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : ((((zero = (X1 @ sF3))) = $false) | (sF3 != ((X1 @ zero)))) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f88])).
% 0.22/0.34 thf(f91,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($false = X3) | (((ite @ X3 @ X2 @ X1)) = X2) | (sF1 = $false)) )),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f80])).
% 0.22/0.34 thf(f92,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((~ X3)) = $false) | (((ite @ X3 @ X2 @ X1)) = X1) | ($false = sF0)) )),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f81])).
% 0.22/0.34 thf(f95,plain,(
% 0.22/0.34 ( ! [X1 : ($i > $i)] : ((sF3 != ((X1 @ zero))) | (zero != ((X1 @ sF3)))) )),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f89])).
% 0.22/0.34 thf(f96,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : (($false = X3) | ($true = $false) | (((ite @ X3 @ X2 @ X1)) = X2)) )),
% 0.22/0.34 inference(forward_demodulation,[],[f91,f87])).
% 0.22/0.34 thf(f97,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X2 @ X1)) = X2) | ($false = X3)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f96])).
% 0.22/0.34 thf(f98,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X2 @ X1)) = X1) | ($true = $false) | (((~ X3)) = $false)) )),
% 0.22/0.34 inference(forward_demodulation,[],[f92,f86])).
% 0.22/0.34 thf(f99,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X2 @ X1)) = X1) | (((~ X3)) = $false)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f98])).
% 0.22/0.34 thf(f100,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((ite @ X3 @ X2 @ X1)) = X1) | ($true = X3)) )),
% 0.22/0.34 inference(not_proxy_clausification,[],[f99])).
% 0.22/0.34 thf(f101,plain,(
% 0.22/0.34 (zero != (((^[Y0 : $i]: (sF3)) @ sF3)))),
% 0.22/0.34 inference(equality_resolution,[],[f95])).
% 0.22/0.34 thf(f102,plain,(
% 0.22/0.34 (zero != sF3)),
% 0.22/0.34 inference(beta-eta_normalization,[],[f101])).
% 0.22/0.34 thf(f103,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ sF3))) | (sF3 != X0) | (((X3 @ zero)) != X5) | ($false = X4) | (((X2 @ zero)) != X0) | (((X1 @ zero)) != X4)) )),
% 0.22/0.34 inference(constrained_superposition,[],[f95,f97])).
% 0.22/0.34 thf(f104,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : (($false = X4) | (((X2 @ zero)) != X0) | (zero != ((ite @ (X1 @ sF3) @ (X2 @ sF3) @ (X3 @ sF3)))) | (sF3 != X0) | (((X3 @ zero)) != X5) | (((X1 @ zero)) != X4)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f103])).
% 0.22/0.34 thf(f106,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != ((ite @ (X1 @ sF3) @ (X2 @ sF3) @ (X3 @ sF3)))) | ($false = ((X1 @ zero))) | (sF3 != X0) | (((X2 @ zero)) != X0) | (((X3 @ zero)) != X5) | ($false = X4) | ($false = X4)) )),
% 0.22/0.34 inference(xor_proxy_clausification,[],[f104])).
% 0.22/0.34 thf(f107,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != ((ite @ (X1 @ sF3) @ (X2 @ sF3) @ (X3 @ sF3)))) | ($false = ((X1 @ zero))) | ($false = X4) | (sF3 != X0) | (((X3 @ zero)) != X5) | (((X2 @ zero)) != X0)) )),
% 0.22/0.34 inference(duplicate_literal_removal,[],[f106])).
% 0.22/0.34 thf(f138,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : $o,X0 : ($i > $i),X1 : ($i > $o),X4 : $i,X5 : $i] : ((zero != ((X0 @ sF3))) | (((X1 @ sF3)) = $true) | ($false = ((X1 @ zero))) | ($false = X3) | (sF3 != X4) | (((X0 @ zero)) != X5) | (((X2 @ zero)) != X4)) )),
% 0.22/0.34 inference(constrained_superposition,[],[f107,f100])).
% 0.22/0.34 thf(f172,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $o,X4 : ($i > $i)] : ((zero != ((X0 @ sF3))) | (((X0 @ zero)) != X3) | (((X4 @ zero)) != X2) | (zero = sF3) | ($false = X1) | (sF3 != X2)) )),
% 0.22/0.34 inference(leibniz_equality_elimination,[],[f138])).
% 0.22/0.34 thf(f186,plain,(
% 0.22/0.34 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $o,X4 : ($i > $i)] : ((zero != ((X0 @ sF3))) | ($false = X1) | (sF3 != X2) | (((X4 @ zero)) != X2) | (((X0 @ zero)) != X3)) )),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f172,f102])).
% 0.22/0.34 thf(f190,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : $i,X0 : $o,X1 : $i] : (((((^[Y0 : $i]: (zero)) @ zero)) != X3) | ($false = X0) | (sF3 != X1) | (((X2 @ zero)) != X1)) )),
% 0.22/0.34 inference(equality_resolution,[],[f186])).
% 0.22/0.34 thf(f192,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X3 : $i,X0 : $o,X1 : $i] : ((sF3 != X1) | ($false = X0) | (zero != X3) | (((X2 @ zero)) != X1)) )),
% 0.22/0.34 inference(beta-eta_normalization,[],[f190])).
% 0.22/0.34 thf(f197,plain,(
% 0.22/0.34 ( ! [X2 : ($i > $i),X0 : $o,X1 : $i] : ((sF3 != ((X2 @ zero))) | (zero != X1) | ($false = X0)) )),
% 0.22/0.34 inference(equality_resolution,[],[f192])).
% 0.22/0.34 thf(f200,plain,(
% 0.22/0.34 ( ! [X0 : $i,X1 : $o] : ((zero != X0) | ($false = X1)) )),
% 0.22/0.34 inference(equality_resolution,[],[f197])).
% 0.22/0.34 thf(f201,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($false = X0)) )),
% 0.22/0.34 inference(equality_resolution,[],[f200])).
% 0.22/0.34 thf(f208,plain,(
% 0.22/0.34 ($false != $false)),
% 0.22/0.34 inference(backward_demodulation,[],[f6,f201])).
% 0.22/0.34 thf(f219,plain,(
% 0.22/0.34 $false),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f208])).
% 0.22/0.34 % SZS output end Proof for theBenchmark
% 0.22/0.34 % (2071436)------------------------------
% 0.22/0.34 % (2071436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (2071436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (2071436)CaDiCaL version: 2.1.3
% 0.22/0.34 % (2071436)Termination reason: Refutation
% 0.22/0.34 % (2071436)Time elapsed: 0.013 s
% 0.22/0.34 % (2071436)Peak memory usage: 12 MB
% 0.22/0.34 % (2071436)Instructions burned: 23 (million)
% 0.22/0.34 % (2071415)Success in time 0.072 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------