%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN046^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:19:55 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN046^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:08:59 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.20/0.27 % (2472074)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2472080)lrs+10_16_si=on:nwc=1.5:random_seed=2185588906:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (2472085)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (2472085)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
% 0.20/0.27 % (2472080)Instruction limit reached!
% 0.20/0.27 % (2472080)------------------------------
% 0.20/0.27 % (2472080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2472080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2472080)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2472080)Termination reason: Instruction limit
% 0.20/0.27 % (2472080)Termination phase: Saturation
% 0.20/0.27 % (2472080)Time elapsed: 0.006 s
% 0.20/0.27 % (2472080)Peak memory usage: 12 MB
% 0.20/0.27 % (2472080)Instructions burned: 19 (million)
% 0.20/0.27 % (2472079)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3566632055:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2472081)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4194500824:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (2472084)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2575479779:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (2472082)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=1643283930: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)
% 0.20/0.27 % (2472083)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3928031699:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (2472085)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=1420492060:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (2472081)Instruction limit reached!
% 0.20/0.27 % (2472081)------------------------------
% 0.20/0.27 % (2472081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2472081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2472081)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2472081)Termination reason: Instruction limit
% 0.20/0.27 % (2472081)Termination phase: Saturation
% 0.20/0.27 % (2472081)Time elapsed: 0.002 s
% 0.20/0.27 % (2472081)Peak memory usage: 12 MB
% 0.20/0.27 % (2472081)Instructions burned: 3 (million)
% 0.20/0.27 % (2472079) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2472074-2472079"...
% 0.20/0.27 % (2472079)...printing done.
% 0.20/0.27 % (2472079)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(type_def_6, type, sK6: $tType).
% 0.20/0.27 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.20/0.27 thf(func_def_1, type, 'const/iterate/neutral': !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_2, type, 'const/iterate/monoidal': !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.20/0.27 thf(func_def_6, type, sK0: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_7, type, sK1: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_8, type, sK2: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_9, type, sK3: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_10, type, sK4: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_11, type, sK5: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.27 thf(func_def_12, type, sK7: (sK6 > sK6 > sK6)).
% 0.20/0.27 thf(func_def_13, type, sK8: sK6).
% 0.20/0.27 thf(func_def_14, type, sK9: sK6).
% 0.20/0.27 thf(func_def_15, type, sK10: sK6).
% 0.20/0.27 thf(func_def_16, type, sK11: sK6).
% 0.20/0.27 thf(func_def_17, type, sK12: sK6).
% 0.20/0.27 thf(func_def_18, type, sK13: sK6).
% 0.20/0.27 thf(func_def_19, type, sK14: sK6).
% 0.20/0.27 thf(func_def_20, type, sK15: sK6).
% 0.20/0.27 thf(func_def_21, type, sK16: sK6).
% 0.20/0.27 thf(func_def_22, type, sK17: sK6).
% 0.20/0.27 thf(f2,axiom,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X4 : X0,X3 : X0,X2 : X0] : (((X1 @ X2 @ (X1 @ X3 @ X4))) = ((X1 @ (X1 @ X2 @ X3) @ X4))) & ! [X2 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2)) = X2) = (('const/iterate/monoidal' @ X0 @ X1)))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/monoidal_')).
% 0.20/0.27 thf(f3,conjecture,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X2 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2)) = X2) & ! [X2 : X0] : (((X1 @ X2 @ ('const/iterate/neutral' @ X0 @ X1))) = X2) & ! [X3 : X0,X4 : X0,X2 : X0] : (((X1 @ X2 @ (X1 @ X3 @ X4))) = ((X1 @ X3 @ (X1 @ X2 @ X4)))) & ! [X3 : X0,X2 : X0,X4 : X0] : (((X1 @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ X2 @ (X1 @ X3 @ X4))))))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_AC_')).
% 0.20/0.27 thf(f4,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X2 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2)) = X2) & ! [X2 : X0] : (((X1 @ X2 @ ('const/iterate/neutral' @ X0 @ X1))) = X2) & ! [X3 : X0,X4 : X0,X2 : X0] : (((X1 @ X2 @ (X1 @ X3 @ X4))) = ((X1 @ X3 @ (X1 @ X2 @ X4)))) & ! [X3 : X0,X2 : X0,X4 : X0] : (((X1 @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ X2 @ (X1 @ X3 @ X4))))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~ ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X4 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4)) = X4) & ! [X5 : X0] : (((X1 @ X5 @ ('const/iterate/neutral' @ X0 @ X1))) = X5) & ! [X6 : X0,X7 : X0,X8 : X0] : (((X1 @ X6 @ (X1 @ X8 @ X7))) = ((X1 @ X8 @ (X1 @ X6 @ X7)))) & ! [X9 : X0,X10 : X0,X11 : X0] : (((X1 @ (X1 @ X10 @ X9) @ X11)) = ((X1 @ X10 @ (X1 @ X9 @ X11))))))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ~ ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X1)) = $true) => (! [X10 : X0,X9 : X0,X11 : X0] : (((X1 @ (X1 @ X10 @ X9) @ X11)) = ((X1 @ X10 @ (X1 @ X9 @ X11)))) & ! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X8 : X0,X6 : X0,X7 : X0] : (((X1 @ X6 @ (X1 @ X8 @ X7))) = ((X1 @ X8 @ (X1 @ X6 @ X7)))) & ! [X5 : X0] : (((X1 @ X5 @ ('const/iterate/neutral' @ X0 @ X1))) = X5) & ! [X4 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4)) = X4)))),
% 0.20/0.27 inference(fool_elimination,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) = ((X1 @ (X1 @ X6 @ X5) @ X4))) & ! [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) = X7) = (('const/iterate/monoidal' @ X0 @ X1)))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X1)) = $true) <=> (! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) = X7) & ! [X4 : X0,X6 : X0,X5 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) = ((X1 @ (X1 @ X6 @ X5) @ X4)))))),
% 0.20/0.27 inference(fool_elimination,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ? [X0 : $tType,X1 : (X0 > X0 > X0)] : ((? [X7 : X0,X8 : X0,X6 : X0] : (((X1 @ X6 @ (X1 @ X8 @ X7))) != ((X1 @ X8 @ (X1 @ X6 @ X7)))) | ? [X4 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4)) != X4) | ? [X3 : X0,X2 : X0] : (((X1 @ X2 @ X3)) != ((X1 @ X3 @ X2))) | ? [X11 : X0,X10 : X0,X9 : X0] : (((X1 @ (X1 @ X10 @ X9) @ X11)) != ((X1 @ X10 @ (X1 @ X9 @ X11)))) | ? [X5 : X0] : (((X1 @ X5 @ ('const/iterate/neutral' @ X0 @ X1))) != X5)) & ((('const/iterate/monoidal' @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f6])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : ((((('const/iterate/monoidal' @ X0 @ X1)) = $true) | (? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) != ((X1 @ X3 @ X2))) | ? [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) != X7) | ? [X4 : X0,X6 : X0,X5 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) != ((X1 @ (X1 @ X6 @ X5) @ X4))))) & ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) = X7) & ! [X4 : X0,X6 : X0,X5 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) = ((X1 @ (X1 @ X6 @ X5) @ X4)))) | ((('const/iterate/monoidal' @ X0 @ X1)) != $true)))),
% 0.20/0.27 inference(nnf_transformation,[],[f8])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : ((((('const/iterate/monoidal' @ X0 @ X1)) = $true) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) != ((X1 @ X3 @ X2))) | ? [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) != X7) | ? [X4 : X0,X6 : X0,X5 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) != ((X1 @ (X1 @ X6 @ X5) @ X4)))) & ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) = ((X1 @ X3 @ X2))) & ! [X7 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X7)) = X7) & ! [X4 : X0,X6 : X0,X5 : X0] : (((X1 @ X6 @ (X1 @ X5 @ X4))) = ((X1 @ (X1 @ X6 @ X5) @ X4)))) | ((('const/iterate/monoidal' @ X0 @ X1)) != $true)))),
% 0.20/0.27 inference(flattening,[],[f10])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : ((((('const/iterate/monoidal' @ X0 @ X1)) = $true) | ? [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3)) != ((X1 @ X3 @ X2))) | ? [X4 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4)) != X4) | ? [X5 : X0,X6 : X0,X7 : X0] : (((X1 @ X6 @ (X1 @ X7 @ X5))) != ((X1 @ (X1 @ X6 @ X7) @ X5)))) & ((! [X8 : X0,X9 : X0] : (((X1 @ X8 @ X9)) = ((X1 @ X9 @ X8))) & ! [X10 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10)) = X10) & ! [X11 : X0,X12 : X0,X13 : X0] : (((X1 @ X12 @ (X1 @ X13 @ X11))) = ((X1 @ (X1 @ X12 @ X13) @ X11)))) | ((('const/iterate/monoidal' @ X0 @ X1)) != $true)))),
% 0.20/0.27 inference(rectify,[],[f11])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : (X0 > X0 > X0)] : ((((('const/iterate/monoidal' @ X0 @ X1)) = $true) | (((X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != ((X1 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1)))) | (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ (sK2 @ X0 @ X1))) != ((sK2 @ X0 @ X1))) | (((X1 @ (sK4 @ X0 @ X1) @ (X1 @ (sK5 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) != ((X1 @ (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1)) @ (sK3 @ X0 @ X1))))) & ((! [X8 : X0,X9 : X0] : (((X1 @ X8 @ X9)) = ((X1 @ X9 @ X8))) & ! [X10 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10)) = X10) & ! [X11 : X0,X12 : X0,X13 : X0] : (((X1 @ X12 @ (X1 @ X13 @ X11))) = ((X1 @ (X1 @ X12 @ X13) @ X11)))) | ((('const/iterate/monoidal' @ X0 @ X1)) != $true)))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X7,sK5 @ X0 @ X1),skolemize(X7,sK5 @ X0 @ X1),skolemize(X7,sK5 @ X0 @ X1),skolemize(X7,sK5 @ X0 @ X1),skolemize(X7,sK5 @ X0 @ X1),skolemize(X7,sK5 @ X0 @ X1)],[f12])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ? [X0 : $tType,X1 : (X0 > X0 > X0)] : ((? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X4 @ (X1 @ X3 @ X2))) != ((X1 @ X3 @ (X1 @ X4 @ X2)))) | ? [X5 : X0] : (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5)) != X5) | ? [X6 : X0,X7 : X0] : (((X1 @ X6 @ X7)) != ((X1 @ X7 @ X6))) | ? [X8 : X0,X9 : X0,X10 : X0] : (((X1 @ (X1 @ X9 @ X10) @ X8)) != ((X1 @ X9 @ (X1 @ X10 @ X8)))) | ? [X11 : X0] : (((X1 @ X11 @ ('const/iterate/neutral' @ X0 @ X1))) != X11)) & ((('const/iterate/monoidal' @ X0 @ X1)) = $true))),
% 0.20/0.27 inference(rectify,[],[f9])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ((((sK7 @ sK10 @ (sK7 @ sK9 @ sK8))) != ((sK7 @ sK9 @ (sK7 @ sK10 @ sK8)))) | (sK11 != ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK11))) | (((sK7 @ sK13 @ sK12)) != ((sK7 @ sK12 @ sK13))) | (((sK7 @ sK15 @ (sK7 @ sK16 @ sK14))) != ((sK7 @ (sK7 @ sK15 @ sK16) @ sK14))) | (sK17 != ((sK7 @ sK17 @ ('const/iterate/neutral' @ sK6 @ sK7))))) & ($true = (('const/iterate/monoidal' @ sK6 @ sK7)))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X5,sK11),skolemize(X6,sK12),skolemize(X7,sK13),skolemize(X8,sK14),skolemize(X9,sK15),skolemize(X10,sK16),skolemize(X11,sK17)],[f14])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ( ! [X0 : $tType,X11 : X0,X1 : (X0 > X0 > X0),X12 : X0,X13 : X0] : (((('const/iterate/monoidal' @ X0 @ X1)) != $true) | (((X1 @ X12 @ (X1 @ X13 @ X11))) = ((X1 @ (X1 @ X12 @ X13) @ X11)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f13])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ( ! [X0 : $tType,X10 : X0,X1 : (X0 > X0 > X0)] : (((('const/iterate/monoidal' @ X0 @ X1)) != $true) | (((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10)) = X10)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f13])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 ( ! [X0 : $tType,X1 : (X0 > X0 > X0),X8 : X0,X9 : X0] : (((('const/iterate/monoidal' @ X0 @ X1)) != $true) | (((X1 @ X8 @ X9)) = ((X1 @ X9 @ X8)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f13])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ($true = (('const/iterate/monoidal' @ sK6 @ sK7)))),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f22,plain,(
% 0.20/0.27 (((sK7 @ sK13 @ sK12)) != ((sK7 @ sK12 @ sK13))) | (sK11 != ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK11))) | (((sK7 @ sK15 @ (sK7 @ sK16 @ sK14))) != ((sK7 @ (sK7 @ sK15 @ sK16) @ sK14))) | (((sK7 @ sK10 @ (sK7 @ sK9 @ sK8))) != ((sK7 @ sK9 @ (sK7 @ sK10 @ sK8)))) | (sK17 != ((sK7 @ sK17 @ ('const/iterate/neutral' @ sK6 @ sK7))))),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 thf(f26,definition,(
% 0.20/0.27 spl18_1 <=> (((sK7 @ sK15 @ (sK7 @ sK16 @ sK14))) = ((sK7 @ (sK7 @ sK15 @ sK16) @ sK14)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 (((sK7 @ sK15 @ (sK7 @ sK16 @ sK14))) != ((sK7 @ (sK7 @ sK15 @ sK16) @ sK14))) | spl18_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f26])).
% 0.20/0.27 thf(f30,definition,(
% 0.20/0.27 spl18_2 <=> (((sK7 @ sK13 @ sK12)) = ((sK7 @ sK12 @ sK13)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 (((sK7 @ sK13 @ sK12)) != ((sK7 @ sK12 @ sK13))) | spl18_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f30])).
% 0.20/0.27 thf(f34,definition,(
% 0.20/0.27 spl18_3 <=> (((sK7 @ sK10 @ (sK7 @ sK9 @ sK8))) = ((sK7 @ sK9 @ (sK7 @ sK10 @ sK8))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition])).
% 0.20/0.27 thf(f36,plain,(
% 0.20/0.27 (((sK7 @ sK10 @ (sK7 @ sK9 @ sK8))) != ((sK7 @ sK9 @ (sK7 @ sK10 @ sK8)))) | spl18_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f34])).
% 0.20/0.27 thf(f38,definition,(
% 0.20/0.27 spl18_4 <=> (sK17 = ((sK7 @ sK17 @ ('const/iterate/neutral' @ sK6 @ sK7))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 (sK17 != ((sK7 @ sK17 @ ('const/iterate/neutral' @ sK6 @ sK7)))) | spl18_4),
% 0.20/0.27 inference(avatar_component_clause,[],[f38])).
% 0.20/0.27 thf(f42,definition,(
% 0.20/0.27 spl18_5 <=> (sK11 = ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK11)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition])).
% 0.20/0.27 thf(f44,plain,(
% 0.20/0.27 (sK11 != ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK11))) | spl18_5),
% 0.20/0.27 inference(avatar_component_clause,[],[f42])).
% 0.20/0.27 thf(f45,plain,(
% 0.20/0.27 ~spl18_1 | ~spl18_2 | ~spl18_3 | ~spl18_4 | ~spl18_5),
% 0.20/0.27 inference(avatar_split_clause,[],[f22,f42,f38,f34,f30,f26])).
% 0.20/0.27 thf(f48,plain,(
% 0.20/0.27 ( ! [X0 : sK6] : ((((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X0)) = X0) | ($true != $true)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f18,f21])).
% 0.20/0.27 thf(f49,plain,(
% 0.20/0.27 ( ! [X0 : sK6] : ((((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X0)) = X0)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f48])).
% 0.20/0.27 thf(f50,plain,(
% 0.20/0.27 ( ! [X0 : sK6,X1 : sK6] : (($true != $true) | (((sK7 @ X0 @ X1)) = ((sK7 @ X1 @ X0)))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f19,f21])).
% 0.20/0.27 thf(f51,plain,(
% 0.20/0.27 ( ! [X0 : sK6,X1 : sK6] : ((((sK7 @ X0 @ X1)) = ((sK7 @ X1 @ X0)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f50])).
% 0.20/0.27 thf(f52,plain,(
% 0.20/0.27 ( ! [X0 : sK6] : ((((sK7 @ X0 @ ('const/iterate/neutral' @ sK6 @ sK7))) = X0)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f51,f49])).
% 0.20/0.27 thf(f65,plain,(
% 0.20/0.27 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : (($true != $true) | (((sK7 @ X0 @ (sK7 @ X1 @ X2))) = ((sK7 @ (sK7 @ X0 @ X1) @ X2)))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f17,f21])).
% 0.20/0.27 thf(f66,plain,(
% 0.20/0.27 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : ((((sK7 @ X0 @ (sK7 @ X1 @ X2))) = ((sK7 @ (sK7 @ X0 @ X1) @ X2)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f65])).
% 0.20/0.27 thf(f68,plain,(
% 0.20/0.27 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : ((((sK7 @ (sK7 @ X0 @ X1) @ X2)) = ((sK7 @ X1 @ (sK7 @ X0 @ X2))))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f66,f51])).
% 0.20/0.27 thf(f78,plain,(
% 0.20/0.27 (((sK7 @ sK15 @ (sK7 @ sK16 @ sK14))) != ((sK7 @ sK15 @ (sK7 @ sK16 @ sK14)))) | spl18_1),
% 0.20/0.27 inference(constrained_superposition,[],[f28,f66])).
% 0.20/0.27 thf(f79,plain,(
% 0.20/0.27 $false | spl18_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f78])).
% 0.20/0.27 thf(f80,plain,(
% 0.20/0.27 spl18_1),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f79])).
% 0.20/0.27 thf(f82,plain,(
% 0.20/0.27 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : ((((sK7 @ X0 @ (sK7 @ X1 @ X2))) = ((sK7 @ X1 @ (sK7 @ X0 @ X2))))) )),
% 0.20/0.27 inference(forward_demodulation,[],[f68,f66])).
% 0.20/0.27 thf(f85,plain,(
% 0.20/0.27 $false | spl18_2),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f32,f51])).
% 0.20/0.27 thf(f86,plain,(
% 0.20/0.27 spl18_2),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f85])).
% 0.20/0.27 thf(f87,plain,(
% 0.20/0.27 $false | spl18_3),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f36,f82])).
% 0.20/0.27 thf(f88,plain,(
% 0.20/0.27 spl18_3),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f87])).
% 0.20/0.27 thf(f89,plain,(
% 0.20/0.27 $false | spl18_4),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f40,f52])).
% 0.20/0.27 thf(f90,plain,(
% 0.20/0.27 spl18_4),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f89])).
% 0.20/0.27 thf(f91,plain,(
% 0.20/0.27 $false | spl18_5),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f44,f49])).
% 0.20/0.27 thf(f92,plain,(
% 0.20/0.27 spl18_5),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f91])).
% 0.20/0.27 cnf(s1, plain, ~spl18_1 | ~spl18_2 | ~spl18_3 | ~spl18_4 | ~spl18_5, inference(sat_conversion,[],[f45])).
% 0.20/0.27 cnf(s2, plain, spl18_1, inference(sat_conversion,[],[f80])).
% 0.20/0.27 cnf(s3, plain, spl18_2, inference(sat_conversion,[],[f86])).
% 0.20/0.27 cnf(s4, plain, spl18_3, inference(sat_conversion,[],[f88])).
% 0.20/0.27 cnf(s5, plain, spl18_4, inference(sat_conversion,[],[f90])).
% 0.20/0.27 cnf(s6, plain, spl18_5, inference(sat_conversion,[],[f92])).
% 0.20/0.27 cnf(s7, plain, $false, inference(rat,[],[s1,s6,s5,s4,s3,s2])).
% 0.20/0.27 thf(f93,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s7])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (2472079)------------------------------
% 0.20/0.27 % (2472079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2472079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2472079)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2472079)Termination reason: Refutation
% 0.20/0.27 % (2472079)Time elapsed: 0.007 s
% 0.20/0.27 % (2472079)Peak memory usage: 13 MB
% 0.20/0.27 % (2472079)Instructions burned: 11 (million)
% 0.20/0.27 % (2472074)Success in time 0.044 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------