%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:19:00 AM UTC 2026
% Result : Theorem 0.05s 0.18s
% Output : Refutation 0.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.12 % Computer : n012.cluster.edu
% 0.05/0.12 % Model : x86_64 x86_64
% 0.05/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.12 % Memory : 8046.5625MB
% 0.05/0.12 % OS : Linux 6.8.0-71-generic
% 0.05/0.12 % CPULimit : 300
% 0.05/0.12 % WCLimit : 300
% 0.05/0.12 % DateTime : Tue Sep 29 13:03:04 UTC 2026
% 0.05/0.12 % CPUTime :
% 0.05/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.13 Running higher-order theorem proving
% 0.05/0.14 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
% 0.05/0.18 % (71620)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.05/0.18 % (71631)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.05/0.18 % (71631)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
% 0.05/0.18 % (71629)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=908663135:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.05/0.18 % (71627)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2695056543:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.05/0.18 % (71625)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2310228396:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.05/0.18 % (71626)lrs+10_16_si=on:nwc=1.5:random_seed=776968714:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.05/0.18 % (71628)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=1576487412: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)
% 0.05/0.18 % (71630)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2880661822:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.05/0.18 % (71631)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=2095903073:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.05/0.18 % (71627)Refutation not found, incomplete strategy
% 0.05/0.18 % (71627)------------------------------
% 0.05/0.18 % (71627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.18 % (71627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.18 % (71627)CaDiCaL version: 2.1.3
% 0.05/0.18 % (71627)Termination reason: Refutation not found, incomplete strategy
% 0.05/0.18 % (71627)Time elapsed: 0.001 s
% 0.05/0.18 % (71627)Peak memory usage: 12 MB
% 0.05/0.18 % (71627)Instructions burned: 2 (million)
% 0.05/0.18 % (71627)------------------------------
% 0.05/0.18 % (71627)------------------------------
% 0.05/0.18 % (71626)Instruction limit reached!
% 0.05/0.18 % (71626)------------------------------
% 0.05/0.18 % (71626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.18 % (71626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.18 % (71626)CaDiCaL version: 2.1.3
% 0.05/0.18 % (71626)Termination reason: Instruction limit
% 0.05/0.18 % (71626)Termination phase: Saturation
% 0.05/0.18 % (71626)Time elapsed: 0.006 s
% 0.05/0.18 % (71626)Peak memory usage: 12 MB
% 0.05/0.18 % (71626)Instructions burned: 22 (million)
% 0.05/0.18 % (71629)Instruction limit reached!
% 0.05/0.18 % (71629)------------------------------
% 0.05/0.18 % (71629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.18 % (71629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.18 % (71629)CaDiCaL version: 2.1.3
% 0.05/0.18 % (71629)Termination reason: Instruction limit
% 0.05/0.18 % (71629)Termination phase: Saturation
% 0.05/0.18 % (71629)Time elapsed: 0.007 s
% 0.05/0.18 % (71629)Peak memory usage: 12 MB
% 0.05/0.18 % (71629)Instructions burned: 27 (million)
% 0.05/0.18 % (71625) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-71620-71625"...
% 0.05/0.18 % (71631) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-71620-71631"...
% 0.05/0.18 % (71625)...printing done.
% 0.05/0.18 % (71625)Refutation found. Thanks to Tanya!
% 0.05/0.18 % SZS status Theorem for theBenchmark
% 0.05/0.18 % SZS output start Proof for theBenchmark
% 0.05/0.18 thf(type_def_5, type, n: $tType).
% 0.05/0.18 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.05/0.18 thf(func_def_0, type, c0: n).
% 0.05/0.18 thf(func_def_1, type, cS: (n > n)).
% 0.05/0.18 thf(func_def_2, type, c_plus: (n > n > n)).
% 0.05/0.18 thf(func_def_3, type, cPA_1: $o).
% 0.05/0.18 thf(func_def_4, type, cPA_2: $o).
% 0.05/0.18 thf(func_def_5, type, cPA_IND_EQ: $o).
% 0.05/0.18 thf(func_def_9, type, sK0: n).
% 0.05/0.18 thf(func_def_10, type, sK1: n).
% 0.05/0.18 thf(func_def_11, type, sK2: (n > n)).
% 0.05/0.18 thf(func_def_12, type, sK3: (n > n)).
% 0.05/0.18 thf(func_def_13, type, sK4: n).
% 0.05/0.18 thf(func_def_14, type, sK5: ((n > n) > (n > n) > n)).
% 0.05/0.18 thf(func_def_15, type, sK6: n).
% 0.05/0.18 thf(func_def_16, type, sK7: n).
% 0.05/0.18 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.05/0.18 thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
% 0.05/0.18 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.05/0.18 thf(f1,axiom,(
% 0.05/0.18 (cPA_1 = ! [X0 : n] : (((c_plus @ X0 @ c0)) = X0))),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_1_def)).
% 0.05/0.18 thf(f2,axiom,(
% 0.05/0.18 (! [X0 : n,X1 : n] : (((c_plus @ X0 @ (cS @ X1))) = ((cS @ (c_plus @ X0 @ X1)))) = cPA_2)),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_2_def)).
% 0.05/0.18 thf(f3,axiom,(
% 0.05/0.18 (! [X0 : (n > n),X1 : (n > n)] : ((! [X2 : n] : ((((X0 @ X2)) = ((X1 @ X2))) => (((X0 @ (cS @ X2))) = ((X1 @ (cS @ X2))))) & (((X0 @ c0)) = ((X1 @ c0)))) => ! [X2 : n] : (((X0 @ X2)) = ((X1 @ X2)))) = cPA_IND_EQ)),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_IND_EQ_def)).
% 0.05/0.18 thf(f4,conjecture,(
% 0.05/0.18 (cPA_2 & cPA_IND_EQ & cPA_1) => ! [X0 : n] : (((c_plus @ X0 @ c0)) = ((c_plus @ c0 @ X0)))),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPA_THM2)).
% 0.05/0.18 thf(f5,negated_conjecture,(
% 0.05/0.18 ~((cPA_2 & cPA_IND_EQ & cPA_1) => ! [X0 : n] : (((c_plus @ X0 @ c0)) = ((c_plus @ c0 @ X0))))),
% 0.05/0.18 inference(negated_conjecture,[status(cth)],[f4])).
% 0.05/0.18 thf(f6,plain,(
% 0.05/0.18 ! [X0 : n] : (((c_plus @ X0 @ c0)) = X0) <=> (cPA_1 = $true)),
% 0.05/0.18 inference(fool_elimination,[],[f1])).
% 0.05/0.18 thf(f7,plain,(
% 0.05/0.18 ~((cPA_2 & cPA_IND_EQ & cPA_1) => ! [X0 : n] : (((c_plus @ X0 @ c0)) = ((c_plus @ c0 @ X0))))),
% 0.05/0.18 inference(rectify,[],[f5])).
% 0.05/0.18 thf(f8,plain,(
% 0.05/0.18 ~(((cPA_2 = $true) & (cPA_IND_EQ = $true) & (cPA_1 = $true)) => ! [X0 : n] : (((c_plus @ X0 @ c0)) = ((c_plus @ c0 @ X0))))),
% 0.05/0.18 inference(fool_elimination,[],[f7])).
% 0.05/0.18 thf(f9,plain,(
% 0.05/0.18 ! [X1 : n,X0 : n] : (((c_plus @ X0 @ (cS @ X1))) = ((cS @ (c_plus @ X0 @ X1)))) <=> (cPA_2 = $true)),
% 0.05/0.18 inference(fool_elimination,[],[f2])).
% 0.05/0.18 thf(f10,plain,(
% 0.05/0.18 (! [X0 : (n > n),X1 : (n > n)] : ((! [X2 : n] : ((((X0 @ X2)) = ((X1 @ X2))) => (((X0 @ (cS @ X2))) = ((X1 @ (cS @ X2))))) & (((X0 @ c0)) = ((X1 @ c0)))) => ! [X3 : n] : (((X0 @ X3)) = ((X1 @ X3)))) = cPA_IND_EQ)),
% 0.05/0.18 inference(rectify,[],[f3])).
% 0.05/0.18 thf(f11,plain,(
% 0.05/0.18 ! [X0 : (n > n),X1 : (n > n)] : (((((X0 @ c0)) = ((X1 @ c0))) & ! [X2 : n] : ((((X0 @ X2)) = ((X1 @ X2))) => (((X0 @ (cS @ X2))) = ((X1 @ (cS @ X2)))))) => ! [X3 : n] : (((X0 @ X3)) = ((X1 @ X3)))) <=> (cPA_IND_EQ = $true)),
% 0.05/0.18 inference(fool_elimination,[],[f10])).
% 0.05/0.18 thf(f12,plain,(
% 0.05/0.18 ! [X0 : (n > n),X1 : (n > n)] : (! [X3 : n] : (((X0 @ X3)) = ((X1 @ X3))) | ((((X0 @ c0)) != ((X1 @ c0))) | ? [X2 : n] : ((((X0 @ (cS @ X2))) != ((X1 @ (cS @ X2)))) & (((X0 @ X2)) = ((X1 @ X2)))))) <=> (cPA_IND_EQ = $true)),
% 0.05/0.18 inference(ennf_transformation,[],[f11])).
% 0.05/0.18 thf(f13,plain,(
% 0.05/0.18 (cPA_IND_EQ = $true) <=> ! [X1 : (n > n),X0 : (n > n)] : (? [X2 : n] : ((((X0 @ (cS @ X2))) != ((X1 @ (cS @ X2)))) & (((X0 @ X2)) = ((X1 @ X2)))) | ! [X3 : n] : (((X0 @ X3)) = ((X1 @ X3))) | (((X0 @ c0)) != ((X1 @ c0))))),
% 0.05/0.18 inference(flattening,[],[f12])).
% 0.05/0.18 thf(f14,plain,(
% 0.05/0.18 ? [X0 : n] : (((c_plus @ X0 @ c0)) != ((c_plus @ c0 @ X0))) & ((cPA_2 = $true) & (cPA_IND_EQ = $true) & (cPA_1 = $true))),
% 0.05/0.18 inference(ennf_transformation,[],[f8])).
% 0.05/0.18 thf(f15,plain,(
% 0.05/0.18 (cPA_1 = $true) & (cPA_IND_EQ = $true) & ? [X0 : n] : (((c_plus @ X0 @ c0)) != ((c_plus @ c0 @ X0))) & (cPA_2 = $true)),
% 0.05/0.18 inference(flattening,[],[f14])).
% 0.05/0.18 thf(f16,plain,(
% 0.05/0.18 (! [X0 : n] : (((c_plus @ X0 @ c0)) = X0) | (cPA_1 != $true)) & ((cPA_1 = $true) | ? [X0 : n] : (((c_plus @ X0 @ c0)) != X0))),
% 0.05/0.18 inference(nnf_transformation,[],[f6])).
% 0.05/0.18 thf(f17,plain,(
% 0.05/0.18 (! [X0 : n] : (((c_plus @ X0 @ c0)) = X0) | (cPA_1 != $true)) & ((cPA_1 = $true) | ? [X1 : n] : (((c_plus @ X1 @ c0)) != X1))),
% 0.05/0.18 inference(rectify,[],[f16])).
% 0.05/0.18 thf(f18,plain,(
% 0.05/0.18 (! [X0 : n] : (((c_plus @ X0 @ c0)) = X0) | (cPA_1 != $true)) & ((cPA_1 = $true) | (sK0 != ((c_plus @ sK0 @ c0))))),
% 0.05/0.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f17])).
% 0.05/0.18 thf(f19,plain,(
% 0.05/0.18 (cPA_1 = $true) & (cPA_IND_EQ = $true) & (((c_plus @ c0 @ sK1)) != ((c_plus @ sK1 @ c0))) & (cPA_2 = $true)),
% 0.05/0.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f15])).
% 0.05/0.18 thf(f20,plain,(
% 0.05/0.18 ((cPA_IND_EQ = $true) | ? [X1 : (n > n),X0 : (n > n)] : (! [X2 : n] : ((((X0 @ (cS @ X2))) = ((X1 @ (cS @ X2)))) | (((X0 @ X2)) != ((X1 @ X2)))) & ? [X3 : n] : (((X0 @ X3)) != ((X1 @ X3))) & (((X0 @ c0)) = ((X1 @ c0))))) & (! [X1 : (n > n),X0 : (n > n)] : (? [X2 : n] : ((((X0 @ (cS @ X2))) != ((X1 @ (cS @ X2)))) & (((X0 @ X2)) = ((X1 @ X2)))) | ! [X3 : n] : (((X0 @ X3)) = ((X1 @ X3))) | (((X0 @ c0)) != ((X1 @ c0)))) | (cPA_IND_EQ != $true))),
% 0.05/0.18 inference(nnf_transformation,[],[f13])).
% 0.05/0.18 thf(f21,plain,(
% 0.05/0.18 ((cPA_IND_EQ = $true) | ? [X0 : (n > n),X1 : (n > n)] : (! [X2 : n] : ((((X0 @ (cS @ X2))) = ((X1 @ (cS @ X2)))) | (((X0 @ X2)) != ((X1 @ X2)))) & ? [X3 : n] : (((X0 @ X3)) != ((X1 @ X3))) & (((X0 @ c0)) = ((X1 @ c0))))) & (! [X4 : (n > n),X5 : (n > n)] : (? [X6 : n] : ((((X5 @ (cS @ X6))) != ((X4 @ (cS @ X6)))) & (((X4 @ X6)) = ((X5 @ X6)))) | ! [X7 : n] : (((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0)))) | (cPA_IND_EQ != $true))),
% 0.05/0.18 inference(rectify,[],[f20])).
% 0.05/0.18 thf(f22,plain,(
% 0.05/0.18 ((cPA_IND_EQ = $true) | (! [X2 : n] : ((((sK2 @ (cS @ X2))) = ((sK3 @ (cS @ X2)))) | (((sK3 @ X2)) != ((sK2 @ X2)))) & (((sK2 @ sK4)) != ((sK3 @ sK4))) & (((sK2 @ c0)) = ((sK3 @ c0))))) & (! [X4 : (n > n),X5 : (n > n)] : (((((X5 @ (cS @ (sK5 @ X5 @ X4)))) != ((X4 @ (cS @ (sK5 @ X5 @ X4))))) & (((X4 @ (sK5 @ X5 @ X4))) = ((X5 @ (sK5 @ X5 @ X4))))) | ! [X7 : n] : (((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0)))) | (cPA_IND_EQ != $true))),
% 0.05/0.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4),skolemize(X6,sK5 @ X5 @ X4)],[f21])).
% 0.05/0.18 thf(f23,plain,(
% 0.05/0.18 (! [X1 : n,X0 : n] : (((c_plus @ X0 @ (cS @ X1))) = ((cS @ (c_plus @ X0 @ X1)))) | (cPA_2 != $true)) & ((cPA_2 = $true) | ? [X1 : n,X0 : n] : (((c_plus @ X0 @ (cS @ X1))) != ((cS @ (c_plus @ X0 @ X1)))))),
% 0.05/0.18 inference(nnf_transformation,[],[f9])).
% 0.05/0.18 thf(f24,plain,(
% 0.05/0.18 (! [X0 : n,X1 : n] : (((c_plus @ X1 @ (cS @ X0))) = ((cS @ (c_plus @ X1 @ X0)))) | (cPA_2 != $true)) & ((cPA_2 = $true) | ? [X2 : n,X3 : n] : (((cS @ (c_plus @ X3 @ X2))) != ((c_plus @ X3 @ (cS @ X2)))))),
% 0.05/0.18 inference(rectify,[],[f23])).
% 0.05/0.18 thf(f25,plain,(
% 0.05/0.18 (! [X0 : n,X1 : n] : (((c_plus @ X1 @ (cS @ X0))) = ((cS @ (c_plus @ X1 @ X0)))) | (cPA_2 != $true)) & ((cPA_2 = $true) | (((c_plus @ sK7 @ (cS @ sK6))) != ((cS @ (c_plus @ sK7 @ sK6)))))),
% 0.05/0.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6),skolemize(X3,sK7)],[f24])).
% 0.05/0.18 thf(f27,plain,(
% 0.05/0.18 ( ! [X0 : n] : ((((c_plus @ X0 @ c0)) = X0) | (cPA_1 != $true)) )),
% 0.05/0.18 inference(cnf_transformation,[],[f18])).
% 0.05/0.18 thf(f28,plain,(
% 0.05/0.18 (cPA_2 = $true)),
% 0.05/0.18 inference(cnf_transformation,[],[f19])).
% 0.05/0.18 thf(f29,plain,(
% 0.05/0.18 (((c_plus @ c0 @ sK1)) != ((c_plus @ sK1 @ c0)))),
% 0.05/0.18 inference(cnf_transformation,[],[f19])).
% 0.05/0.18 thf(f30,plain,(
% 0.05/0.18 (cPA_IND_EQ = $true)),
% 0.05/0.18 inference(cnf_transformation,[],[f19])).
% 0.05/0.18 thf(f31,plain,(
% 0.05/0.18 (cPA_1 = $true)),
% 0.05/0.18 inference(cnf_transformation,[],[f19])).
% 0.05/0.18 thf(f32,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X4 @ (sK5 @ X5 @ X4))) = ((X5 @ (sK5 @ X5 @ X4)))) | (((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0))) | (cPA_IND_EQ != $true)) )),
% 0.05/0.18 inference(cnf_transformation,[],[f22])).
% 0.05/0.18 thf(f33,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X5 @ (cS @ (sK5 @ X5 @ X4)))) != ((X4 @ (cS @ (sK5 @ X5 @ X4))))) | (((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0))) | (cPA_IND_EQ != $true)) )),
% 0.05/0.18 inference(cnf_transformation,[],[f22])).
% 0.05/0.18 thf(f38,plain,(
% 0.05/0.18 ( ! [X0 : n,X1 : n] : ((((c_plus @ X1 @ (cS @ X0))) = ((cS @ (c_plus @ X1 @ X0)))) | (cPA_2 != $true)) )),
% 0.05/0.18 inference(cnf_transformation,[],[f25])).
% 0.05/0.18 thf(f41,plain,(
% 0.05/0.18 ( ! [X0 : n] : ((((c_plus @ X0 @ c0)) = X0) | ($true != $true)) )),
% 0.05/0.18 inference(definition_unfolding,[],[f27,f31])).
% 0.05/0.18 thf(f46,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X4 @ X7)) = ((X5 @ X7))) | (((X5 @ (cS @ (sK5 @ X5 @ X4)))) != ((X4 @ (cS @ (sK5 @ X5 @ X4))))) | (((X4 @ c0)) != ((X5 @ c0))) | ($true != $true)) )),
% 0.05/0.18 inference(definition_unfolding,[],[f33,f30])).
% 0.05/0.18 thf(f47,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X4 @ (sK5 @ X5 @ X4))) = ((X5 @ (sK5 @ X5 @ X4)))) | (((X4 @ c0)) != ((X5 @ c0))) | (((X4 @ X7)) = ((X5 @ X7))) | ($true != $true)) )),
% 0.05/0.18 inference(definition_unfolding,[],[f32,f30])).
% 0.05/0.18 thf(f48,plain,(
% 0.05/0.18 ( ! [X0 : n,X1 : n] : ((((c_plus @ X1 @ (cS @ X0))) = ((cS @ (c_plus @ X1 @ X0)))) | ($true != $true)) )),
% 0.05/0.18 inference(definition_unfolding,[],[f38,f28])).
% 0.05/0.18 thf(f50,plain,(
% 0.05/0.18 ( ! [X0 : n] : ((((c_plus @ X0 @ c0)) = X0)) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f41])).
% 0.05/0.18 thf(f51,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X4 @ (sK5 @ X5 @ X4))) = ((X5 @ (sK5 @ X5 @ X4)))) | (((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0)))) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f47])).
% 0.05/0.18 thf(f52,plain,(
% 0.05/0.18 ( ! [X7 : n,X4 : (n > n),X5 : (n > n)] : ((((X4 @ X7)) = ((X5 @ X7))) | (((X4 @ c0)) != ((X5 @ c0))) | (((X5 @ (cS @ (sK5 @ X5 @ X4)))) != ((X4 @ (cS @ (sK5 @ X5 @ X4)))))) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f46])).
% 0.05/0.18 thf(f53,plain,(
% 0.05/0.18 ( ! [X0 : n,X1 : n] : ((((c_plus @ X1 @ (cS @ X0))) = ((cS @ (c_plus @ X1 @ X0))))) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f48])).
% 0.05/0.18 thf(f54,plain,(
% 0.05/0.18 (((c_plus @ c0 @ sK1)) != sK1)),
% 0.05/0.18 inference(forward_demodulation,[],[f29,f50])).
% 0.05/0.18 thf(f78,plain,(
% 0.05/0.18 ( ! [X0 : (n > n),X1 : (n > n)] : ((((X1 @ (sK5 @ X0 @ X1))) != ((X1 @ (sK5 @ X0 @ X1)))) | (((X0 @ c0)) != ((X1 @ c0))) | (((X0 @ (sK5 @ X0 @ X1))) = ((X1 @ (sK5 @ X0 @ X1))))) )),
% 0.05/0.18 inference(equality_factoring,[],[f51])).
% 0.05/0.18 thf(f79,plain,(
% 0.05/0.18 ( ! [X0 : (n > n),X1 : (n > n)] : ((((X0 @ (sK5 @ X0 @ X1))) = ((X1 @ (sK5 @ X0 @ X1)))) | (((X0 @ c0)) != ((X1 @ c0)))) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f78])).
% 0.05/0.18 thf(f125,plain,(
% 0.05/0.18 ( ! [X0 : (n > n)] : ((((X0 @ c0)) != ((c_plus @ c0 @ c0))) | (sK1 != ((X0 @ sK1))) | (((X0 @ (cS @ (sK5 @ (c_plus @ c0) @ X0)))) != ((c_plus @ c0 @ (cS @ (sK5 @ (c_plus @ c0) @ X0)))))) )),
% 0.05/0.18 inference(constrained_superposition,[],[f54,f52])).
% 0.05/0.18 thf(f134,plain,(
% 0.05/0.18 ( ! [X0 : (n > n)] : ((sK1 != ((X0 @ sK1))) | (((X0 @ (cS @ (sK5 @ (c_plus @ c0) @ X0)))) != ((c_plus @ c0 @ (cS @ (sK5 @ (c_plus @ c0) @ X0))))) | (c0 != ((X0 @ c0)))) )),
% 0.05/0.18 inference(forward_demodulation,[],[f125,f50])).
% 0.05/0.18 thf(f142,plain,(
% 0.05/0.18 ( ! [X0 : (n > n)] : ((((X0 @ (cS @ (sK5 @ (c_plus @ c0) @ X0)))) != ((cS @ (c_plus @ c0 @ (sK5 @ (c_plus @ c0) @ X0))))) | (sK1 != ((X0 @ sK1))) | (c0 != ((X0 @ c0)))) )),
% 0.05/0.18 inference(forward_demodulation,[],[f134,f53])).
% 0.05/0.18 thf(f167,plain,(
% 0.05/0.18 (c0 != (((^[Y0 : n]: (Y0)) @ c0))) | (sK1 != (((^[Y0 : n]: (Y0)) @ sK1))) | ((((^[Y0 : n]: (Y0)) @ (cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0)))))) != ((cS @ (c_plus @ c0 @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0)))))))),
% 0.05/0.18 inference(projection,[],[f142])).
% 0.05/0.18 thf(f187,plain,(
% 0.05/0.18 (sK1 != sK1) | (((cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))) != ((cS @ (c_plus @ c0 @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))))) | (c0 != c0)),
% 0.05/0.18 inference(beta-eta_normalization,[],[f167])).
% 0.05/0.18 thf(f188,plain,(
% 0.05/0.18 (((cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))) != ((cS @ (c_plus @ c0 @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0)))))))),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f187])).
% 0.05/0.18 thf(f199,plain,(
% 0.05/0.18 (((c_plus @ c0 @ c0)) != (((^[Y0 : n]: (Y0)) @ c0))) | (((cS @ ((^[Y0 : n]: (Y0)) @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0)))))) != ((cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))))),
% 0.05/0.18 inference(constrained_superposition,[],[f188,f79])).
% 0.05/0.18 thf(f211,plain,(
% 0.05/0.18 (c0 != ((c_plus @ c0 @ c0))) | (((cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))) != ((cS @ (sK5 @ (c_plus @ c0) @ (^[Y0 : n]: (Y0))))))),
% 0.05/0.18 inference(beta-eta_normalization,[],[f199])).
% 0.05/0.18 thf(f212,plain,(
% 0.05/0.18 (c0 != ((c_plus @ c0 @ c0)))),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f211])).
% 0.05/0.18 thf(f215,plain,(
% 0.05/0.18 $false),
% 0.05/0.18 inference(forward_subsumption_resolution,[],[f212,f50])).
% 0.05/0.18 % SZS output end Proof for theBenchmark
% 0.05/0.18 % (71625)------------------------------
% 0.05/0.18 % (71625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.18 % (71625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.18 % (71625)CaDiCaL version: 2.1.3
% 0.05/0.18 % (71625)Termination reason: Refutation
% 0.05/0.18 % (71625)Time elapsed: 0.009 s
% 0.05/0.18 % (71625)Peak memory usage: 12 MB
% 0.05/0.18 % (71625)Instructions burned: 33 (million)
% 0.05/0.18 % (71620)Success in time 0.032 s
% 0.05/0.18 % Vampire exiting
%------------------------------------------------------------------------------