%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:18:35 AM UTC 2026
% Result : Theorem 0.18s 0.29s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n004.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:40:52 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 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
% 0.18/0.29 % (1225734)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.29 % (1225742)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=4158307750: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)
% 0.18/0.29 % (1225745)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.29 % (1225745)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.18/0.29 % (1225739)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=450181886:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.29 % (1225740)lrs+10_16_si=on:nwc=1.5:random_seed=2601434803:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.29 % (1225741)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1125983078:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.29 % (1225744)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=222620641:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.29 % (1225743)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3648426357:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.29 % (1225745)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=1902777511:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.29 % (1225739) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1225734-1225739"...
% 0.18/0.29 % (1225740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1225734-1225740"...
% 0.18/0.29 % (1225741)Instruction limit reached!
% 0.18/0.29 % (1225741)------------------------------
% 0.18/0.29 % (1225741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (1225741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (1225741)CaDiCaL version: 2.1.3
% 0.18/0.29 % (1225741)Termination reason: Instruction limit
% 0.18/0.29 % (1225741)Termination phase: Saturation
% 0.18/0.29 % (1225741)Time elapsed: 0.004 s
% 0.18/0.29 % (1225741)Peak memory usage: 12 MB
% 0.18/0.29 % (1225741)Instructions burned: 5 (million)
% 0.18/0.29 % (1225743) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1225734-1225743"...
% 0.18/0.29 % (1225740)...printing done.
% 0.18/0.29 % (1225739)...printing done.
% 0.18/0.29 % (1225739)Refutation found. Thanks to Tanya!
% 0.18/0.29 % SZS status Theorem for theBenchmark
% 0.18/0.29 % SZS output start Proof for theBenchmark
% 0.18/0.29 thf(type_def_5, type, nat: $tType).
% 0.18/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.29 thf(func_def_0, type, x: nat).
% 0.18/0.29 thf(func_def_1, type, y: nat).
% 0.18/0.29 thf(func_def_2, type, pl: (nat > nat > nat)).
% 0.18/0.29 thf(func_def_4, type, n_1: nat).
% 0.18/0.29 thf(func_def_7, type, sK0: (nat > nat > nat > nat)).
% 0.18/0.29 thf(func_def_8, type, sK1: (nat > nat)).
% 0.18/0.29 thf(func_def_9, type, sK2: nat).
% 0.18/0.29 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.18/0.29 thf(f1,axiom,(
% 0.18/0.29 ~ ! [X0 : nat] : (y != ((pl @ x @ X0)))),
% 0.18/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)).
% 0.18/0.29 thf(f3,axiom,(
% 0.18/0.29 ! [X0 : nat] : (~ ~ ! [X1 : nat] : (X0 != ((pl @ n_1 @ X1))) => (X0 = n_1))),
% 0.18/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24)).
% 0.18/0.29 thf(f4,axiom,(
% 0.18/0.29 ! [X1 : nat,X2 : nat,X0 : nat] : (~ ! [X3 : nat] : (X0 != ((pl @ X1 @ X3))) => ~ ! [X3 : nat] : (((pl @ X0 @ X2)) != ((pl @ (pl @ X1 @ X2) @ X3))))),
% 0.18/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a)).
% 0.18/0.29 thf(f5,axiom,(
% 0.18/0.29 ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))),
% 0.18/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6)).
% 0.18/0.29 thf(f6,conjecture,(
% 0.18/0.29 ~ ~ ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1)))),
% 0.18/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25)).
% 0.18/0.29 thf(f7,negated_conjecture,(
% 0.18/0.29 ~(~ ~ ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1))))),
% 0.18/0.29 inference(negated_conjecture,[status(cth)],[f6])).
% 0.18/0.29 thf(f10,plain,(
% 0.18/0.29 ~(! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1))))),
% 0.18/0.29 inference(flattening,[],[f7])).
% 0.18/0.29 thf(f11,plain,(
% 0.18/0.29 ! [X1 : nat,X0 : nat,X2 : nat] : (~ ! [X3 : nat] : (((pl @ X0 @ X3)) != X2) => ~ ! [X4 : nat] : (((pl @ X2 @ X1)) != ((pl @ (pl @ X0 @ X1) @ X4))))),
% 0.18/0.29 inference(rectify,[],[f4])).
% 0.18/0.29 thf(f13,plain,(
% 0.18/0.29 ! [X0 : nat] : (! [X1 : nat] : (X0 != ((pl @ n_1 @ X1))) => (X0 = n_1))),
% 0.18/0.29 inference(flattening,[],[f3])).
% 0.18/0.29 thf(f15,plain,(
% 0.18/0.29 ! [X0 : nat] : (? [X1 : nat] : (((pl @ n_1 @ X1)) = X0) | (X0 = n_1))),
% 0.18/0.29 inference(ennf_transformation,[],[f13])).
% 0.18/0.29 thf(f16,plain,(
% 0.18/0.29 ! [X1 : nat,X0 : nat,X2 : nat] : (! [X3 : nat] : (((pl @ X0 @ X3)) != X2) | ? [X4 : nat] : (((pl @ X2 @ X1)) = ((pl @ (pl @ X0 @ X1) @ X4))))),
% 0.18/0.29 inference(ennf_transformation,[],[f11])).
% 0.18/0.29 thf(f17,plain,(
% 0.18/0.29 (y != ((pl @ x @ n_1))) & ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0)))),
% 0.18/0.29 inference(ennf_transformation,[],[f10])).
% 0.18/0.29 thf(f18,plain,(
% 0.18/0.29 ? [X0 : nat] : (y = ((pl @ x @ X0)))),
% 0.18/0.29 inference(ennf_transformation,[],[f1])).
% 0.18/0.29 thf(f19,plain,(
% 0.18/0.29 ! [X0 : nat,X1 : nat,X2 : nat] : (! [X3 : nat] : (((pl @ X1 @ X3)) != X2) | ? [X4 : nat] : (((pl @ X2 @ X0)) = ((pl @ (pl @ X1 @ X0) @ X4))))),
% 0.18/0.29 inference(rectify,[],[f16])).
% 0.18/0.29 thf(f20,plain,(
% 0.18/0.29 ! [X0 : nat,X1 : nat,X2 : nat] : (! [X3 : nat] : (((pl @ X1 @ X3)) != X2) | (((pl @ X2 @ X0)) = ((pl @ (pl @ X1 @ X0) @ (sK0 @ X2 @ X1 @ X0)))))),
% 0.18/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X2 @ X1 @ X0)],[f19])).
% 0.18/0.29 thf(f21,plain,(
% 0.18/0.29 ! [X0 : nat] : ((((pl @ n_1 @ (sK1 @ X0))) = X0) | (X0 = n_1))),
% 0.18/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X2 @ X1 @ X0)],[f15])).
% 0.18/0.29 thf(f22,plain,(
% 0.18/0.29 (y = ((pl @ x @ sK2)))),
% 0.18/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f18])).
% 0.18/0.29 thf(f23,plain,(
% 0.18/0.29 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((((pl @ X1 @ X3)) != X2) | (((pl @ X2 @ X0)) = ((pl @ (pl @ X1 @ X0) @ (sK0 @ X2 @ X1 @ X0))))) )),
% 0.18/0.29 inference(cnf_transformation,[],[f20])).
% 0.18/0.29 thf(f25,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((y != ((pl @ (pl @ x @ n_1) @ X0)))) )),
% 0.18/0.29 inference(cnf_transformation,[],[f17])).
% 0.18/0.29 thf(f26,plain,(
% 0.18/0.29 (y != ((pl @ x @ n_1)))),
% 0.18/0.29 inference(cnf_transformation,[],[f17])).
% 0.18/0.29 thf(f27,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((((pl @ n_1 @ (sK1 @ X0))) = X0) | (n_1 = X0)) )),
% 0.18/0.29 inference(cnf_transformation,[],[f21])).
% 0.18/0.29 thf(f28,plain,(
% 0.18/0.29 ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))) )),
% 0.18/0.29 inference(cnf_transformation,[],[f5])).
% 0.18/0.29 thf(f29,plain,(
% 0.18/0.29 (y = ((pl @ x @ sK2)))),
% 0.18/0.29 inference(cnf_transformation,[],[f22])).
% 0.18/0.29 thf(f32,plain,(
% 0.18/0.29 ( ! [X3 : nat,X0 : nat,X1 : nat] : ((((pl @ (pl @ X1 @ X3) @ X0)) = ((pl @ (pl @ X1 @ X0) @ (sK0 @ (pl @ X1 @ X3) @ X1 @ X0))))) )),
% 0.18/0.29 inference(equality_resolution,[],[f23])).
% 0.18/0.29 thf(f34,plain,(
% 0.18/0.29 (y != ((pl @ n_1 @ x)))),
% 0.18/0.29 inference(forward_demodulation,[],[f26,f28])).
% 0.18/0.29 thf(f35,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((y != ((pl @ (pl @ n_1 @ x) @ X0)))) )),
% 0.18/0.29 inference(forward_demodulation,[],[f25,f28])).
% 0.18/0.29 thf(f50,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((y != ((pl @ (pl @ n_1 @ X0) @ x)))) )),
% 0.18/0.29 inference(constrained_superposition,[],[f35,f32])).
% 0.18/0.29 thf(f51,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((y != ((pl @ x @ (pl @ n_1 @ X0))))) )),
% 0.18/0.29 inference(forward_demodulation,[],[f50,f28])).
% 0.18/0.29 thf(f55,plain,(
% 0.18/0.29 ( ! [X0 : nat] : ((y != ((pl @ x @ X0))) | (n_1 = X0)) )),
% 0.18/0.29 inference(constrained_superposition,[],[f51,f27])).
% 0.18/0.29 thf(f58,plain,(
% 0.18/0.29 (y != y) | (n_1 = sK2)),
% 0.18/0.29 inference(constrained_superposition,[],[f55,f29])).
% 0.18/0.29 thf(f59,plain,(
% 0.18/0.29 (n_1 = sK2)),
% 0.18/0.29 inference(trivial_inequality_removal,[],[f58])).
% 0.18/0.29 thf(f60,plain,(
% 0.18/0.29 (y = ((pl @ x @ n_1)))),
% 0.18/0.29 inference(constrained_superposition,[],[f29,f59])).
% 0.18/0.29 thf(f61,plain,(
% 0.18/0.29 (y = ((pl @ n_1 @ x)))),
% 0.18/0.29 inference(forward_demodulation,[],[f60,f28])).
% 0.18/0.29 thf(f62,plain,(
% 0.18/0.29 $false),
% 0.18/0.29 inference(forward_subsumption_resolution,[],[f61,f34])).
% 0.18/0.29 % SZS output end Proof for theBenchmark
% 0.18/0.29 % (1225739)------------------------------
% 0.18/0.29 % (1225739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (1225739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (1225739)CaDiCaL version: 2.1.3
% 0.18/0.29 % (1225739)Termination reason: Refutation
% 0.18/0.29 % (1225739)Time elapsed: 0.005 s
% 0.18/0.29 % (1225739)Peak memory usage: 12 MB
% 0.18/0.29 % (1225739)Instructions burned: 6 (million)
% 0.18/0.29 % (1225734)Success in time 0.052 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------