%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n009.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 08:19:20 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:41:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.27 % (3930316)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (3930323)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1610416199:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.27 % (3930322)% WARNING: option uhcvi not known.
% 0.21/0.27 % (3930323) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3930316-3930323"...
% 0.21/0.27 % (3930323)...printing done.
% 0.21/0.27 % (3930323)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, nat: $tType).
% 0.21/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_0, type, x: nat).
% 0.21/0.27 thf(func_def_1, type, y: nat).
% 0.21/0.27 thf(func_def_2, type, pl: (nat > nat > nat)).
% 0.21/0.27 thf(func_def_4, type, n_1: nat).
% 0.21/0.27 thf(func_def_7, type, sK0: nat).
% 0.21/0.27 thf(func_def_8, type, sK1: (nat > nat)).
% 0.21/0.27 thf(func_def_9, type, sK2: (nat > nat > nat > nat)).
% 0.21/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.21/0.27 thf(f1,axiom,(
% 0.21/0.27 ~ ! [X0 : nat] : (y != ((pl @ x @ X0)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)).
% 0.21/0.27 thf(f3,axiom,(
% 0.21/0.27 ! [X0 : nat] : (~ ~ ! [X1 : nat] : (X0 != ((pl @ n_1 @ X1))) => (X0 = n_1))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24)).
% 0.21/0.27 thf(f4,axiom,(
% 0.21/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (~ ! [X3 : nat] : (X0 != ((pl @ X1 @ X3))) => ~ ! [X3 : nat] : (((pl @ X0 @ X2)) != ((pl @ (pl @ X1 @ X2) @ X3))))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a)).
% 0.21/0.27 thf(f5,axiom,(
% 0.21/0.27 ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6)).
% 0.21/0.27 thf(f6,conjecture,(
% 0.21/0.27 ~ ~ ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25)).
% 0.21/0.27 thf(f7,negated_conjecture,(
% 0.21/0.27 ~(~ ~ ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1))))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 ! [X0 : nat] : (! [X1 : nat] : (X0 != ((pl @ n_1 @ X1))) => (X0 = n_1))),
% 0.21/0.27 inference(flattening,[],[f3])).
% 0.21/0.27 thf(f12,plain,(
% 0.21/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (~ ! [X3 : nat] : (X0 != ((pl @ X1 @ X3))) => ~ ! [X4 : nat] : (((pl @ X0 @ X2)) != ((pl @ (pl @ X1 @ X2) @ X4))))),
% 0.21/0.27 inference(rectify,[],[f4])).
% 0.21/0.27 thf(f13,plain,(
% 0.21/0.27 ~(! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0))) => (y = ((pl @ x @ n_1))))),
% 0.21/0.27 inference(flattening,[],[f7])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 ? [X0 : nat] : (y = ((pl @ x @ X0)))),
% 0.21/0.27 inference(ennf_transformation,[],[f1])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ! [X0 : nat] : ((X0 = n_1) | ? [X1 : nat] : (((pl @ n_1 @ X1)) = X0))),
% 0.21/0.27 inference(ennf_transformation,[],[f11])).
% 0.21/0.27 thf(f17,plain,(
% 0.21/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X4 : nat] : (((pl @ X0 @ X2)) = ((pl @ (pl @ X1 @ X2) @ X4))) | ! [X3 : nat] : (X0 != ((pl @ X1 @ X3))))),
% 0.21/0.27 inference(ennf_transformation,[],[f12])).
% 0.21/0.27 thf(f18,plain,(
% 0.21/0.27 (y != ((pl @ x @ n_1))) & ! [X0 : nat] : (y != ((pl @ (pl @ x @ n_1) @ X0)))),
% 0.21/0.27 inference(ennf_transformation,[],[f13])).
% 0.21/0.27 thf(f19,plain,(
% 0.21/0.27 (y = ((pl @ x @ sK0)))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14])).
% 0.21/0.27 thf(f20,plain,(
% 0.21/0.27 ! [X0 : nat] : ((X0 = n_1) | (((pl @ n_1 @ (sK1 @ X0))) = X0))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK1 @ X0)],[f16])).
% 0.21/0.27 thf(f21,plain,(
% 0.21/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : (((pl @ X0 @ X2)) = ((pl @ (pl @ X1 @ X2) @ X3))) | ! [X4 : nat] : (((pl @ X1 @ X4)) != X0))),
% 0.21/0.27 inference(rectify,[],[f17])).
% 0.21/0.27 thf(f22,plain,(
% 0.21/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((pl @ X0 @ X2)) = ((pl @ (pl @ X1 @ X2) @ (sK2 @ X2 @ X1 @ X0)))) | ! [X4 : nat] : (((pl @ X1 @ X4)) != X0))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK1 @ X0)],[f21])).
% 0.21/0.27 thf(f23,plain,(
% 0.21/0.27 (y = ((pl @ x @ sK0)))),
% 0.21/0.27 inference(cnf_transformation,[],[f19])).
% 0.21/0.27 thf(f25,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((((pl @ n_1 @ (sK1 @ X0))) = X0) | (n_1 = X0)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f20])).
% 0.21/0.27 thf(f26,plain,(
% 0.21/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat,X4 : nat] : ((((pl @ X0 @ X2)) = ((pl @ (pl @ X1 @ X2) @ (sK2 @ X2 @ X1 @ X0)))) | (((pl @ X1 @ X4)) != X0)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f22])).
% 0.21/0.27 thf(f27,plain,(
% 0.21/0.27 ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f5])).
% 0.21/0.27 thf(f28,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((y != ((pl @ (pl @ x @ n_1) @ X0)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f18])).
% 0.21/0.27 thf(f29,plain,(
% 0.21/0.27 (y != ((pl @ x @ n_1)))),
% 0.21/0.27 inference(cnf_transformation,[],[f18])).
% 0.21/0.27 thf(f33,plain,(
% 0.21/0.27 ( ! [X2 : nat,X1 : nat,X4 : nat] : ((((pl @ (pl @ X1 @ X4) @ X2)) = ((pl @ (pl @ X1 @ X2) @ (sK2 @ X2 @ X1 @ (pl @ X1 @ X4)))))) )),
% 0.21/0.27 inference(equality_resolution,[],[f26])).
% 0.21/0.27 thf(f113,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((y != ((pl @ (pl @ n_1 @ x) @ X0)))) )),
% 0.21/0.27 inference(constrained_superposition,[],[f28,f27])).
% 0.21/0.27 thf(f138,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((y != ((pl @ (pl @ n_1 @ X0) @ x)))) )),
% 0.21/0.27 inference(constrained_superposition,[],[f113,f33])).
% 0.21/0.27 thf(f139,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((y != ((pl @ x @ (pl @ n_1 @ X0))))) )),
% 0.21/0.27 inference(forward_demodulation,[],[f138,f27])).
% 0.21/0.27 thf(f148,plain,(
% 0.21/0.27 ( ! [X0 : nat] : ((y != ((pl @ x @ X0))) | (n_1 = X0)) )),
% 0.21/0.27 inference(constrained_superposition,[],[f139,f25])).
% 0.21/0.27 thf(f163,plain,(
% 0.21/0.27 (y != y) | (n_1 = sK0)),
% 0.21/0.27 inference(constrained_superposition,[],[f148,f23])).
% 0.21/0.27 thf(f164,plain,(
% 0.21/0.27 (n_1 = sK0)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f163])).
% 0.21/0.27 thf(f170,plain,(
% 0.21/0.27 (y = ((pl @ x @ n_1)))),
% 0.21/0.27 inference(constrained_superposition,[],[f23,f164])).
% 0.21/0.27 thf(f171,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f170,f29])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (3930323)------------------------------
% 0.21/0.27 % (3930323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (3930323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (3930323)CaDiCaL version: 2.1.3
% 0.21/0.27 % (3930323)Termination reason: Refutation
% 0.21/0.27 % (3930323)Time elapsed: 0.004 s
% 0.21/0.27 % (3930323)Peak memory usage: 12 MB
% 0.21/0.27 % (3930323)Instructions burned: 10 (million)
% 0.21/0.27 % (3930316)Success in time 0.033 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------