%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI180_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 : Tue Sep 29 09:34:08 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI180_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:46:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.23 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
% 0.08/0.27 % (36733)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (36741)dis+10_1_sil=32000:sp=arity:random_seed=1583103596:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (36739)% WARNING: option uhcvi not known.
% 0.08/0.27 % (36741) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-36733-36741"...
% 0.08/0.27 % (36741)...printing done.
% 0.08/0.27 % (36741)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% 0.08/0.27 tff(func_def_0, type, f: $int > $int).
% 0.08/0.27 tff(func_def_6, type, sK0: $int).
% 0.08/0.27 tff(func_def_7, type, sK1: $int).
% 0.08/0.27 tff(f1,conjecture,(
% 0.08/0.27 ! [X0 : $int,X1 : $int] : (($sum(X0,X1) = f(X0) & $difference(X1,f(X0)) = 0) => X1 = f(0))),
% 0.08/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.08/0.27 tff(f2,negated_conjecture,(
% 0.08/0.27 ~ ! [X0 : $int,X1 : $int] : (($sum(X0,X1) = f(X0) & $difference(X1,f(X0)) = 0) => X1 = f(0))),
% 0.08/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.27 tff(f3,plain,(
% 0.08/0.27 ~ ! [X0 : $int,X1 : $int] : (($sum(X0,X1) = f(X0) & 0 = $sum(X1,$uminus(f(X0)))) => X1 = f(0))),
% 0.08/0.27 inference(theory_normalization,[],[f2])).
% 0.08/0.27 tff(f5,definition,(
% 0.08/0.27 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.08/0.27 introduced(theory,[tha_associativity])).
% 0.08/0.27 tff(f8,definition,(
% 0.08/0.27 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.08/0.27 introduced(theory,[tha_inverse_op_unit])).
% 0.08/0.27 tff(f16,plain,(
% 0.08/0.27 ? [X0 : $int,X1 : $int] : (f(0) != X1 & ($sum(X0,X1) = f(X0) & 0 = $sum(X1,$uminus(f(X0)))))),
% 0.08/0.27 inference(ennf_transformation,[],[f3])).
% 0.08/0.27 tff(f17,plain,(
% 0.08/0.27 ? [X0 : $int,X1 : $int] : (f(0) != X1 & $sum(X0,X1) = f(X0) & 0 = $sum(X1,$uminus(f(X0))))),
% 0.08/0.27 inference(flattening,[],[f16])).
% 0.08/0.27 tff(f18,plain,(
% 0.08/0.27 f(0) != sK1 & $sum(sK0,sK1) = f(sK0) & 0 = $sum(sK1,$uminus(f(sK0)))),
% 0.08/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17])).
% 0.08/0.27 tff(f19,plain,(
% 0.08/0.27 0 = $sum(sK1,$uminus(f(sK0)))),
% 0.08/0.27 inference(cnf_transformation,[],[f18])).
% 0.08/0.27 tff(f20,plain,(
% 0.08/0.27 $sum(sK0,sK1) = f(sK0)),
% 0.08/0.27 inference(cnf_transformation,[],[f18])).
% 0.08/0.27 tff(f21,plain,(
% 0.08/0.27 f(0) != sK1),
% 0.08/0.27 inference(cnf_transformation,[],[f18])).
% 0.08/0.27 tff(f102,plain,(
% 0.08/0.27 ( ! [X0 : $int] : ($sum(sK0,$sum(sK1,X0)) = $sum(f(sK0),X0)) )),
% 0.08/0.27 inference(superposition,[],[f5,f20])).
% 0.08/0.27 tff(f103,plain,(
% 0.08/0.27 ( ! [X0 : $int] : ($sum(0,X0) = $sum(sK1,$sum($uminus(f(sK0)),X0))) )),
% 0.08/0.27 inference(superposition,[],[f5,f19])).
% 0.08/0.27 tff(f118,plain,(
% 0.08/0.27 ( ! [X0 : $int] : ($sum(sK1,$sum($uminus(f(sK0)),X0)) = X0) )),
% 0.08/0.27 inference(evaluation,[],[f103])).
% 0.08/0.27 tff(f129,plain,(
% 0.08/0.27 $uminus($uminus(f(sK0))) = $sum(sK1,0)),
% 0.08/0.27 inference(superposition,[],[f118,f8])).
% 0.08/0.27 tff(f135,plain,(
% 0.08/0.27 sK1 = f(sK0)),
% 0.08/0.27 inference(evaluation,[],[f129])).
% 0.08/0.27 tff(f187,plain,(
% 0.08/0.27 ( ! [X0 : $int] : ($sum(sK1,X0) = $sum(sK0,$sum(sK1,X0))) )),
% 0.08/0.27 inference(forward_demodulation,[],[f102,f135])).
% 0.08/0.27 tff(f193,plain,(
% 0.08/0.27 0 = $sum(sK0,0)),
% 0.08/0.27 inference(superposition,[],[f187,f8])).
% 0.08/0.27 tff(f199,plain,(
% 0.08/0.27 0 = sK0),
% 0.08/0.27 inference(evaluation,[],[f193])).
% 0.08/0.27 tff(f207,plain,(
% 0.08/0.27 f(0) = sK1),
% 0.08/0.27 inference(superposition,[],[f135,f199])).
% 0.08/0.27 tff(f210,plain,(
% 0.08/0.27 $false),
% 0.08/0.27 inference(forward_subsumption_resolution,[],[f207,f21])).
% 0.08/0.27 % SZS output end Proof for theBenchmark
% 0.08/0.27 % (36741)------------------------------
% 0.08/0.27 % (36741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (36741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (36741)CaDiCaL version: 2.1.3
% 0.08/0.27 % (36741)Termination reason: Refutation
% 0.08/0.27 % (36741)Time elapsed: 0.004 s
% 0.08/0.27 % (36741)Peak memory usage: 12 MB
% 0.08/0.27 % (36741)Instructions burned: 9 (million)
% 0.08/0.27 % (36733)Success in time 0.03 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------