%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM729^1 : 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 : n020.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 08:19:24 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM729^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n020.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:46:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.26 % (999043)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (999049)% WARNING: option uhcvi not known.
% 0.09/0.26 % (999049)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1849227653:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (999049)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % (999049)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.26 % (999049) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-999043-999049"...
% 0.09/0.26 % (999049)...printing done.
% 0.09/0.26 % (999049)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, nat: $tType).
% 0.09/0.26 thf(type_def_6, type, frac: $tType).
% 0.09/0.26 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_0, type, x1: nat).
% 0.09/0.26 thf(func_def_1, type, x2: nat).
% 0.09/0.26 thf(func_def_2, type, n: nat).
% 0.09/0.26 thf(func_def_3, type, eq: (frac > frac > $o)).
% 0.09/0.26 thf(func_def_4, type, fr: (nat > nat > frac)).
% 0.09/0.26 thf(func_def_5, type, ts: (nat > nat > nat)).
% 0.09/0.26 thf(f1,axiom,(
% 0.09/0.26 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38)).
% 0.09/0.26 thf(f2,axiom,(
% 0.09/0.26 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (fr @ X0 @ X1) @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40b)).
% 0.09/0.26 thf(f3,conjecture,(
% 0.09/0.26 (eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40c)).
% 0.09/0.26 thf(f4,negated_conjecture,(
% 0.09/0.26 ~(eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 0.09/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 0.09/0.26 inference(rectify,[],[f1])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 ! [X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) = $true) => (((eq @ X1 @ X0)) = $true))),
% 0.09/0.26 inference(fool_elimination,[],[f5])).
% 0.09/0.26 thf(f7,plain,(
% 0.09/0.26 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (fr @ X0 @ X1) @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)))),
% 0.09/0.26 inference(rectify,[],[f2])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 ! [X0 : nat,X1 : nat,X2 : nat] : (((eq @ (fr @ X0 @ X1) @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)))) = $true)),
% 0.09/0.26 inference(fool_elimination,[],[f7])).
% 0.09/0.26 thf(f9,plain,(
% 0.09/0.26 ~(eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 0.09/0.26 inference(rectify,[],[f4])).
% 0.09/0.26 thf(f10,plain,(
% 0.09/0.26 ~ (((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))) = $true)),
% 0.09/0.26 inference(fool_elimination,[],[f9])).
% 0.09/0.26 thf(f11,plain,(
% 0.09/0.26 (((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))) != $true)),
% 0.09/0.26 inference(flattening,[],[f10])).
% 0.09/0.26 thf(f12,plain,(
% 0.09/0.26 ! [X0 : frac,X1 : frac] : ((((eq @ X1 @ X0)) = $true) | (((eq @ X0 @ X1)) != $true))),
% 0.09/0.26 inference(ennf_transformation,[],[f6])).
% 0.09/0.26 thf(f13,plain,(
% 0.09/0.26 ( ! [X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | (((eq @ X1 @ X0)) = $true)) )),
% 0.09/0.26 inference(cnf_transformation,[],[f12])).
% 0.09/0.26 thf(f14,plain,(
% 0.09/0.26 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((eq @ (fr @ X0 @ X1) @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)))) = $true)) )),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f15,plain,(
% 0.09/0.26 (((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))) != $true)),
% 0.09/0.26 inference(cnf_transformation,[],[f11])).
% 0.09/0.26 thf(f17,definition,(
% 0.09/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.26 thf(f20,plain,(
% 0.09/0.26 ($true != $true) | (((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))) = $false)),
% 0.09/0.26 inference(constrained_superposition,[],[f15,f17])).
% 0.09/0.26 thf(f22,plain,(
% 0.09/0.26 (((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))) = $false)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f20])).
% 0.09/0.26 thf(f33,plain,(
% 0.09/0.26 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = ((eq @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)) @ (fr @ X0 @ X1))))) )),
% 0.09/0.26 inference(constrained_superposition,[],[f13,f14])).
% 0.09/0.26 thf(f34,plain,(
% 0.09/0.26 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = ((eq @ (fr @ (ts @ X0 @ X2) @ (ts @ X1 @ X2)) @ (fr @ X0 @ X1))))) )),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f33])).
% 0.09/0.26 thf(f56,plain,(
% 0.09/0.26 ($true = $false)),
% 0.09/0.26 inference(constrained_superposition,[],[f22,f34])).
% 0.09/0.26 thf(f61,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f56])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (999049)------------------------------
% 0.09/0.26 % (999049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (999049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (999049)CaDiCaL version: 2.1.3
% 0.09/0.26 % (999049)Termination reason: Refutation
% 0.09/0.26 % (999049)Time elapsed: 0.002 s
% 0.09/0.26 % (999049)Peak memory usage: 12 MB
% 0.09/0.26 % (999049)Instructions burned: 5 (million)
% 0.09/0.26 % (999043)Success in time 0.033 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------