%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM752^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:19:27 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM752^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 12:54:03 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.25 % (3472925)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (3472931)% WARNING: option uhcvi not known.
% 0.10/0.25 % (3472931)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2576402907:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.25 % (3472931)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (3472931)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.25 % (3472931) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3472925-3472931"...
% 0.10/0.25 % (3472931)...printing done.
% 0.10/0.25 % (3472931)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% 0.10/0.25 thf(type_def_5, type, frac: $tType).
% 0.10/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.25 thf(func_def_0, type, x: frac).
% 0.10/0.25 thf(func_def_1, type, y: frac).
% 0.10/0.25 thf(func_def_2, type, z: frac).
% 0.10/0.25 thf(func_def_3, type, eq: (frac > frac > $o)).
% 0.10/0.25 thf(func_def_5, type, pf: (frac > frac > frac)).
% 0.10/0.25 thf(f1,axiom,(
% 0.10/0.25 (eq @ x @ y)),
% 0.10/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e)).
% 0.10/0.25 thf(f2,axiom,(
% 0.10/0.25 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.10/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56)).
% 0.10/0.25 thf(f3,axiom,(
% 0.10/0.25 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.10/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37)).
% 0.10/0.25 thf(f4,conjecture,(
% 0.10/0.25 (eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.10/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62e)).
% 0.10/0.25 thf(f5,negated_conjecture,(
% 0.10/0.25 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.10/0.25 inference(negated_conjecture,[status(cth)],[f4])).
% 0.10/0.25 thf(f6,plain,(
% 0.10/0.25 (eq @ x @ y)),
% 0.10/0.25 inference(rectify,[],[f1])).
% 0.10/0.25 thf(f7,plain,(
% 0.10/0.25 (((eq @ x @ y)) = $true)),
% 0.10/0.25 inference(fool_elimination,[],[f6])).
% 0.10/0.25 thf(f8,plain,(
% 0.10/0.25 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.10/0.25 inference(rectify,[],[f2])).
% 0.10/0.25 thf(f9,plain,(
% 0.10/0.25 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((eq @ X2 @ X3)) = $true) => (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.10/0.25 inference(fool_elimination,[],[f8])).
% 0.10/0.25 thf(f10,plain,(
% 0.10/0.25 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.10/0.25 inference(rectify,[],[f3])).
% 0.10/0.25 thf(f11,plain,(
% 0.10/0.25 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 0.10/0.25 inference(fool_elimination,[],[f10])).
% 0.10/0.25 thf(f12,plain,(
% 0.10/0.25 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 0.10/0.25 inference(rectify,[],[f5])).
% 0.10/0.25 thf(f13,plain,(
% 0.10/0.25 ~ (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $true)),
% 0.10/0.25 inference(fool_elimination,[],[f12])).
% 0.10/0.25 thf(f14,plain,(
% 0.10/0.25 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.10/0.25 inference(flattening,[],[f13])).
% 0.10/0.25 thf(f15,plain,(
% 0.10/0.25 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 0.10/0.25 inference(ennf_transformation,[],[f9])).
% 0.10/0.25 thf(f16,plain,(
% 0.10/0.25 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 0.10/0.25 inference(flattening,[],[f15])).
% 0.10/0.25 thf(f17,plain,(
% 0.10/0.25 (((eq @ x @ y)) = $true)),
% 0.10/0.25 inference(cnf_transformation,[],[f7])).
% 0.10/0.25 thf(f18,plain,(
% 0.10/0.25 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X2 @ X3)) != $true) | (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X0 @ X1)) != $true)) )),
% 0.10/0.25 inference(cnf_transformation,[],[f16])).
% 0.10/0.25 thf(f19,plain,(
% 0.10/0.25 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 0.10/0.25 inference(cnf_transformation,[],[f11])).
% 0.10/0.25 thf(f20,plain,(
% 0.10/0.25 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) != $true)),
% 0.10/0.25 inference(cnf_transformation,[],[f14])).
% 0.10/0.25 thf(f22,definition,(
% 0.10/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.10/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.10/0.25 thf(f25,plain,(
% 0.10/0.25 ($true != $true) | (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $false)),
% 0.10/0.25 inference(constrained_superposition,[],[f20,f22])).
% 0.10/0.25 thf(f27,plain,(
% 0.10/0.25 (((eq @ (pf @ z @ x) @ (pf @ z @ y))) = $false)),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f25])).
% 0.10/0.25 thf(f36,plain,(
% 0.10/0.25 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true = ((eq @ (pf @ X0 @ x) @ (pf @ X1 @ y)))) | (((eq @ X0 @ X1)) != $true)) )),
% 0.10/0.25 inference(constrained_superposition,[],[f18,f17])).
% 0.10/0.25 thf(f40,plain,(
% 0.10/0.25 ( ! [X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | ($true = ((eq @ (pf @ X0 @ x) @ (pf @ X1 @ y))))) )),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f36])).
% 0.10/0.25 thf(f51,plain,(
% 0.10/0.25 ( ! [X0 : frac] : (($true != $true) | ($true = ((eq @ (pf @ X0 @ x) @ (pf @ X0 @ y))))) )),
% 0.10/0.25 inference(constrained_superposition,[],[f40,f19])).
% 0.10/0.25 thf(f53,plain,(
% 0.10/0.25 ( ! [X0 : frac] : (($true = ((eq @ (pf @ X0 @ x) @ (pf @ X0 @ y))))) )),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f51])).
% 0.10/0.25 thf(f77,plain,(
% 0.10/0.25 ($true = $false)),
% 0.10/0.25 inference(constrained_superposition,[],[f27,f53])).
% 0.10/0.25 thf(f78,plain,(
% 0.10/0.25 $false),
% 0.10/0.25 inference(trivial_inequality_removal,[],[f77])).
% 0.10/0.25 % SZS output end Proof for theBenchmark
% 0.10/0.25 % (3472931)------------------------------
% 0.10/0.25 % (3472931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (3472931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (3472931)CaDiCaL version: 2.1.3
% 0.10/0.25 % (3472931)Termination reason: Refutation
% 0.10/0.25 % (3472931)Time elapsed: 0.002 s
% 0.10/0.25 % (3472931)Peak memory usage: 12 MB
% 0.10/0.25 % (3472931)Instructions burned: 6 (million)
% 0.10/0.25 % (3472925)Success in time 0.026 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------