%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 11:57:46 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 53 unt; 0 def)
% Number of atoms : 67 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 100 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
fof(f10,axiom,
! [X0,X1] :
( ~ ordered(X0,X1)
| implies(X0,X1) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',partial_order_definition1) ).
fof(f11,plain,
! [X0,X1] :
( ~ ordered(X0,X1)
| truth = implies(X0,X1) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( implies(X0,X1) != truth
| ordered(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',partial_order_definition2) ).
fof(f13,plain,
! [X0,X1] :
( truth != implies(X0,X1)
| ordered(X0,X1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f15,plain,
! [X0,X1] : big_hat(X0,X1) = not(implies(implies(not(X0),not(X1)),not(X1))),
inference(definition_unfolding,[],[f9,f8]) ).
fof(f16,plain,
implies(implies(not(x),not(y)),not(y)) != not(not(implies(implies(not(x),not(y)),not(y)))),
inference(definition_unfolding,[],[f14,f15,f8]) ).
fof(f154,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f156,plain,
implies(implies(not(y),not(x)),not(x)) != not(not(implies(implies(not(y),not(x)),not(x)))),
inference(superposition,[],[f16,f4]) ).
fof(f235,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f417,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f436,plain,
! [X2,X0,X1] :
( truth != truth
| ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) ),
inference(superposition,[],[f13,f3]) ).
fof(f439,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(trivial_inequality_removal,[],[f436]) ).
fof(f449,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f417,f1]) ).
fof(f538,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f449]) ).
fof(f545,plain,
! [X0,X1] :
( truth != truth
| ordered(X0,implies(implies(X0,X1),X1)) ),
inference(superposition,[],[f13,f449]) ).
fof(f548,plain,
! [X0,X1] : ordered(X0,implies(implies(X0,X1),X1)),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f554,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f538,f1]) ).
fof(f637,plain,
! [X0] : ordered(X0,implies(X0,X0)),
inference(superposition,[],[f548,f154]) ).
fof(f2262,plain,
! [X0] : ordered(X0,truth),
inference(forward_demodulation,[],[f637,f554]) ).
fof(f2263,plain,
! [X0] : truth = implies(X0,truth),
inference(resolution,[],[f2262,f11]) ).
fof(f2271,plain,
! [X0,X1] : truth = implies(truth,implies(implies(truth,X1),implies(X0,X1))),
inference(superposition,[],[f3,f2263]) ).
fof(f2306,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(forward_demodulation,[],[f2271,f1]) ).
fof(f2315,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f2306,f1]) ).
fof(f2409,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f439,f2315]) ).
fof(f2421,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f2409,f1]) ).
fof(f2454,plain,
! [X2,X0,X1] : ordered(truth,implies(X0,implies(X2,implies(X1,X0)))),
inference(superposition,[],[f2421,f2315]) ).
fof(f2506,plain,
! [X2,X0,X1] : truth = implies(truth,implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[],[f2454,f11]) ).
fof(f2544,plain,
! [X2,X0,X1] : truth = implies(X0,implies(X1,implies(X2,X0))),
inference(forward_demodulation,[],[f2506,f1]) ).
fof(f2584,plain,
! [X2,X0,X1] :
( truth != truth
| ordered(X0,implies(X1,implies(X2,X0))) ),
inference(superposition,[],[f13,f2544]) ).
fof(f2599,plain,
! [X2,X0,X1] : ordered(X0,implies(X1,implies(X2,X0))),
inference(trivial_inequality_removal,[],[f2584]) ).
fof(f2649,plain,
! [X2,X0,X1] : ordered(X1,implies(implies(implies(X0,X1),X2),X2)),
inference(superposition,[],[f2599,f4]) ).
fof(f2734,plain,
! [X0,X1] : ordered(not(X0),implies(truth,implies(X0,X1))),
inference(superposition,[],[f2649,f6]) ).
fof(f2735,plain,
! [X0] : ordered(not(truth),implies(truth,X0)),
inference(superposition,[],[f2649,f235]) ).
fof(f2750,plain,
! [X0] : ordered(not(truth),X0),
inference(forward_demodulation,[],[f2735,f1]) ).
fof(f2751,plain,
! [X0,X1] : ordered(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f2734,f1]) ).
fof(f2772,plain,
! [X0] : truth = implies(not(truth),X0),
inference(resolution,[],[f2750,f11]) ).
fof(f2773,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(resolution,[],[f2751,f11]) ).
fof(f2796,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f4,f2772]) ).
fof(f2847,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f2796,f1]) ).
fof(f3281,plain,
! [X0] : truth = implies(not(implies(X0,not(truth))),X0),
inference(superposition,[],[f2773,f2847]) ).
fof(f3368,plain,
! [X0] : truth = implies(truth,implies(X0,implies(not(X0),not(truth)))),
inference(superposition,[],[f6,f3281]) ).
fof(f3384,plain,
! [X0] : truth = implies(X0,implies(not(X0),not(truth))),
inference(forward_demodulation,[],[f3368,f1]) ).
fof(f3478,plain,
! [X0] : implies(implies(implies(not(X0),not(truth)),X0),X0) = implies(truth,implies(not(X0),not(truth))),
inference(superposition,[],[f4,f3384]) ).
fof(f3526,plain,
! [X0] : implies(not(X0),not(truth)) = implies(implies(implies(not(X0),not(truth)),X0),X0),
inference(forward_demodulation,[],[f3478,f1]) ).
fof(f3534,plain,
! [X0] : implies(truth,X0) = implies(not(X0),not(truth)),
inference(forward_demodulation,[],[f3526,f235]) ).
fof(f3536,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(forward_demodulation,[],[f3534,f1]) ).
fof(f3555,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(superposition,[],[f2847,f3536]) ).
fof(f3638,plain,
! [X0] : not(not(X0)) = X0,
inference(superposition,[],[f3555,f3536]) ).
fof(f3768,plain,
implies(implies(not(y),not(x)),not(x)) != implies(implies(not(y),not(x)),not(x)),
inference(superposition,[],[f156,f3638]) ).
fof(f3788,plain,
$false,
inference(trivial_inequality_removal,[],[f3768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.43 % Computer : n014.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 15:23:16 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.47 Running first-order model finding
% 0.21/0.48 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
% 0.21/0.56 % (934121)Will run a generic schedule for satisfiability detection.
% 0.21/0.56 % (934128)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=928415870:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.56 % (934127)% WARNING: option uhcvi not known.
% 0.21/0.56 % (934126)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=329473454_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.56 % (934130)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2561919608:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.56 % (934127)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2353213274:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.56 % (934129)dis+10_1_sil=32000:sp=arity:random_seed=5666588:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.56 % (934131)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=327403789:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.56 % (934132)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1187080758:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.56 % TRYING [1]
% 0.21/0.56 % TRYING [2]
% 0.21/0.56 % TRYING [3]
% 0.21/0.56 % TRYING [4]
% 0.21/0.56 % TRYING [5]
% 0.21/0.56 % (934128) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-934121-934128"...
% 0.21/0.56 % (934128)...printing done.
% 0.21/0.56 % (934128)Refutation found. Thanks to Tanya!
% 0.21/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56 % (934128)------------------------------
% 0.21/0.56 % (934128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.56 % (934128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.56 % (934128)CaDiCaL version: 2.1.3
% 0.21/0.56 % (934128)Termination reason: Refutation
% 0.21/0.56 % (934128)Time elapsed: 0.050 s
% 0.21/0.56 % (934128)Peak memory usage: 12 MB
% 0.21/0.56 % (934128)Instructions burned: 94 (million)
% 0.21/0.56 % (934121)Success in time 0.075 s
% 0.21/0.56 % Vampire exiting
%------------------------------------------------------------------------------