%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL145-1 : 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 : n007.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 0.64s 0.58s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% 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_V(x,y)) != big_hat(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,
not(implies(implies(x,y),y)) != not(implies(implies(not(not(x)),not(not(y))),not(not(y)))),
inference(definition_unfolding,[],[f14,f8,f15]) ).
fof(f109,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f192,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f374,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f393,plain,
! [X2,X0,X1] :
( truth != truth
| ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) ),
inference(superposition,[],[f13,f3]) ).
fof(f396,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(trivial_inequality_removal,[],[f393]) ).
fof(f406,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f374,f1]) ).
fof(f495,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f406]) ).
fof(f502,plain,
! [X0,X1] :
( truth != truth
| ordered(X0,implies(implies(X0,X1),X1)) ),
inference(superposition,[],[f13,f406]) ).
fof(f505,plain,
! [X0,X1] : ordered(X0,implies(implies(X0,X1),X1)),
inference(trivial_inequality_removal,[],[f502]) ).
fof(f511,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f495,f1]) ).
fof(f594,plain,
! [X0] : ordered(X0,implies(X0,X0)),
inference(superposition,[],[f505,f109]) ).
fof(f2233,plain,
! [X0] : ordered(X0,truth),
inference(forward_demodulation,[],[f594,f511]) ).
fof(f2234,plain,
! [X0] : truth = implies(X0,truth),
inference(resolution,[],[f2233,f11]) ).
fof(f2242,plain,
! [X0,X1] : truth = implies(truth,implies(implies(truth,X1),implies(X0,X1))),
inference(superposition,[],[f3,f2234]) ).
fof(f2277,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(forward_demodulation,[],[f2242,f1]) ).
fof(f2286,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f2277,f1]) ).
fof(f2380,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f396,f2286]) ).
fof(f2392,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f2380,f1]) ).
fof(f2425,plain,
! [X2,X0,X1] : ordered(truth,implies(X0,implies(X2,implies(X1,X0)))),
inference(superposition,[],[f2392,f2286]) ).
fof(f2477,plain,
! [X2,X0,X1] : truth = implies(truth,implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[],[f2425,f11]) ).
fof(f2515,plain,
! [X2,X0,X1] : truth = implies(X0,implies(X1,implies(X2,X0))),
inference(forward_demodulation,[],[f2477,f1]) ).
fof(f2555,plain,
! [X2,X0,X1] :
( truth != truth
| ordered(X0,implies(X1,implies(X2,X0))) ),
inference(superposition,[],[f13,f2515]) ).
fof(f2570,plain,
! [X2,X0,X1] : ordered(X0,implies(X1,implies(X2,X0))),
inference(trivial_inequality_removal,[],[f2555]) ).
fof(f2620,plain,
! [X2,X0,X1] : ordered(X1,implies(implies(implies(X0,X1),X2),X2)),
inference(superposition,[],[f2570,f4]) ).
fof(f2705,plain,
! [X0,X1] : ordered(not(X0),implies(truth,implies(X0,X1))),
inference(superposition,[],[f2620,f6]) ).
fof(f2706,plain,
! [X0] : ordered(not(truth),implies(truth,X0)),
inference(superposition,[],[f2620,f192]) ).
fof(f2721,plain,
! [X0] : ordered(not(truth),X0),
inference(forward_demodulation,[],[f2706,f1]) ).
fof(f2722,plain,
! [X0,X1] : ordered(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f2705,f1]) ).
fof(f2743,plain,
! [X0] : truth = implies(not(truth),X0),
inference(resolution,[],[f2721,f11]) ).
fof(f2744,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(resolution,[],[f2722,f11]) ).
fof(f2767,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f4,f2743]) ).
fof(f2818,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f2767,f1]) ).
fof(f3252,plain,
! [X0] : truth = implies(not(implies(X0,not(truth))),X0),
inference(superposition,[],[f2744,f2818]) ).
fof(f3339,plain,
! [X0] : truth = implies(truth,implies(X0,implies(not(X0),not(truth)))),
inference(superposition,[],[f6,f3252]) ).
fof(f3355,plain,
! [X0] : truth = implies(X0,implies(not(X0),not(truth))),
inference(forward_demodulation,[],[f3339,f1]) ).
fof(f3449,plain,
! [X0] : implies(implies(implies(not(X0),not(truth)),X0),X0) = implies(truth,implies(not(X0),not(truth))),
inference(superposition,[],[f4,f3355]) ).
fof(f3497,plain,
! [X0] : implies(not(X0),not(truth)) = implies(implies(implies(not(X0),not(truth)),X0),X0),
inference(forward_demodulation,[],[f3449,f1]) ).
fof(f3505,plain,
! [X0] : implies(truth,X0) = implies(not(X0),not(truth)),
inference(forward_demodulation,[],[f3497,f192]) ).
fof(f3507,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(forward_demodulation,[],[f3505,f1]) ).
fof(f3526,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(superposition,[],[f2818,f3507]) ).
fof(f3609,plain,
! [X0] : not(not(X0)) = X0,
inference(superposition,[],[f3526,f3507]) ).
fof(f3741,plain,
not(implies(implies(x,y),y)) != not(implies(implies(not(not(x)),y),y)),
inference(superposition,[],[f16,f3609]) ).
fof(f3765,plain,
not(implies(implies(x,y),y)) != not(implies(implies(x,y),y)),
inference(forward_demodulation,[],[f3741,f3609]) ).
fof(f3766,plain,
$false,
inference(trivial_inequality_removal,[],[f3765]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.44 % Computer : n007.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 15:21:25 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.50 Running first-order model finding
% 0.21/0.50 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
% 0.64/0.58 % (1578581)Will run a generic schedule for satisfiability detection.
% 0.64/0.58 % (1578588)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3879551956:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.58 % (1578591)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1139990375:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.58 % (1578587)% WARNING: option uhcvi not known.
% 0.64/0.58 % (1578586)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4159918612_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.58 % (1578587)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=357040140:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.58 % (1578589)dis+10_1_sil=32000:sp=arity:random_seed=967159215:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.58 % (1578590)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=416321136:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.58 % TRYING [1]
% 0.64/0.58 % TRYING [2]
% 0.64/0.58 % (1578592)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=167083799:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.58 % TRYING [3]
% 0.64/0.58 % TRYING [4]
% 0.64/0.58 % TRYING [5]
% 0.64/0.58 % (1578588) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1578581-1578588"...
% 0.64/0.58 % (1578588)...printing done.
% 0.64/0.58 % (1578588)Refutation found. Thanks to Tanya!
% 0.64/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.59 % (1578588)------------------------------
% 0.64/0.59 % (1578588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.59 % (1578588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.59 % (1578588)CaDiCaL version: 2.1.3
% 0.64/0.59 % (1578588)Termination reason: Refutation
% 0.64/0.59 % (1578588)Time elapsed: 0.050 s
% 0.64/0.59 % (1578588)Peak memory usage: 12 MB
% 0.64/0.59 % (1578588)Instructions burned: 94 (million)
% 0.64/0.59 % (1578581)Success in time 0.074 s
% 0.64/0.59 % Vampire exiting
%------------------------------------------------------------------------------