%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT043-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:45:54 AM UTC 2026
% Result : Unsatisfiable 9.32s 2.24s
% Output : Refutation 9.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : meet(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f8,axiom,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
fof(f9,axiom,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
fof(f10,axiom,
! [X0] : join(complement(X0),X0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability1) ).
fof(f11,axiom,
! [X0] : meet(complement(X0),X0) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability2) ).
fof(f12,axiom,
! [X0] : complement(complement(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invertability3) ).
fof(f13,negated_conjecture,
complement(join(c,d)) != meet(complement(c),complement(d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatability_law) ).
fof(f14,plain,
! [X0] : n0 = meet(X0,complement(X0)),
inference(forward_demodulation,[],[f11,f5]) ).
fof(f15,plain,
! [X0] : n1 = join(X0,complement(X0)),
inference(forward_demodulation,[],[f10,f6]) ).
fof(f17,plain,
! [X0,X1] : meet(X1,join(X0,X1)) = X1,
inference(superposition,[],[f3,f6]) ).
fof(f21,plain,
! [X0] : meet(X0,n1) = X0,
inference(superposition,[],[f3,f15]) ).
fof(f28,plain,
! [X0,X1] : meet(X0,join(complement(X0),X1)) = join(n0,meet(X0,X1)),
inference(superposition,[],[f9,f14]) ).
fof(f53,plain,
! [X0,X1] : join(n0,meet(complement(X0),X1)) = meet(complement(X0),join(X0,X1)),
inference(superposition,[],[f28,f12]) ).
fof(f58,plain,
! [X0] : join(n0,meet(X0,X0)) = X0,
inference(superposition,[],[f17,f28]) ).
fof(f62,plain,
! [X0] : join(n0,X0) = X0,
inference(forward_demodulation,[],[f58,f1]) ).
fof(f74,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = meet(X0,join(n1,X1)),
inference(superposition,[],[f9,f21]) ).
fof(f77,plain,
! [X0,X1] : meet(X0,join(n1,X1)) = X0,
inference(forward_demodulation,[],[f74,f4]) ).
fof(f81,plain,
! [X0,X1] : join(X1,meet(X0,X1)) = X1,
inference(superposition,[],[f4,f5]) ).
fof(f105,plain,
! [X0,X1] : join(n1,X1) = join(X0,join(complement(X0),X1)),
inference(superposition,[],[f8,f15]) ).
fof(f116,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f6,f8]) ).
fof(f119,plain,
! [X0,X1] : n1 = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f15,f8]) ).
fof(f137,plain,
! [X0,X1] : meet(X0,n1) = join(n0,meet(X0,join(X1,complement(join(complement(X0),X1))))),
inference(superposition,[],[f28,f119]) ).
fof(f138,plain,
! [X0,X1] : meet(X0,n1) = meet(X0,join(X1,complement(join(complement(X0),X1)))),
inference(forward_demodulation,[],[f137,f62]) ).
fof(f148,plain,
! [X0,X1] : meet(X0,join(X1,complement(join(complement(X0),X1)))) = X0,
inference(forward_demodulation,[],[f138,f21]) ).
fof(f159,plain,
! [X0,X1] : join(n0,meet(complement(X1),X0)) = meet(complement(X1),join(X0,X1)),
inference(superposition,[],[f53,f6]) ).
fof(f189,plain,
! [X0,X1] : meet(complement(X1),X0) = meet(complement(X1),join(X0,X1)),
inference(forward_demodulation,[],[f159,f62]) ).
fof(f223,plain,
! [X0,X1] : meet(complement(X0),X1) = meet(complement(X0),join(X0,X1)),
inference(superposition,[],[f189,f6]) ).
fof(f341,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,join(complement(X0),X1)),
inference(superposition,[],[f223,f12]) ).
fof(f435,plain,
! [X0,X1] : meet(complement(join(complement(X1),X0)),X1) = meet(complement(join(complement(X1),X0)),join(n1,X0)),
inference(superposition,[],[f189,f105]) ).
fof(f447,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(complement(join(complement(X1),X0)),X1),
inference(forward_demodulation,[],[f435,f77]) ).
fof(f462,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(X1,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f447,f5]) ).
fof(f470,plain,
! [X0,X1] : complement(join(X0,complement(X1))) = meet(X1,complement(join(X0,complement(X1)))),
inference(superposition,[],[f462,f6]) ).
fof(f477,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(superposition,[],[f4,f462]) ).
fof(f485,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f477,f12]) ).
fof(f2218,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(join(X1,complement(join(complement(X0),X1))),X0),
inference(superposition,[],[f81,f148]) ).
fof(f2245,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(X0,join(X1,complement(join(complement(X0),X1)))),
inference(forward_demodulation,[],[f2218,f6]) ).
fof(f2324,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(complement(X0),join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f2245,f12]) ).
fof(f4170,plain,
! [X0,X1] : join(X0,complement(join(X1,X0))) = join(X0,join(complement(join(X1,X0)),complement(X1))),
inference(superposition,[],[f2324,f116]) ).
fof(f4186,plain,
! [X0,X1] : join(X0,complement(join(X1,X0))) = join(X0,join(complement(X1),complement(join(X1,X0)))),
inference(forward_demodulation,[],[f4170,f6]) ).
fof(f4261,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f4186,f485]) ).
fof(f4363,plain,
! [X0,X1] : meet(X0,complement(join(X1,complement(X0)))) = meet(X0,join(complement(X0),complement(X1))),
inference(superposition,[],[f341,f4261]) ).
fof(f4370,plain,
! [X0,X1] : join(n0,meet(X0,complement(X1))) = meet(X0,complement(join(X1,complement(X0)))),
inference(forward_demodulation,[],[f4363,f28]) ).
fof(f4417,plain,
! [X0,X1] : join(n0,meet(X0,complement(X1))) = complement(join(X1,complement(X0))),
inference(forward_demodulation,[],[f4370,f470]) ).
fof(f4450,plain,
! [X0,X1] : meet(X0,complement(X1)) = complement(join(X1,complement(X0))),
inference(forward_demodulation,[],[f4417,f62]) ).
fof(f4485,plain,
! [X0,X1] : complement(join(X1,X0)) = meet(complement(X0),complement(X1)),
inference(superposition,[],[f4450,f12]) ).
fof(f4675,plain,
complement(join(c,d)) != complement(join(d,c)),
inference(superposition,[],[f13,f4485]) ).
fof(f4739,plain,
complement(join(c,d)) != complement(join(c,d)),
inference(forward_demodulation,[],[f4675,f6]) ).
fof(f4740,plain,
$false,
inference(trivial_inequality_removal,[],[f4739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT043-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 14:00:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.78/2.06 % (3546656)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.78/2.06 % (3546709)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2093092847:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.78/2.06 % (3546706)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2235152197:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.78/2.06 % (3546707)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2747296457:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.78/2.06 % (3546708)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3573309342:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.78/2.06 % (3546705)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3404695154:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.78/2.06 % (3546704)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2680309490:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.78/2.06 % (3546703)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=4065489046:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.78/2.06 % (3546706)Instruction limit reached!
% 7.78/2.06 % (3546706)------------------------------
% 7.78/2.06 % (3546706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.06 % (3546706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.06 % (3546706)CaDiCaL version: 2.1.3
% 7.78/2.06 % (3546706)Termination reason: Instruction limit
% 7.78/2.06 % (3546706)Termination phase: Saturation
% 7.78/2.06 % (3546706)Time elapsed: 0.081 s
% 7.78/2.06 % (3546706)Peak memory usage: 88 MB
% 7.78/2.06 % (3546706)Instructions burned: 137 (million)
% 7.78/2.06 % (3546707)Instruction limit reached!
% 7.78/2.06 % (3546707)------------------------------
% 7.78/2.06 % (3546707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.06 % (3546707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.06 % (3546707)CaDiCaL version: 2.1.3
% 7.78/2.06 % (3546707)Termination reason: Instruction limit
% 7.78/2.06 % (3546707)Termination phase: Saturation
% 7.78/2.06 % (3546707)Time elapsed: 0.103 s
% 7.78/2.06 % (3546707)Peak memory usage: 89 MB
% 7.78/2.06 % (3546707)Instructions burned: 182 (million)
% 7.78/2.06 % (3546708)Instruction limit reached!
% 7.78/2.06 % (3546708)------------------------------
% 7.78/2.06 % (3546708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.06 % (3546708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.06 % (3546708)CaDiCaL version: 2.1.3
% 7.78/2.06 % (3546708)Termination reason: Instruction limit
% 7.78/2.06 % (3546708)Termination phase: Saturation
% 7.78/2.06 % (3546708)Time elapsed: 0.167 s
% 7.78/2.06 % (3546708)Peak memory usage: 90 MB
% 7.78/2.06 % (3546708)Instructions burned: 258 (million)
% 7.78/2.06 % (3546717)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3509860216:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.78/2.06 % (3546718)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1652151050:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 7.78/2.06 % (3546709)Instruction limit reached!
% 7.78/2.06 % (3546709)------------------------------
% 7.78/2.06 % (3546709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.78/2.06 % (3546709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.78/2.06 % (3546709)CaDiCaL version: 2.1.3
% 7.78/2.06 % (3546709)Termination reason: Instruction limit
% 7.78/2.06 % (3546709)Termination phase: Saturation
% 7.78/2.06 % (3546709)Time elapsed: 0.341 s
% 7.78/2.06 % (3546709)Peak memory usage: 98 MB
% 7.78/2.06 % (3546709)Instructions burned: 1187 (million)
% 7.78/2.06 % (3546719)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=678368207:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 9.32/2.24 % (3546722)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3250694531:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 9.32/2.24 % (3546719)Instruction limit reached!
% 9.32/2.24 % (3546719)------------------------------
% 9.32/2.24 % (3546719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.24 % (3546719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.24 % (3546719)CaDiCaL version: 2.1.3
% 9.32/2.24 % (3546719)Termination reason: Instruction limit
% 9.32/2.24 % (3546719)Termination phase: Saturation
% 9.32/2.24 % (3546719)Time elapsed: 0.111 s
% 9.32/2.24 % (3546719)Peak memory usage: 90 MB
% 9.32/2.24 % (3546719)Instructions burned: 215 (million)
% 9.32/2.24 % (3546722)Instruction limit reached!
% 9.32/2.24 % (3546722)------------------------------
% 9.32/2.24 % (3546722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.24 % (3546722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.24 % (3546722)CaDiCaL version: 2.1.3
% 9.32/2.24 % (3546722)Termination reason: Instruction limit
% 9.32/2.24 % (3546722)Termination phase: Saturation
% 9.32/2.24 % (3546722)Time elapsed: 0.107 s
% 9.32/2.24 % (3546722)Peak memory usage: 93 MB
% 9.32/2.24 % (3546722)Instructions burned: 320 (million)
% 9.32/2.24 % (3546725)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2049547627:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 9.32/2.24 % (3546726)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2679400026:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 9.32/2.24 % (3546704)First to succeed.
% 9.32/2.24 % (3546704)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3546656"
% 9.32/2.24 % (3546726)Also succeeded, but the first one will report.
% 9.32/2.24 % (3546717)Also succeeded, but the first one will report.
% 9.32/2.24 % (3546705)Also succeeded, but the first one will report.
% 9.32/2.24 % (3546704)Refutation found. Thanks to Tanya!
% 9.32/2.24 % SZS status Unsatisfiable for theBenchmark
% 9.32/2.24 % SZS output start Proof for theBenchmark
% See solution above
% 9.32/2.25 % (3546704)------------------------------
% 9.32/2.25 % (3546704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.32/2.25 % (3546704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.32/2.25 % (3546704)CaDiCaL version: 2.1.3
% 9.32/2.25 % (3546704)Termination reason: Refutation
% 9.32/2.25 % (3546704)Time elapsed: 0.827 s
% 9.32/2.25 % (3546704)Peak memory usage: 131 MB
% 9.32/2.25 % (3546704)Instructions burned: 1267 (million)
% 9.32/2.25 % (3546704)------------------------------
% 9.32/2.25 % (3546704)------------------------------
% 9.32/2.25 % (3546656)Success in time 1.244 s
% 9.32/2.25 % Vampire exiting
%------------------------------------------------------------------------------