%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL031-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:33:58 PM UTC 2026
% Result : Unsatisfiable 8.37s 2.06s
% Output : Refutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f23,negated_conjecture,
join(composition(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
one = join(composition(converse(sk1),sk1),one),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
join(composition(converse(sk2),sk2),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
one = join(composition(converse(sk2),sk2),one),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one) != one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_19) ).
fof(f28,plain,
one != join(composition(converse(composition(sk1,sk2)),composition(sk1,sk2)),one),
inference(reorient_equations,[],[f27]) ).
fof(f34,plain,
one != join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f35,plain,
one = join(one,composition(converse(sk2),sk2)),
inference(forward_demodulation,[],[f26,f1]) ).
fof(f36,plain,
one = join(one,composition(converse(sk1),sk1)),
inference(forward_demodulation,[],[f24,f1]) ).
fof(f67,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f70,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f79,plain,
! [X2,X0,X1] : converse(composition(composition(converse(X1),X0),X2)) = composition(converse(X2),composition(converse(X0),X1)),
inference(superposition,[],[f12,f67]) ).
fof(f83,plain,
! [X2,X0,X1] : composition(converse(X2),composition(converse(X0),X1)) = converse(composition(converse(X1),composition(X0,X2))),
inference(forward_demodulation,[],[f79,f7]) ).
fof(f87,plain,
! [X2,X0,X1] : composition(converse(X2),composition(converse(X0),X1)) = composition(converse(composition(X0,X2)),X1),
inference(forward_demodulation,[],[f83,f67]) ).
fof(f116,plain,
! [X0] : join(one,X0) = join(one,join(composition(converse(sk2),sk2),X0)),
inference(superposition,[],[f2,f35]) ).
fof(f128,plain,
! [X0] : join(one,composition(X0,sk2)) = join(one,composition(join(converse(sk2),X0),sk2)),
inference(superposition,[],[f116,f9]) ).
fof(f328,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f70,f12]) ).
fof(f340,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f328,f11]) ).
fof(f353,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f340,f11]) ).
fof(f362,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f353,f12]) ).
fof(f417,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f362]) ).
fof(f435,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f417,f10]) ).
fof(f465,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(one,X1)),
inference(superposition,[],[f435,f8]) ).
fof(f516,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,composition(converse(sk1),sk1))),
inference(superposition,[],[f465,f36]) ).
fof(f555,plain,
! [X0] : join(X0,composition(X0,composition(converse(sk1),sk1))) = X0,
inference(forward_demodulation,[],[f516,f8]) ).
fof(f595,plain,
join(one,composition(converse(sk2),sk2)) = join(one,composition(composition(converse(sk2),composition(converse(sk1),sk1)),sk2)),
inference(superposition,[],[f128,f555]) ).
fof(f608,plain,
join(one,composition(converse(sk2),sk2)) = join(one,composition(converse(sk2),composition(composition(converse(sk1),sk1),sk2))),
inference(forward_demodulation,[],[f595,f7]) ).
fof(f622,plain,
join(one,composition(converse(sk2),sk2)) = join(one,composition(converse(sk2),composition(converse(sk1),composition(sk1,sk2)))),
inference(forward_demodulation,[],[f608,f7]) ).
fof(f630,plain,
join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))) = join(one,composition(converse(sk2),sk2)),
inference(forward_demodulation,[],[f622,f87]) ).
fof(f635,plain,
one = join(one,composition(converse(composition(sk1,sk2)),composition(sk1,sk2))),
inference(forward_demodulation,[],[f630,f35]) ).
fof(f639,plain,
$false,
inference(forward_subsumption_resolution,[],[f635,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:55:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 5.92/1.97 % (1700088)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.92/1.97 % (1700136)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3547691658:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.92/1.97 % (1700132)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=3376470845:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.92/1.97 % (1700135)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3973240180:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.92/1.97 % (1700134)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3372871708:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.92/1.97 % (1700133)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=1979024593:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.92/1.97 % (1700138)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1645253066:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.92/1.97 % (1700137)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2514494227:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.92/1.97 % (1700136)Instruction limit reached!
% 5.92/1.97 % (1700136)------------------------------
% 5.92/1.97 % (1700136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.97 % (1700136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.97 % (1700136)CaDiCaL version: 2.1.3
% 5.92/1.97 % (1700136)Termination reason: Instruction limit
% 5.92/1.97 % (1700136)Termination phase: Saturation
% 5.92/1.97 % (1700136)Time elapsed: 0.059 s
% 5.92/1.97 % (1700136)Peak memory usage: 89 MB
% 5.92/1.97 % (1700136)Instructions burned: 183 (million)
% 5.92/1.97 % (1700135)Instruction limit reached!
% 5.92/1.97 % (1700135)------------------------------
% 5.92/1.97 % (1700135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.97 % (1700135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.97 % (1700135)CaDiCaL version: 2.1.3
% 5.92/1.97 % (1700135)Termination reason: Instruction limit
% 5.92/1.97 % (1700135)Termination phase: Saturation
% 5.92/1.97 % (1700135)Time elapsed: 0.085 s
% 5.92/1.97 % (1700135)Peak memory usage: 89 MB
% 5.92/1.97 % (1700135)Instructions burned: 137 (million)
% 5.92/1.97 % (1700146)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=794736695:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 5.92/1.97 % (1700137)Instruction limit reached!
% 5.92/1.97 % (1700137)------------------------------
% 5.92/1.97 % (1700137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.97 % (1700137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.97 % (1700137)CaDiCaL version: 2.1.3
% 5.92/1.97 % (1700137)Termination reason: Instruction limit
% 5.92/1.97 % (1700137)Termination phase: Saturation
% 5.92/1.97 % (1700137)Time elapsed: 0.170 s
% 5.92/1.97 % (1700137)Peak memory usage: 90 MB
% 5.92/1.97 % (1700137)Instructions burned: 258 (million)
% 5.92/1.97 % (1700147)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2241689442:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.92/1.97 % (1700149)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2663355240:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.92/1.97 % (1700149)Instruction limit reached!
% 5.92/1.97 % (1700149)------------------------------
% 5.92/1.97 % (1700149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.92/1.97 % (1700149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.97 % (1700149)CaDiCaL version: 2.1.3
% 5.92/1.97 % (1700149)Termination reason: Instruction limit
% 5.92/1.97 % (1700149)Termination phase: Saturation
% 5.92/1.97 % (1700149)Time elapsed: 0.121 s
% 8.37/2.06 % (1700149)Peak memory usage: 92 MB
% 8.37/2.06 % (1700149)Instructions burned: 216 (million)
% 8.37/2.06 % (1700152)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=276228927:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 8.37/2.06 % (1700138)Instruction limit reached!
% 8.37/2.06 % (1700138)------------------------------
% 8.37/2.06 % (1700138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/2.06 % (1700138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/2.06 % (1700138)CaDiCaL version: 2.1.3
% 8.37/2.06 % (1700138)Termination reason: Instruction limit
% 8.37/2.06 % (1700138)Termination phase: Saturation
% 8.37/2.06 % (1700138)Time elapsed: 0.652 s
% 8.37/2.06 % (1700138)Peak memory usage: 101 MB
% 8.37/2.06 % (1700138)Instructions burned: 1187 (million)
% 8.37/2.06 % (1700133)First to succeed.
% 8.37/2.06 % (1700133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1700088"
% 8.37/2.06 % (1700154)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=533183576:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 8.37/2.06 % (1700152)Instruction limit reached!
% 8.37/2.06 % (1700152)------------------------------
% 8.37/2.06 % (1700152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/2.06 % (1700152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/2.06 % (1700152)CaDiCaL version: 2.1.3
% 8.37/2.06 % (1700152)Termination reason: Instruction limit
% 8.37/2.06 % (1700152)Termination phase: Saturation
% 8.37/2.06 % (1700152)Time elapsed: 0.201 s
% 8.37/2.06 % (1700152)Peak memory usage: 94 MB
% 8.37/2.06 % (1700152)Instructions burned: 318 (million)
% 8.37/2.06 % (1700146)Instruction limit reached!
% 8.37/2.06 % (1700146)------------------------------
% 8.37/2.06 % (1700146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/2.06 % (1700146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/2.06 % (1700146)CaDiCaL version: 2.1.3
% 8.37/2.06 % (1700146)Termination reason: Instruction limit
% 8.37/2.06 % (1700146)Termination phase: Saturation
% 8.37/2.06 % (1700146)Time elapsed: 0.754 s
% 8.37/2.06 % (1700146)Peak memory usage: 141 MB
% 8.37/2.06 % (1700146)Instructions burned: 2052 (million)
% 8.37/2.06 % (1700133)Refutation found. Thanks to Tanya!
% 8.37/2.06 % SZS status Unsatisfiable for theBenchmark
% 8.37/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 8.37/2.06 % (1700133)------------------------------
% 8.37/2.06 % (1700133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/2.06 % (1700133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/2.06 % (1700133)CaDiCaL version: 2.1.3
% 8.37/2.06 % (1700133)Termination reason: Refutation
% 8.37/2.06 % (1700133)Time elapsed: 0.678 s
% 8.37/2.06 % (1700133)Peak memory usage: 129 MB
% 8.37/2.06 % (1700133)Instructions burned: 1032 (million)
% 8.37/2.06 % (1700133)------------------------------
% 8.37/2.06 % (1700133)------------------------------
% 8.37/2.06 % (1700088)Success in time 1.106 s
% 8.37/2.06 % Vampire exiting
%------------------------------------------------------------------------------