%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:09:30 AM UTC 2026
% Result : Theorem 0.64s 0.96s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 17 unt; 0 def)
% Number of atoms : 228 ( 84 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 281 ( 117 ~; 109 |; 35 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 76 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
? [X0] :
( sorti1(X0)
& ? [X1] :
( sorti1(X1)
& op1(X0,X0) = X1
& op1(X1,X1) = X0
& op1(X0,X1) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(X0,X0) = X1
& op2(X1,X1) = X0
& op2(X0,X1) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f5,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f6,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = X0 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
( ! [X0] :
( ! [X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f8]) ).
fof(f13,plain,
( sorti1(sK0)
& sorti1(sK1)
& sK1 = op1(sK0,sK0)
& sK0 = op1(sK1,sK1)
& sK0 != op1(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f15,plain,
! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) ),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
sK0 != op1(sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
sK0 = op1(sK1,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
sK1 = op1(sK0,sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0] :
( op2(op2(X0,X0),op2(X0,X0)) != X0
| ~ sorti2(op2(X0,X0))
| ~ sorti2(X0)
| op2(X0,op2(X0,X0)) = X0 ),
inference(equality_resolution,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(h(X0))
| ~ sorti2(X1)
| ~ sorti1(X0) ),
inference(superposition,[],[f18,f16]) ).
fof(f33,plain,
! [X0,X1] :
( j(op2(X1,h(X0))) = op1(j(X1),X0)
| ~ sorti2(X1)
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f32,f15]) ).
fof(f40,plain,
! [X0,X1] :
( op1(j(h(X0)),X1) = j(h(op1(X0,X1)))
| ~ sorti2(h(X0))
| ~ sorti1(X1)
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(superposition,[],[f33,f19]) ).
fof(f45,plain,
! [X0,X1] :
( op1(j(h(X0)),X1) = j(h(op1(X0,X1)))
| ~ sorti2(h(X0))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(duplicate_literal_removal,[],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( op1(j(h(X0)),X1) = j(h(op1(X0,X1)))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f45,f15]) ).
fof(f134,plain,
! [X0,X1] :
( sorti2(h(op1(X0,X1)))
| ~ sorti2(h(X1))
| ~ sorti2(h(X0))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(superposition,[],[f27,f19]) ).
fof(f135,plain,
! [X0,X1] :
( sorti2(h(op1(X0,X1)))
| ~ sorti2(h(X0))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f134,f15]) ).
fof(f136,plain,
! [X0,X1] :
( sorti2(h(op1(X0,X1)))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f135,f15]) ).
fof(f138,plain,
( sorti2(h(sK0))
| ~ sorti1(sK1)
| ~ sorti1(sK1) ),
inference(superposition,[],[f136,f22]) ).
fof(f139,plain,
( sorti2(h(sK1))
| ~ sorti1(sK0)
| ~ sorti1(sK0) ),
inference(superposition,[],[f136,f23]) ).
fof(f144,plain,
( sorti2(h(sK1))
| ~ sorti1(sK0) ),
inference(duplicate_literal_removal,[],[f139]) ).
fof(f145,plain,
( sorti2(h(sK0))
| ~ sorti1(sK1) ),
inference(duplicate_literal_removal,[],[f138]) ).
fof(f148,plain,
sorti2(h(sK1)),
inference(forward_subsumption_resolution,[],[f144,f25]) ).
fof(f149,plain,
sorti2(h(sK0)),
inference(forward_subsumption_resolution,[],[f145,f24]) ).
fof(f152,plain,
! [X0] :
( h(X0) != op2(h(op1(X0,X0)),h(op1(X0,X0)))
| ~ sorti2(h(op1(X0,X0)))
| ~ sorti2(h(X0))
| h(X0) = op2(h(X0),h(op1(X0,X0)))
| ~ sorti1(X0)
| ~ sorti1(X0) ),
inference(superposition,[],[f28,f19]) ).
fof(f153,plain,
! [X0] :
( h(X0) != op2(h(op1(X0,X0)),h(op1(X0,X0)))
| ~ sorti2(h(op1(X0,X0)))
| ~ sorti2(h(X0))
| h(X0) = op2(h(X0),h(op1(X0,X0)))
| ~ sorti1(X0) ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f154,plain,
! [X0] :
( h(X0) != op2(h(op1(X0,X0)),h(op1(X0,X0)))
| ~ sorti2(h(op1(X0,X0)))
| h(X0) = op2(h(X0),h(op1(X0,X0)))
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f153,f15]) ).
fof(f157,plain,
( h(sK0) != op2(h(sK1),h(sK1))
| ~ sorti2(h(sK1))
| h(sK0) = op2(h(sK0),h(sK1))
| ~ sorti1(sK0) ),
inference(superposition,[],[f154,f23]) ).
fof(f168,plain,
( h(sK0) != op2(h(sK1),h(sK1))
| h(sK0) = op2(h(sK0),h(sK1))
| ~ sorti1(sK0) ),
inference(forward_subsumption_resolution,[],[f157,f148]) ).
fof(f171,plain,
( h(sK0) != op2(h(sK1),h(sK1))
| h(sK0) = op2(h(sK0),h(sK1)) ),
inference(forward_subsumption_resolution,[],[f168,f25]) ).
fof(f235,plain,
( j(h(sK0)) = op1(j(h(sK1)),sK1)
| ~ sorti1(sK1)
| ~ sorti1(sK1) ),
inference(superposition,[],[f46,f22]) ).
fof(f236,plain,
( j(h(sK1)) = op1(j(h(sK0)),sK0)
| ~ sorti1(sK0)
| ~ sorti1(sK0) ),
inference(superposition,[],[f46,f23]) ).
fof(f255,plain,
( j(h(sK1)) = op1(j(h(sK0)),sK0)
| ~ sorti1(sK0) ),
inference(duplicate_literal_removal,[],[f236]) ).
fof(f256,plain,
( j(h(sK0)) = op1(j(h(sK1)),sK1)
| ~ sorti1(sK1) ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f271,plain,
j(h(sK1)) = op1(j(h(sK0)),sK0),
inference(forward_subsumption_resolution,[],[f255,f25]) ).
fof(f272,plain,
j(h(sK0)) = op1(j(h(sK1)),sK1),
inference(forward_subsumption_resolution,[],[f256,f24]) ).
fof(f277,plain,
( op1(sK0,sK0) = j(h(sK1))
| ~ sorti1(sK0) ),
inference(superposition,[],[f271,f16]) ).
fof(f289,plain,
op1(sK0,sK0) = j(h(sK1)),
inference(forward_subsumption_resolution,[],[f277,f25]) ).
fof(f294,plain,
sK1 = j(h(sK1)),
inference(forward_demodulation,[],[f289,f23]) ).
fof(f611,plain,
op1(sK1,sK1) = j(h(sK0)),
inference(forward_demodulation,[],[f272,f294]) ).
fof(f612,plain,
sK0 = j(h(sK0)),
inference(forward_demodulation,[],[f611,f22]) ).
fof(f644,plain,
( h(op1(sK1,sK1)) != h(sK0)
| h(sK0) = op2(h(sK0),h(sK1))
| ~ sorti1(sK1)
| ~ sorti1(sK1) ),
inference(superposition,[],[f171,f19]) ).
fof(f645,plain,
( h(op1(sK1,sK1)) != h(sK0)
| h(sK0) = op2(h(sK0),h(sK1))
| ~ sorti1(sK1) ),
inference(duplicate_literal_removal,[],[f644]) ).
fof(f646,plain,
( h(op1(sK1,sK1)) != h(sK0)
| h(sK0) = op2(h(sK0),h(sK1)) ),
inference(forward_subsumption_resolution,[],[f645,f24]) ).
fof(f647,plain,
( h(sK0) != h(sK0)
| h(sK0) = op2(h(sK0),h(sK1)) ),
inference(forward_demodulation,[],[f646,f22]) ).
fof(f648,plain,
h(sK0) = op2(h(sK0),h(sK1)),
inference(trivial_inequality_removal,[],[f647]) ).
fof(f696,plain,
( j(h(sK0)) = op1(j(h(sK0)),sK1)
| ~ sorti2(h(sK0))
| ~ sorti1(sK1) ),
inference(superposition,[],[f33,f648]) ).
fof(f705,plain,
( j(h(sK0)) = op1(j(h(sK0)),sK1)
| ~ sorti1(sK1) ),
inference(forward_subsumption_resolution,[],[f696,f149]) ).
fof(f710,plain,
j(h(sK0)) = op1(j(h(sK0)),sK1),
inference(forward_subsumption_resolution,[],[f705,f24]) ).
fof(f715,plain,
sK0 = op1(sK0,sK1),
inference(forward_demodulation,[],[f710,f612]) ).
fof(f717,plain,
$false,
inference(forward_subsumption_resolution,[],[f715,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 19:26:28 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.96 % (1897805)Detected formulas, will run a generic FOF schedule.
% 0.64/0.96 % (1897814)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1525454895:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/0.96 % (1897814)First to succeed.
% 0.64/0.96 % (1897814)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1897805"
% 0.64/0.96 % (1897813)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3974489643:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/0.96 % (1897816)dis-21_1_sil=8000:lcm=predicate:random_seed=1992042010:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.64/0.96 % (1897812)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3149138753:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/0.96 % (1897811)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=204201568:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/0.96 % (1897810)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3700771194:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/0.96 % (1897816)Refutation not found, incomplete strategy
% 0.64/0.96 % (1897816)------------------------------
% 0.64/0.96 % (1897816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/0.96 % (1897816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.96 % (1897816)CaDiCaL version: 2.1.3
% 0.64/0.96 % (1897816)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.96 % (1897816)Time elapsed: 0.002 s
% 0.64/0.96 % (1897816)Peak memory usage: 88 MB
% 0.64/0.96 % (1897816)Instructions burned: 1 (million)
% 0.64/0.96 % (1897815)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2825578603:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/0.96 % (1897813)Also succeeded, but the first one will report.
% 0.64/0.96 % (1897815)Also succeeded, but the first one will report.
% 0.64/0.96 % (1897814)Refutation found. Thanks to Tanya!
% 0.64/0.96 % SZS status Theorem for theBenchmark
% 0.64/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.15 % (1897814)------------------------------
% 2.76/1.15 % (1897814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.15 % (1897814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.15 % (1897814)CaDiCaL version: 2.1.3
% 2.76/1.15 % (1897814)Termination reason: Refutation
% 2.76/1.15 % (1897814)Time elapsed: 0.008 s
% 2.76/1.15 % (1897814)Peak memory usage: 88 MB
% 2.76/1.15 % (1897814)Instructions burned: 21 (million)
% 2.76/1.15 % (1897814)------------------------------
% 2.76/1.15 % (1897814)------------------------------
% 2.76/1.15 % (1897805)Success in time 0.298 s
% 2.76/1.15 % Vampire exiting
%------------------------------------------------------------------------------