%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG069+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 : n018.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 09:09:29 AM UTC 2026
% Result : Theorem 2.79s 1.17s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 3 unt; 0 def)
% Number of atoms : 125 ( 37 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 160 ( 63 ~; 48 |; 29 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ? [X1] :
( sorti1(X1)
& op1(X1,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ? [X1] :
( sorti2(X1)
& op2(X1,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] :
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != X0 )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( sorti1(X1)
& op1(X1,X1) = X0 )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,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(f14,plain,
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != sK0 )
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f9]) ).
fof(f15,plain,
! [X0] :
( ( sorti1(sK1(X0))
& op1(sK1(X0),sK1(X0)) = X0 )
| ~ sorti1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f10]) ).
fof(f16,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f13]) ).
fof(f17,plain,
! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X1] :
( op2(X1,X1) != sK0
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0] :
( op1(sK1(X0),sK1(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] :
( sorti1(sK1(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f72,plain,
! [X0] :
( sK0 != h(op1(X0,X0))
| ~ sorti2(h(X0))
| ~ sorti1(X0)
| ~ sorti1(X0) ),
inference(superposition,[],[f23,f21]) ).
fof(f73,plain,
! [X0] :
( sK0 != h(op1(X0,X0))
| ~ sorti2(h(X0))
| ~ sorti1(X0) ),
inference(duplicate_literal_removal,[],[f72]) ).
fof(f74,plain,
! [X0] :
( sK0 != h(op1(X0,X0))
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f73,f17]) ).
fof(f109,plain,
! [X0] :
( h(X0) != sK0
| ~ sorti1(sK1(X0))
| ~ sorti1(X0) ),
inference(superposition,[],[f74,f24]) ).
fof(f114,plain,
! [X0] :
( h(X0) != sK0
| ~ sorti1(X0) ),
inference(forward_subsumption_resolution,[],[f109,f25]) ).
fof(f115,plain,
! [X0] :
( sK0 != X0
| ~ sorti1(j(X0))
| ~ sorti2(X0) ),
inference(superposition,[],[f114,f19]) ).
fof(f117,plain,
! [X0] :
( sK0 != X0
| ~ sorti2(X0) ),
inference(forward_subsumption_resolution,[],[f115,f16]) ).
fof(f118,plain,
~ sorti2(sK0),
inference(equality_resolution,[],[f117]) ).
fof(f119,plain,
$false,
inference(forward_subsumption_resolution,[],[f118,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 19:27:10 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.79/1.17 % (3689068)Detected formulas, will run a generic FOF schedule.
% 2.79/1.17 % (3689077)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3879324720:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.79/1.17 % (3689077)First to succeed.
% 2.79/1.17 % (3689077)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3689068"
% 2.79/1.17 % (3689075)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=618327094:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.79/1.17 % (3689076)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4038911059:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.79/1.17 % (3689074)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=1942436232:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.79/1.17 % (3689073)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=4179981581:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.79/1.17 % (3689076)Also succeeded, but the first one will report.
% 2.79/1.17 % (3689078)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1035144240:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.79/1.17 % (3689079)dis-21_1_sil=8000:lcm=predicate:random_seed=1137552789: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)
% 2.79/1.17 % (3689079)Refutation not found, incomplete strategy
% 2.79/1.17 % (3689079)------------------------------
% 2.79/1.17 % (3689079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.17 % (3689079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.17 % (3689079)CaDiCaL version: 2.1.3
% 2.79/1.17 % (3689079)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.17 % (3689079)Time elapsed: 0.001 s
% 2.79/1.17 % (3689079)Peak memory usage: 88 MB
% 2.79/1.17 % (3689078)Also succeeded, but the first one will report.
% 2.79/1.17 % (3689077)Refutation found. Thanks to Tanya!
% 2.79/1.17 % SZS status Theorem for theBenchmark
% 2.79/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.17 % (3689077)------------------------------
% 2.79/1.17 % (3689077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.17 % (3689077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.17 % (3689077)CaDiCaL version: 2.1.3
% 2.79/1.17 % (3689077)Termination reason: Refutation
% 2.79/1.17 % (3689077)Time elapsed: 0.003 s
% 2.79/1.17 % (3689077)Peak memory usage: 88 MB
% 2.79/1.17 % (3689077)Instructions burned: 4 (million)
% 2.79/1.17 % (3689077)------------------------------
% 2.79/1.17 % (3689077)------------------------------
% 2.79/1.17 % (3689068)Success in time 0.303 s
% 2.79/1.17 % Vampire exiting
%------------------------------------------------------------------------------