%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:36:15 PM UTC 2026
% Result : Unsatisfiable 3.00s 1.19s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 15 unt; 2 def)
% Number of atoms : 29 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 5 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
fof(f3,axiom,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
fof(f4,axiom,
negate(add(a,negate(add(b,c)))) = negate(add(b,negate(add(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f5,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
fof(f7,definition,
( spl0_1
<=> a = b ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f12,definition,
( spl0_2
<=> negate(add(a,negate(add(b,c)))) = negate(add(b,negate(add(a,c)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f14,plain,
( negate(add(a,negate(add(b,c)))) = negate(add(b,negate(add(a,c))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,plain,
spl0_2,
inference(avatar_split_clause,[],[f4,f12]) ).
fof(f17,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f24,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[],[f17,f2]) ).
fof(f227,plain,
! [X2,X0,X1] : negate(add(negate(add(X0,add(X1,X2))),negate(add(X1,negate(add(X0,X2)))))) = X1,
inference(superposition,[],[f3,f24]) ).
fof(f241,plain,
( b = negate(add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c))))))
| ~ spl0_2 ),
inference(superposition,[],[f3,f14]) ).
fof(f249,plain,
( a = b
| ~ spl0_2 ),
inference(forward_demodulation,[],[f241,f227]) ).
fof(f255,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f249,f12,f7]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f15]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f255]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s6,s2]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f256,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.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 23:26:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.00/1.19 % (3997940)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.00/1.19 % (3997950)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=3816164987:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.00/1.19 % (3997953)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3950816097:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.00/1.19 % (3997954)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2469313779:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.00/1.19 % (3997949)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=2136488279:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.00/1.19 % (3997955)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2462671766:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.00/1.19 % (3997952)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2068059404:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.00/1.19 % (3997951)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2038943938:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.00/1.19 % (3997954)First to succeed.
% 3.00/1.19 % (3997955)Also succeeded, but the first one will report.
% 3.00/1.19 % (3997954)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3997940"
% 3.00/1.19 % (3997952)Also succeeded, but the first one will report.
% 3.00/1.19 % (3997953)Also succeeded, but the first one will report.
% 3.00/1.19 % (3997954)Refutation found. Thanks to Tanya!
% 3.00/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.00/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/1.19 % (3997954)------------------------------
% 3.00/1.19 % (3997954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.19 % (3997954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.19 % (3997954)CaDiCaL version: 2.1.3
% 3.00/1.19 % (3997954)Termination reason: Refutation
% 3.00/1.19 % (3997954)Time elapsed: 0.006 s
% 3.00/1.19 % (3997954)Peak memory usage: 89 MB
% 3.00/1.19 % (3997954)Instructions burned: 8 (million)
% 3.00/1.19 % (3997954)------------------------------
% 3.00/1.19 % (3997954)------------------------------
% 3.00/1.19 % (3997940)Success in time 0.373 s
% 3.00/1.19 % Vampire exiting
%------------------------------------------------------------------------------