%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 01:46:40 PM UTC 2026
% Result : Theorem 0.19s 0.36s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 30 unt; 0 def)
% Number of atoms : 127 ( 88 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 55 ~; 58 |; 1 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 154 ( 146 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(f5,axiom,
! [X0] : s(X0) != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f7,axiom,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f8,axiom,
! [X0,X1] :
( x2(s(X0),s(X1))
<=> x2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f9,axiom,
! [X0] : ~ x2(s(X0),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f10,axiom,
! [X0] : x2(z,s(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f12,axiom,
! [X0] : x(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f13,axiom,
! [X0,X1,X2] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f15,axiom,
! [X0,X1,X2] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,axiom,
! [X0] : rotate(z,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f17,conjecture,
? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_017) ).
fof(f18,negated_conjecture,
~ ? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| rotate(X0,X3) != rotate(X1,X2)
| rotate(s(z),X3) = X3
| X2 != X3
| ~ x2(X1,length(X2))
| ~ x2(X0,length(X3)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| rotate(X0,X3) != rotate(X1,X2)
| rotate(s(z),X3) = X3
| X2 != X3
| ~ x2(X1,length(X2))
| ~ x2(X0,length(X3)) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( x2(s(X0),s(X1))
| ~ x2(X0,X1) )
& ( x2(X0,X1)
| ~ x2(s(X0),s(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ x2(X0,X1)
| x2(s(X0),s(X1)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0] : ~ x2(s(X0),z),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X0] : x2(z,s(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0] : x(nil,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f35,plain,
! [X2,X0,X1] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
! [X2,X0,X1] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0] : rotate(z,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| rotate(X0,X3) != rotate(X1,X2)
| rotate(s(z),X3) = X3
| X2 != X3
| ~ x2(X1,length(X2))
| ~ x2(X0,length(X3)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ x2(X0,length(X3))
| rotate(X0,X3) != rotate(X1,X3)
| rotate(s(z),X3) = X3
| ~ x2(X1,length(X3))
| X0 = X1 ),
inference(equality_resolution,[],[f39]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ x2(X3,s(length(X0)))
| rotate(X1,cons(X2,X0)) != rotate(X3,cons(X2,X0))
| cons(X2,X0) = rotate(s(z),cons(X2,X0))
| ~ x2(X1,s(length(X0)))
| X1 = X3 ),
inference(superposition,[],[f40,f28]) ).
fof(f43,plain,
! [X2,X0,X1] :
( rotate(X0,cons(X1,X2)) != rotate(z,cons(X1,X2))
| cons(X1,X2) = rotate(s(z),cons(X1,X2))
| ~ x2(X0,s(length(X2)))
| z = X0 ),
inference(resolution,[],[f42,f32]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ x2(X0,s(length(X2)))
| cons(X1,X2) = rotate(s(z),cons(X1,X2))
| cons(X1,X2) != rotate(X0,cons(X1,X2))
| z = X0 ),
inference(forward_demodulation,[],[f43,f38]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ x2(X1,s(s(length(X0))))
| cons(X3,cons(X2,X0)) = rotate(s(z),cons(X3,cons(X2,X0)))
| cons(X3,cons(X2,X0)) != rotate(X1,cons(X3,cons(X2,X0)))
| z = X1 ),
inference(superposition,[],[f46,f28]) ).
fof(f50,plain,
! [X0] : x2(s(z),s(s(X0))),
inference(resolution,[],[f30,f32]) ).
fof(f55,plain,
! [X2,X3,X0,X1] : rotate(s(X3),cons(X2,cons(X0,X1))) = rotate(X3,cons(X0,x(X1,cons(X2,nil)))),
inference(superposition,[],[f37,f35]) ).
fof(f57,plain,
! [X0,X1] : rotate(s(z),cons(X0,X1)) = x(X1,cons(X0,nil)),
inference(superposition,[],[f38,f37]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( cons(X3,cons(X2,X0)) = x(cons(X2,X0),cons(X3,nil))
| ~ x2(X1,s(s(length(X0))))
| cons(X3,cons(X2,X0)) != rotate(X1,cons(X3,cons(X2,X0)))
| z = X1 ),
inference(backward_demodulation,[],[f49,f57]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( ~ x2(X1,s(s(length(X0))))
| cons(X3,cons(X2,X0)) = cons(X2,x(X0,cons(X3,nil)))
| cons(X3,cons(X2,X0)) != rotate(X1,cons(X3,cons(X2,X0)))
| z = X1 ),
inference(forward_demodulation,[],[f60,f35]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( ~ x2(X1,s(s(s(length(X0)))))
| cons(X3,cons(X4,cons(X2,X0))) = cons(X4,x(cons(X2,X0),cons(X3,nil)))
| cons(X3,cons(X4,cons(X2,X0))) != rotate(X1,cons(X3,cons(X4,cons(X2,X0))))
| z = X1 ),
inference(superposition,[],[f65,f28]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( ~ x2(X1,s(s(s(length(X0)))))
| cons(X3,cons(X4,cons(X2,X0))) = cons(X4,cons(X2,x(X0,cons(X3,nil))))
| cons(X3,cons(X4,cons(X2,X0))) != rotate(X1,cons(X3,cons(X4,cons(X2,X0))))
| z = X1 ),
inference(forward_demodulation,[],[f77,f35]) ).
fof(f82,plain,
! [X0] : x2(s(s(z)),s(s(s(X0)))),
inference(resolution,[],[f50,f30]) ).
fof(f120,plain,
! [X2,X0,X1] : rotate(s(s(z)),cons(X0,cons(X1,X2))) = x(x(X2,cons(X0,nil)),cons(X1,nil)),
inference(superposition,[],[f57,f55]) ).
fof(f128,plain,
! [X0] : x2(s(s(s(z))),s(s(s(s(X0))))),
inference(resolution,[],[f82,f30]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,X3))) != rotate(s(s(z)),cons(X0,cons(X1,cons(X2,X3))))
| z = s(s(z)) ),
inference(resolution,[],[f78,f82]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil))))
| cons(X0,cons(X1,cons(X2,X3))) != rotate(s(s(z)),cons(X0,cons(X1,cons(X2,X3)))) ),
inference(forward_subsumption_resolution,[],[f142,f26]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) != x(x(cons(X2,X3),cons(X0,nil)),cons(X1,nil))
| cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f147,f120]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) != x(cons(X2,x(X3,cons(X0,nil))),cons(X1,nil))
| cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f149,f35]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) != cons(X2,x(x(X3,cons(X0,nil)),cons(X1,nil)))
| cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f151,f35]) ).
fof(f160,plain,
! [X2,X3,X0,X1,X4] :
( cons(X2,cons(X3,cons(X4,cons(X0,X1)))) != cons(X4,x(cons(X0,x(X1,cons(X2,nil))),cons(X3,nil)))
| cons(X2,cons(X3,cons(X4,cons(X0,X1)))) = cons(X3,cons(X4,cons(X0,x(X1,cons(X2,nil))))) ),
inference(superposition,[],[f153,f35]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X4] :
( cons(X2,cons(X3,cons(X4,cons(X0,X1)))) != cons(X4,cons(X0,x(x(X1,cons(X2,nil)),cons(X3,nil))))
| cons(X2,cons(X3,cons(X4,cons(X0,X1)))) = cons(X3,cons(X4,cons(X0,x(X1,cons(X2,nil))))) ),
inference(forward_demodulation,[],[f160,f35]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) != cons(X2,cons(X3,x(cons(X0,nil),cons(X1,nil))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil)))) ),
inference(superposition,[],[f161,f34]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) != cons(X2,cons(X3,cons(X0,x(nil,cons(X1,nil)))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f209,f35]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) != cons(X2,cons(X3,cons(X0,cons(X1,nil))))
| cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f212,f34]) ).
fof(f236,plain,
! [X0,X1] : cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))),
inference(equality_resolution,[],[f213]) ).
fof(f276,plain,
! [X0,X1] : head(cons(X0,cons(X1,cons(X0,cons(X1,nil))))) = X1,
inference(superposition,[],[f22,f236]) ).
fof(f288,plain,
! [X0,X1] : X0 = X1,
inference(forward_demodulation,[],[f276,f22]) ).
fof(f578,plain,
! [X0] : x2(s(s(s(z))),X0),
inference(superposition,[],[f128,f288]) ).
fof(f612,plain,
! [X0,X1] : ~ x2(s(X1),X0),
inference(superposition,[],[f31,f288]) ).
fof(f659,plain,
$false,
inference(forward_subsumption_resolution,[],[f578,f612]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 15:06:31 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36 % (849700)Will run a generic schedule for satisfiability detection.
% 0.19/0.36 % (849709)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=724703370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.36 % (849706)% WARNING: option uhcvi not known.
% 0.19/0.36 % (849705)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1088781142_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.36 % (849707)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2970347570:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.36 % (849708)dis+10_1_sil=32000:sp=arity:random_seed=3740961091:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.36 % (849706)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=174306678:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.36 % (849711)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2817610041:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.36 % TRYING [1]
% 0.19/0.36 % TRYING [2]
% 0.19/0.36 % TRYING [3]
% 0.19/0.36 % TRYING [4]
% 0.19/0.36 % TRYING [5]
% 0.19/0.36 % (849710)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1806190546:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.36 % (849709)Instruction limit reached!
% 0.19/0.36 % (849709)------------------------------
% 0.19/0.36 % (849709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (849709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (849709)CaDiCaL version: 2.1.3
% 0.19/0.36 % (849709)Termination reason: Instruction limit
% 0.19/0.36 % (849709)Termination phase: Saturation
% 0.19/0.36 % (849709)Time elapsed: 0.032 s
% 0.19/0.36 % (849709)Peak memory usage: 12 MB
% 0.19/0.36 % (849709)Instructions burned: 118 (million)
% 0.19/0.36 % TRYING [6]
% 0.19/0.36 % (849719)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4121775870:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.36 % TRYING [1]
% 0.19/0.36 % TRYING [2]
% 0.19/0.36 % TRYING [3]
% 0.19/0.36 % TRYING [4]
% 0.19/0.36 % TRYING [5]
% 0.19/0.36 % (849708)Instruction limit reached!
% 0.19/0.36 % (849708)------------------------------
% 0.19/0.36 % (849708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (849708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (849708)CaDiCaL version: 2.1.3
% 0.19/0.36 % (849708)Termination reason: Instruction limit
% 0.19/0.36 % (849708)Termination phase: Saturation
% 0.19/0.36 % (849708)Time elapsed: 0.054 s
% 0.19/0.36 % (849708)Peak memory usage: 12 MB
% 0.19/0.36 % (849708)Instructions burned: 104 (million)
% 0.19/0.36 % TRYING [6]
% 0.19/0.36 % TRYING [7]
% 0.19/0.36 % (849721)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3703701204:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.36 % (849721) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-849700-849721"...
% 0.19/0.36 % (849721)...printing done.
% 0.19/0.36 % TRYING [7]
% 0.19/0.36 % (849721)Refutation found. Thanks to Tanya!
% 0.19/0.36 % SZS status Theorem for theBenchmark
% 0.19/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.36 % (849721)------------------------------
% 0.58/0.36 % (849721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.36 % (849721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.36 % (849721)CaDiCaL version: 2.1.3
% 0.58/0.36 % (849721)Termination reason: Refutation
% 0.58/0.36 % (849721)Time elapsed: 0.021 s
% 0.58/0.36 % (849721)Peak memory usage: 12 MB
% 0.58/0.36 % (849721)Instructions burned: 32 (million)
% 0.58/0.36 % (849700)Success in time 0.135 s
% 0.58/0.36 % Vampire exiting
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