%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:46:06 PM UTC 2026
% Result : Theorem 3.22s 1.14s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 29 unt; 0 def)
% Number of atoms : 127 ( 90 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 58 ~; 59 |; 1 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 162 ( 154 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f5,axiom,
! [X0] : s(X0) != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f7,axiom,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f8,axiom,
! [X0,X1] :
( x2(s(X0),s(X1))
<=> x2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f10,axiom,
! [X0] : x2(z,s(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f12,axiom,
! [X0] : x(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f13,axiom,
! [X0,X1,X2] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,axiom,
! [X0] : rotate(z,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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(s(X0),s(X1))
| ~ x2(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
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(X1,length(X3))
| rotate(X0,X3) != rotate(X1,X3)
| rotate(s(z),X3) = X3
| X0 = X1
| ~ x2(X0,length(X3)) ),
inference(equality_resolution,[],[f39]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( cons(X2,X0) = rotate(s(z),cons(X2,X0))
| rotate(X3,cons(X2,X0)) != rotate(X1,cons(X2,X0))
| ~ x2(X1,s(length(X0)))
| X1 = X3
| ~ x2(X3,s(length(X0))) ),
inference(superposition,[],[f40,f28]) ).
fof(f58,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(f59,plain,
! [X0,X1] : x(X0,cons(X1,nil)) = rotate(s(z),cons(X1,X0)),
inference(superposition,[],[f37,f38]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ x2(X3,s(length(X1)))
| rotate(X2,cons(X0,X1)) != rotate(X3,cons(X0,X1))
| cons(X0,X1) = x(X1,cons(X0,nil))
| X2 = X3
| ~ x2(X2,s(length(X1))) ),
inference(superposition,[],[f59,f52]) ).
fof(f71,plain,
! [X2,X0,X1] :
( rotate(X0,cons(X1,X2)) != rotate(z,cons(X1,X2))
| cons(X1,X2) = x(X2,cons(X1,nil))
| z = X0
| ~ x2(X0,s(length(X2))) ),
inference(resolution,[],[f64,f32]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ x2(X0,s(length(X2)))
| cons(X1,X2) = x(X2,cons(X1,nil))
| z = X0
| cons(X1,X2) != rotate(X0,cons(X1,X2)) ),
inference(forward_demodulation,[],[f71,f38]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] : rotate(s(X3),cons(X2,cons(X4,cons(X0,X1)))) = rotate(X3,cons(X4,cons(X0,x(X1,cons(X2,nil))))),
inference(superposition,[],[f58,f35]) ).
fof(f81,plain,
! [X2,X0,X1] : x(x(X0,cons(X1,nil)),cons(X2,nil)) = rotate(s(s(z)),cons(X1,cons(X2,X0))),
inference(superposition,[],[f58,f59]) ).
fof(f101,plain,
! [X2,X0,X1] :
( cons(X0,X1) = x(X1,cons(X0,nil))
| z = s(X2)
| cons(X0,X1) != rotate(s(X2),cons(X0,X1))
| ~ x2(X2,length(X1)) ),
inference(resolution,[],[f77,f30]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ x2(X2,length(X1))
| cons(X0,X1) != rotate(s(X2),cons(X0,X1))
| cons(X0,X1) = x(X1,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[],[f101,f26]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ x2(X1,s(length(X0)))
| cons(X3,cons(X2,X0)) != rotate(s(X1),cons(X3,cons(X2,X0)))
| cons(X3,cons(X2,X0)) = x(cons(X2,X0),cons(X3,nil)) ),
inference(superposition,[],[f105,f28]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( cons(X3,cons(X2,X0)) != rotate(s(X1),cons(X3,cons(X2,X0)))
| ~ x2(X1,s(length(X0)))
| cons(X3,cons(X2,X0)) = cons(X2,x(X0,cons(X3,nil))) ),
inference(forward_demodulation,[],[f107,f35]) ).
fof(f181,plain,
! [X2,X3,X0,X1] : rotate(s(s(z)),cons(X2,cons(X3,cons(X0,X1)))) = x(cons(X0,x(X1,cons(X2,nil))),cons(X3,nil)),
inference(superposition,[],[f81,f35]) ).
fof(f186,plain,
! [X2,X3,X0,X1] : rotate(s(s(z)),cons(X2,cons(X3,cons(X0,X1)))) = cons(X0,x(x(X1,cons(X2,nil)),cons(X3,nil))),
inference(forward_demodulation,[],[f181,f35]) ).
fof(f188,plain,
! [X2,X3,X0,X1] : rotate(s(s(z)),cons(X2,cons(X3,cons(X0,X1)))) = cons(X0,rotate(s(s(z)),cons(X2,cons(X3,X1)))),
inference(forward_demodulation,[],[f186,f81]) ).
fof(f195,plain,
! [X2,X3,X0,X1] : rotate(s(X1),cons(X0,cons(X2,cons(X3,nil)))) = rotate(X1,cons(X2,cons(X3,cons(X0,nil)))),
inference(superposition,[],[f79,f34]) ).
fof(f496,plain,
! [X2,X3,X0,X1] :
( cons(X0,rotate(s(s(z)),cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,cons(X0,X3)))
| ~ x2(s(z),s(length(cons(X0,X3))))
| cons(X1,cons(X2,cons(X0,X3))) = cons(X2,x(cons(X0,X3),cons(X1,nil))) ),
inference(superposition,[],[f108,f188]) ).
fof(f497,plain,
! [X2,X3,X0,X1] :
( ~ x2(s(z),s(s(length(X3))))
| cons(X0,rotate(s(s(z)),cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,cons(X0,X3)))
| cons(X1,cons(X2,cons(X0,X3))) = cons(X2,x(cons(X0,X3),cons(X1,nil))) ),
inference(forward_demodulation,[],[f496,f28]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ x2(s(z),s(s(length(X3))))
| cons(X1,cons(X2,cons(X0,X3))) = cons(X2,cons(X0,x(X3,cons(X1,nil))))
| cons(X0,rotate(s(s(z)),cons(X1,cons(X2,X3)))) != cons(X1,cons(X2,cons(X0,X3))) ),
inference(forward_demodulation,[],[f497,f35]) ).
fof(f518,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))) != cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3))))
| ~ x2(z,s(length(X3))) ),
inference(resolution,[],[f502,f30]) ).
fof(f523,plain,
! [X2,X3,X0,X1] :
( cons(X0,cons(X1,cons(X2,X3))) != cons(X2,rotate(s(s(z)),cons(X0,cons(X1,X3))))
| cons(X0,cons(X1,cons(X2,X3))) = cons(X1,cons(X2,x(X3,cons(X0,nil)))) ),
inference(forward_subsumption_resolution,[],[f518,f32]) ).
fof(f533,plain,
! [X2,X3,X0,X1] :
( cons(X2,cons(X0,cons(X3,cons(X1,nil)))) != cons(X3,rotate(s(z),cons(X0,cons(X1,cons(X2,nil)))))
| cons(X2,cons(X0,cons(X3,cons(X1,nil)))) = cons(X0,cons(X3,x(cons(X1,nil),cons(X2,nil)))) ),
inference(superposition,[],[f523,f195]) ).
fof(f536,plain,
! [X2,X3,X0,X1] :
( cons(X2,cons(X0,cons(X3,cons(X1,nil)))) != cons(X3,rotate(z,cons(X1,cons(X2,cons(X0,nil)))))
| cons(X2,cons(X0,cons(X3,cons(X1,nil)))) = cons(X0,cons(X3,x(cons(X1,nil),cons(X2,nil)))) ),
inference(forward_demodulation,[],[f533,f195]) ).
fof(f540,plain,
! [X2,X3,X0,X1] :
( cons(X2,cons(X0,cons(X3,cons(X1,nil)))) != cons(X3,cons(X1,cons(X2,cons(X0,nil))))
| cons(X2,cons(X0,cons(X3,cons(X1,nil)))) = cons(X0,cons(X3,x(cons(X1,nil),cons(X2,nil)))) ),
inference(forward_demodulation,[],[f536,f38]) ).
fof(f542,plain,
! [X2,X3,X0,X1] :
( cons(X2,cons(X0,cons(X3,cons(X1,nil)))) = cons(X0,cons(X3,cons(X1,x(nil,cons(X2,nil)))))
| cons(X2,cons(X0,cons(X3,cons(X1,nil)))) != cons(X3,cons(X1,cons(X2,cons(X0,nil)))) ),
inference(forward_demodulation,[],[f540,f35]) ).
fof(f544,plain,
! [X2,X3,X0,X1] :
( cons(X2,cons(X0,cons(X3,cons(X1,nil)))) != cons(X3,cons(X1,cons(X2,cons(X0,nil))))
| cons(X2,cons(X0,cons(X3,cons(X1,nil)))) = cons(X0,cons(X3,cons(X1,cons(X2,nil)))) ),
inference(forward_demodulation,[],[f542,f34]) ).
fof(f575,plain,
! [X0,X1] : cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))),
inference(equality_resolution,[],[f544]) ).
fof(f746,plain,
! [X0,X1] : head(cons(X0,cons(X1,cons(X0,cons(X1,nil))))) = X1,
inference(superposition,[],[f22,f575]) ).
fof(f779,plain,
! [X0,X1] : X0 = X1,
inference(forward_demodulation,[],[f746,f22]) ).
fof(f1677,plain,
! [X0] : z != X0,
inference(superposition,[],[f26,f779]) ).
fof(f1801,plain,
$false,
inference(forward_subsumption_resolution,[],[f1677,f779]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:07:02 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.22/1.14 % (1994480)Detected formulas, will run a generic FOF schedule.
% 3.22/1.14 % (1994485)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=224172018:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.22/1.14 % (1994487)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=2789308956:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.22/1.14 % (1994491)dis-21_1_sil=8000:lcm=predicate:random_seed=1649753554: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)
% 3.22/1.14 % (1994488)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=342922271:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.22/1.14 % (1994490)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2511826490:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.22/1.14 % (1994489)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3963813976:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.22/1.14 % (1994486)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=764868069:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.22/1.14 % (1994488)Refutation not found, incomplete strategy
% 3.22/1.14 % (1994488)------------------------------
% 3.22/1.14 % (1994488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.14 % (1994491)Refutation not found, incomplete strategy
% 3.22/1.14 % (1994491)------------------------------
% 3.22/1.14 % (1994491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.14 % (1994491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.14 % (1994488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.14 % (1994488)CaDiCaL version: 2.1.3
% 3.22/1.14 % (1994491)CaDiCaL version: 2.1.3
% 3.22/1.14 % (1994488)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.14 % (1994488)Time elapsed: 0.002 s
% 3.22/1.14 % (1994491)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.14 % (1994491)Time elapsed: 0.002 s
% 3.22/1.14 % (1994488)Peak memory usage: 88 MB
% 3.22/1.14 % (1994491)Peak memory usage: 88 MB
% 3.22/1.14 % (1994488)Instructions burned: 1 (million)
% 3.22/1.14 % (1994491)Instructions burned: 1 (million)
% 3.22/1.14 % (1994489)Refutation not found, incomplete strategy
% 3.22/1.14 % (1994489)------------------------------
% 3.22/1.14 % (1994489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.14 % (1994489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.14 % (1994489)CaDiCaL version: 2.1.3
% 3.22/1.14 % (1994489)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.14 % (1994489)Time elapsed: 0.002 s
% 3.22/1.14 % (1994489)Peak memory usage: 87 MB
% 3.22/1.14 % (1994489)Instructions burned: 1 (million)
% 3.22/1.14 % (1994490)First to succeed.
% 3.22/1.14 % (1994490)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1994480"
% 3.22/1.14 % (1994488)------------------------------
% 3.22/1.14 % (1994488)------------------------------
% 3.22/1.14 % (1994489)------------------------------
% 3.22/1.14 % (1994489)------------------------------
% 3.22/1.14 % (1994491)------------------------------
% 3.22/1.14 % (1994491)------------------------------
% 3.22/1.14 % (1994490)Refutation found. Thanks to Tanya!
% 3.22/1.14 % SZS status Theorem for theBenchmark
% 3.22/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.34 % (1994490)------------------------------
% 4.03/1.34 % (1994490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.34 % (1994490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.34 % (1994490)CaDiCaL version: 2.1.3
% 4.03/1.34 % (1994490)Termination reason: Refutation
% 4.03/1.34 % (1994490)Time elapsed: 0.050 s
% 4.03/1.34 % (1994490)Peak memory usage: 89 MB
% 4.03/1.34 % (1994490)Instructions burned: 93 (million)
% 4.03/1.34 % (1994490)------------------------------
% 4.03/1.34 % (1994490)------------------------------
% 4.03/1.34 % (1994480)Success in time 0.479 s
% 4.03/1.34 % Vampire exiting
%------------------------------------------------------------------------------