%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 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 01:46:08 PM UTC 2026
% Result : Theorem 9.06s 2.18s
% Output : Refutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 25 unt; 0 def)
% Number of atoms : 69 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 20 |; 1 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(f2,axiom,
! [X0,X1] : tail(cons(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(f5,axiom,
! [X0] : z != s(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f6,axiom,
! [X0] : leqNat(z,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f8,axiom,
! [X0,X1] :
( leqNat(s(X0),s(X1))
<=> leqNat(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f9,axiom,
! [X0] : merge(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f10,axiom,
! [X0,X1] : merge(cons(X0,X1),nil) = cons(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( leqNat(X0,X2)
=> merge(cons(X0,X1),cons(X2,X3)) = cons(X0,merge(X1,cons(X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f13,conjecture,
? [X0,X1,X2] :
~ ( merge(X0,X1) = merge(X1,X0)
=> ( merge(X0,X2) = merge(X2,X0)
=> merge(X1,X2) = merge(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_013) ).
fof(f14,negated_conjecture,
~ ? [X0,X1,X2] :
~ ( merge(X0,X1) = merge(X1,X0)
=> ( merge(X0,X2) = merge(X2,X0)
=> merge(X1,X2) = merge(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( merge(X1,X2) = merge(X2,X1)
| merge(X0,X2) != merge(X2,X0)
| merge(X0,X1) != merge(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( merge(X1,X2) = merge(X2,X1)
| merge(X0,X2) != merge(X2,X0)
| merge(X0,X1) != merge(X1,X0) ),
inference(flattening,[],[f15]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( merge(cons(X0,X1),cons(X2,X3)) = cons(X0,merge(X1,cons(X2,X3)))
| ~ leqNat(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0,X1] :
( ( leqNat(s(X0),s(X1))
| ~ leqNat(X0,X1) )
& ( leqNat(X0,X1)
| ~ leqNat(s(X0),s(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f20,plain,
! [X2,X0,X1] :
( merge(X0,X2) != merge(X2,X0)
| merge(X1,X2) = merge(X2,X1)
| merge(X0,X1) != merge(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f22,plain,
! [X2,X3,X0,X1] :
( ~ leqNat(X0,X2)
| merge(cons(X0,X1),cons(X2,X3)) = cons(X0,merge(X1,cons(X2,X3))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0,X1] : cons(X0,X1) = merge(cons(X0,X1),nil),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0] : merge(nil,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] : tail(cons(X0,X1)) = X1,
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0,X1] :
( leqNat(s(X0),s(X1))
| ~ leqNat(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0] : leqNat(z,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f32,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0,X1] :
( merge(X0,nil) != X0
| merge(X0,X1) = merge(X1,X0)
| merge(X1,nil) != merge(nil,X1) ),
inference(superposition,[],[f20,f24]) ).
fof(f37,plain,
! [X0,X1] :
( merge(X1,nil) != X1
| merge(X0,nil) != X0
| merge(X0,X1) = merge(X1,X0) ),
inference(forward_demodulation,[],[f36,f24]) ).
fof(f47,plain,
! [X2,X0,X1] :
( cons(X0,X1) != cons(X0,X1)
| merge(X2,nil) != X2
| merge(X2,cons(X0,X1)) = merge(cons(X0,X1),X2) ),
inference(superposition,[],[f37,f23]) ).
fof(f52,plain,
! [X2,X0,X1] :
( merge(X2,nil) != X2
| merge(X2,cons(X0,X1)) = merge(cons(X0,X1),X2) ),
inference(trivial_inequality_removal,[],[f47]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X0,X1)
| merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1)) ),
inference(superposition,[],[f52,f23]) ).
fof(f63,plain,
! [X2,X3,X0,X1] : merge(cons(X0,X1),cons(X2,X3)) = merge(cons(X2,X3),cons(X0,X1)),
inference(trivial_inequality_removal,[],[f62]) ).
fof(f66,plain,
! [X2,X0,X1] : merge(cons(z,X0),cons(X1,X2)) = cons(z,merge(X0,cons(X1,X2))),
inference(resolution,[],[f22,f31]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ leqNat(X0,X2)
| merge(cons(s(X0),X1),cons(s(X2),X3)) = cons(s(X0),merge(X1,cons(s(X2),X3))) ),
inference(resolution,[],[f22,f29]) ).
fof(f235,plain,
! [X2,X0,X1] : merge(cons(s(z),X0),cons(s(X1),X2)) = cons(s(z),merge(X0,cons(s(X1),X2))),
inference(resolution,[],[f67,f31]) ).
fof(f419,plain,
! [X2,X0,X1] : cons(s(z),merge(X0,cons(s(X1),X2))) = merge(cons(s(X1),X2),cons(s(z),X0)),
inference(superposition,[],[f63,f235]) ).
fof(f2367,plain,
! [X0,X1] : cons(s(z),merge(X0,cons(s(z),X1))) = cons(s(z),merge(X1,cons(s(z),X0))),
inference(superposition,[],[f235,f419]) ).
fof(f2605,plain,
! [X0,X1] : merge(X1,cons(s(z),X0)) = tail(cons(s(z),merge(X0,cons(s(z),X1)))),
inference(superposition,[],[f26,f2367]) ).
fof(f2626,plain,
! [X0,X1] : merge(X0,cons(s(z),X1)) = merge(X1,cons(s(z),X0)),
inference(forward_demodulation,[],[f2605,f26]) ).
fof(f2770,plain,
! [X0] : cons(s(z),X0) = merge(X0,cons(s(z),nil)),
inference(superposition,[],[f24,f2626]) ).
fof(f2909,plain,
! [X0] : cons(s(z),cons(z,X0)) = cons(z,merge(X0,cons(s(z),nil))),
inference(superposition,[],[f66,f2770]) ).
fof(f2935,plain,
! [X0] : cons(s(z),cons(z,X0)) = cons(z,cons(s(z),X0)),
inference(forward_demodulation,[],[f2909,f2770]) ).
fof(f3510,plain,
! [X0] : s(z) = head(cons(z,cons(s(z),X0))),
inference(superposition,[],[f27,f2935]) ).
fof(f3550,plain,
z = s(z),
inference(forward_demodulation,[],[f3510,f27]) ).
fof(f3593,plain,
$false,
inference(forward_subsumption_resolution,[],[f3550,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n004.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 15:08:07 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running first-order theorem proving
% 0.24/0.31 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
% 9.06/2.18 % (447622)Detected formulas, will run a generic FOF schedule.
% 9.06/2.18 % (447627)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=1478833897:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.06/2.18 % (447633)dis-21_1_sil=8000:lcm=predicate:random_seed=4213242724: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)
% 9.06/2.18 % (447633)Refutation not found, incomplete strategy
% 9.06/2.18 % (447633)------------------------------
% 9.06/2.18 % (447633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447633)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447633)Termination reason: Refutation not found, incomplete strategy
% 9.06/2.18 % (447633)Time elapsed: 0.002 s
% 9.06/2.18 % (447633)Peak memory usage: 88 MB
% 9.06/2.18 % (447628)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=1697069250:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.06/2.18 % (447629)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=541247539:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.06/2.18 % (447631)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3356644888:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.06/2.18 % (447630)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=899302087:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.06/2.18 % (447632)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3950125930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.06/2.18 % (447631)Instruction limit reached!
% 9.06/2.18 % (447631)------------------------------
% 9.06/2.18 % (447631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447631)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447631)Termination reason: Instruction limit
% 9.06/2.18 % (447631)Termination phase: Saturation
% 9.06/2.18 % (447631)Time elapsed: 0.100 s
% 9.06/2.18 % (447631)Peak memory usage: 87 MB
% 9.06/2.18 % (447631)Instructions burned: 119 (million)
% 9.06/2.18 % (447630)Instruction limit reached!
% 9.06/2.18 % (447630)------------------------------
% 9.06/2.18 % (447630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447630)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447630)Termination reason: Instruction limit
% 9.06/2.18 % (447630)Termination phase: Saturation
% 9.06/2.18 % (447630)Time elapsed: 0.104 s
% 9.06/2.18 % (447630)Peak memory usage: 88 MB
% 9.06/2.18 % (447630)Instructions burned: 109 (million)
% 9.06/2.18 % (447632)Instruction limit reached!
% 9.06/2.18 % (447632)------------------------------
% 9.06/2.18 % (447632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447632)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447632)Termination reason: Instruction limit
% 9.06/2.18 % (447632)Termination phase: Saturation
% 9.06/2.18 % (447632)Time elapsed: 0.128 s
% 9.06/2.18 % (447632)Peak memory usage: 89 MB
% 9.06/2.18 % (447632)Instructions burned: 139 (million)
% 9.06/2.18 % (447633)------------------------------
% 9.06/2.18 % (447633)------------------------------
% 9.06/2.18 % (447642)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3849919132:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 9.06/2.18 % (447641)lrs+10_1_sil=8000:sp=occurrence:random_seed=3255065323:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 9.06/2.18 % (447642)Refutation not found, incomplete strategy
% 9.06/2.18 % (447642)------------------------------
% 9.06/2.18 % (447642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447642)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447642)Termination reason: Refutation not found, incomplete strategy
% 9.06/2.18 % (447642)Time elapsed: 0.005 s
% 9.06/2.18 % (447642)Peak memory usage: 88 MB
% 9.06/2.18 % (447642)Instructions burned: 3 (million)
% 9.06/2.18 % (447643)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1544163071:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 9.06/2.18 % (447641)First to succeed.
% 9.06/2.18 % (447641)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-447622"
% 9.06/2.18 % (447644)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3210034703:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 9.06/2.18 % (447643)Also succeeded, but the first one will report.
% 9.06/2.18 % (447642)------------------------------
% 9.06/2.18 % (447642)------------------------------
% 9.06/2.18 % (447644)Instruction limit reached!
% 9.06/2.18 % (447644)------------------------------
% 9.06/2.18 % (447644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.18 % (447644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.18 % (447644)CaDiCaL version: 2.1.3
% 9.06/2.18 % (447644)Termination reason: Instruction limit
% 9.06/2.18 % (447644)Termination phase: Saturation
% 9.06/2.18 % (447644)Time elapsed: 0.237 s
% 9.06/2.18 % (447644)Peak memory usage: 90 MB
% 9.06/2.18 % (447644)Instructions burned: 248 (million)
% 9.06/2.18 % (447641)Refutation found. Thanks to Tanya!
% 9.06/2.18 % SZS status Theorem for theBenchmark
% 9.06/2.18 % SZS output start Proof for theBenchmark
% See solution above
% 9.06/2.19 % (447641)------------------------------
% 9.06/2.19 % (447641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.19 % (447641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.19 % (447641)CaDiCaL version: 2.1.3
% 9.06/2.19 % (447641)Termination reason: Refutation
% 9.06/2.19 % (447641)Time elapsed: 0.182 s
% 9.06/2.19 % (447641)Peak memory usage: 89 MB
% 9.06/2.19 % (447641)Instructions burned: 198 (million)
% 9.06/2.19 % (447641)------------------------------
% 9.06/2.19 % (447641)------------------------------
% 9.06/2.19 % (447622)Success in time 1.165 s
% 9.06/2.19 % Vampire exiting
%------------------------------------------------------------------------------