%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:48:45 PM UTC 2026
% Result : Theorem 4.71s 1.83s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 145 ( 14 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 195 ( 84 ~; 61 |; 48 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 46 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3] :
~ ( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = k2_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ( ~ r2_hidden(X0,k4_xboole_0(X2,X3))
| ~ r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ( ~ r2_hidden(X0,X3)
| ~ r2_hidden(X1,X3) )
& ( ~ r2_hidden(X0,k4_xboole_0(X2,X3))
| ~ r2_hidden(X1,X3) )
& ( ~ r2_hidden(X0,X3)
| ~ r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f34,plain,
( r2_hidden(sK0,k2_xboole_0(sK2,sK3))
& r2_hidden(sK1,k2_xboole_0(sK2,sK3))
& ( ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3)) )
& ( ~ r2_hidden(sK0,sK3)
| ~ r2_hidden(sK1,sK3) )
& ( ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK1,sK3) )
& ( ~ r2_hidden(sK0,sK3)
| ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f27]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) ) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) ) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ? [X3] :
( ( ( ~ r2_hidden(X3,X0)
& ~ r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) )
& ( r2_hidden(X3,X0)
| r2_hidden(X3,X1)
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ( ~ r2_hidden(X4,X0)
& ~ r2_hidden(X4,X1) ) )
& ( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ( ( ( ~ r2_hidden(sK4(X0,X1,X2),X0)
& ~ r2_hidden(sK4(X0,X1,X2),X1) )
| ~ r2_hidden(sK4(X0,X1,X2),X2) )
& ( r2_hidden(sK4(X0,X1,X2),X0)
| r2_hidden(sK4(X0,X1,X2),X1)
| r2_hidden(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ( ~ r2_hidden(X4,X0)
& ~ r2_hidden(X4,X1) ) )
& ( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2) ) )
| k2_xboole_0(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f37]) ).
fof(f41,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f42,plain,
( ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK1,sK3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f44,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
r2_hidden(sK1,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
fof(f70,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k2_xboole_0(X0,X1))
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f139,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k4_xboole_0(X1,X0))
| ~ r2_hidden(X2,k2_xboole_0(X0,X1))
| r2_hidden(X2,X0) ),
inference(superposition,[],[f70,f61]) ).
fof(f315,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK3,sK2))
| r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(resolution,[],[f139,f44]) ).
fof(f316,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK3,sK2))
| r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) ),
inference(resolution,[],[f139,f41]) ).
fof(f327,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK3,sK2))
| ~ r2_hidden(sK0,sK3) ),
inference(forward_subsumption_resolution,[],[f316,f43]) ).
fof(f328,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK3,sK2))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(forward_subsumption_resolution,[],[f315,f42]) ).
fof(f330,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,sK3) ),
inference(forward_demodulation,[],[f327,f50]) ).
fof(f331,plain,
( ~ r2_hidden(sK1,k2_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(forward_demodulation,[],[f328,f50]) ).
fof(f333,plain,
~ r2_hidden(sK0,sK3),
inference(forward_subsumption_resolution,[],[f330,f45]) ).
fof(f334,plain,
~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f331,f45]) ).
fof(f475,plain,
( ~ r2_hidden(sK0,k2_xboole_0(sK3,sK2))
| r2_hidden(sK0,sK3) ),
inference(resolution,[],[f334,f139]) ).
fof(f479,plain,
~ r2_hidden(sK0,k2_xboole_0(sK3,sK2)),
inference(forward_subsumption_resolution,[],[f475,f333]) ).
fof(f480,plain,
~ r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(forward_demodulation,[],[f479,f50]) ).
fof(f481,plain,
$false,
inference(forward_subsumption_resolution,[],[f480,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 28 05:12:22 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 4.71/1.83 % (4163874)Detected formulas, will run a generic FOF schedule.
% 4.71/1.83 % (4163901)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=839282482:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.71/1.83 % (4163903)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1708343093:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.71/1.83 % (4163906)dis-21_1_sil=8000:lcm=predicate:random_seed=1715749507: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)
% 4.71/1.83 % (4163903)First to succeed.
% 4.71/1.83 % (4163903)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4163874"
% 4.71/1.83 % (4163900)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=3527433877:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.71/1.83 % (4163902)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4029751370:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.71/1.83 % (4163899)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=705100984:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.71/1.83 % (4163902)Refutation not found, incomplete strategy
% 4.71/1.83 % (4163902)------------------------------
% 4.71/1.83 % (4163902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.83 % (4163902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.83 % (4163902)CaDiCaL version: 2.1.3
% 4.71/1.83 % (4163902)Termination reason: Refutation not found, incomplete strategy
% 4.71/1.83 % (4163902)Time elapsed: 0.004 s
% 4.71/1.83 % (4163902)Peak memory usage: 89 MB
% 4.71/1.83 % (4163902)Instructions burned: 2 (million)
% 4.71/1.83 % (4163905)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3536648420:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.71/1.83 % (4163905)Also succeeded, but the first one will report.
% 4.71/1.83 % (4163906)Instruction limit reached!
% 4.71/1.83 % (4163906)------------------------------
% 4.71/1.83 % (4163906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.83 % (4163906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.83 % (4163906)CaDiCaL version: 2.1.3
% 4.71/1.83 % (4163906)Termination reason: Instruction limit
% 4.71/1.83 % (4163906)Termination phase: Saturation
% 4.71/1.83 % (4163906)Time elapsed: 0.124 s
% 4.71/1.83 % (4163906)Peak memory usage: 89 MB
% 4.71/1.83 % (4163906)Instructions burned: 129 (million)
% 4.71/1.83 % (4163919)lrs+10_1_sil=8000:sp=occurrence:random_seed=1089931973:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.71/1.83 % (4163903)Refutation found. Thanks to Tanya!
% 4.71/1.83 % SZS status Theorem for theBenchmark
% 4.71/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 4.71/1.83 % (4163903)------------------------------
% 4.71/1.83 % (4163903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.83 % (4163903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.83 % (4163903)CaDiCaL version: 2.1.3
% 4.71/1.83 % (4163903)Termination reason: Refutation
% 4.71/1.83 % (4163903)Time elapsed: 0.013 s
% 4.71/1.83 % (4163903)Peak memory usage: 88 MB
% 4.71/1.83 % (4163903)Instructions burned: 16 (million)
% 4.71/1.83 % (4163903)------------------------------
% 4.71/1.83 % (4163903)------------------------------
% 4.71/1.83 % (4163874)Success in time 0.547 s
% 4.71/1.83 % Vampire exiting
%------------------------------------------------------------------------------