%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 01:20:30 PM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 311 ( 74 equ)
% Maximal formula atoms : 47 ( 14 avg)
% Number of connectives : 435 ( 145 ~; 126 |; 138 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-3 aty)
% Number of variables : 90 ( 84 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f53,conjecture,
( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,n5)
& leq(X7,n5) )
=> ( ( X6 = pv57
& gt(pv58,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,n5)
& leq(X9,n5) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X10] :
( ( leq(n0,X10)
& leq(X10,pred(pv57)) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,n5) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) ) )
=> ! [X12] :
( ( leq(n0,X12)
& leq(X12,pred(pv57)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,n5) )
=> ( ( ~ ( pv57 = X13
& X13 = X12 )
& pv57 != X12 )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0401) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) )
& ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4) )
& ! [X6,X7] :
( ( leq(n0,X6)
& leq(n0,X7)
& leq(X6,n5)
& leq(X7,n5) )
=> ( ( X6 = pv57
& gt(pv58,X7) )
=> a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6) ) )
& ! [X8,X9] :
( ( leq(n0,X8)
& leq(n0,X9)
& leq(X8,n5)
& leq(X9,n5) )
=> ( gt(pv57,X8)
=> a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8) ) )
& ! [X10] :
( ( leq(n0,X10)
& leq(X10,pred(pv57)) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,n5) )
=> a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10) ) ) )
=> ! [X12] :
( ( leq(n0,X12)
& leq(X12,pred(pv57)) )
=> ! [X13] :
( ( leq(n0,X13)
& leq(X13,n5) )
=> ( ( ~ ( pv57 = X13
& X13 = X12 )
& pv57 != X12 )
=> a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f143,plain,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& ( pv57 != X13
| X12 != X13 )
& pv57 != X12
& leq(n0,X13)
& leq(X13,n5) )
& leq(n0,X12)
& leq(X12,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n5)
| ~ leq(X5,n5) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| pv57 != X6
| ~ gt(pv58,X7)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ gt(pv57,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,n5) )
| ~ leq(n0,X10)
| ~ leq(X10,pred(pv57)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f144,plain,
( ? [X12] :
( ? [X13] :
( a_select3(id_ds1_filter,X12,X13) != a_select3(id_ds1_filter,X13,X12)
& ( pv57 != X13
| X12 != X13 )
& pv57 != X12
& leq(n0,X13)
& leq(X13,n5) )
& leq(n0,X12)
& leq(X12,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) )
& ! [X4,X5] :
( a_select3(pminus_ds1_filter,X4,X5) = a_select3(pminus_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n5)
| ~ leq(X5,n5) )
& ! [X6,X7] :
( a_select3(id_ds1_filter,X6,X7) = a_select3(id_ds1_filter,X7,X6)
| pv57 != X6
| ~ gt(pv58,X7)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| ~ gt(pv57,X8)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10] :
( ! [X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(n0,X11)
| ~ leq(X11,n5) )
| ~ leq(n0,X10)
| ~ leq(X10,pred(pv57)) ) ),
inference(flattening,[],[f143]) ).
fof(f197,plain,
( ? [X0] :
( ? [X1] :
( a_select3(id_ds1_filter,X0,X1) != a_select3(id_ds1_filter,X1,X0)
& ( pv57 != X1
| X0 != X1 )
& pv57 != X0
& leq(n0,X1)
& leq(X1,n5) )
& leq(n0,X0)
& leq(X0,pred(pv57)) )
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| pv57 != X8
| ~ gt(pv58,X9)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10,X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ gt(pv57,X10)
| ~ leq(n0,X10)
| ~ leq(n0,X11)
| ~ leq(X10,n5)
| ~ leq(X11,n5) )
& ! [X12] :
( ! [X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5) )
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( a_select3(id_ds1_filter,sK31,sK32) != a_select3(id_ds1_filter,sK32,sK31)
& ( pv57 != sK32
| sK31 != sK32 )
& pv57 != sK31
& leq(n0,sK32)
& leq(sK32,n5)
& leq(n0,sK31)
& leq(sK31,pred(pv57))
& leq(n0,pv5)
& leq(n0,pv57)
& leq(pv5,n998)
& leq(pv57,n5)
& leq(pv58,n5)
& gt(pv58,pv57)
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) )
& ! [X6,X7] :
( a_select3(pminus_ds1_filter,X6,X7) = a_select3(pminus_ds1_filter,X7,X6)
| ~ leq(n0,X6)
| ~ leq(n0,X7)
| ~ leq(X6,n5)
| ~ leq(X7,n5) )
& ! [X8,X9] :
( a_select3(id_ds1_filter,X8,X9) = a_select3(id_ds1_filter,X9,X8)
| pv57 != X8
| ~ gt(pv58,X9)
| ~ leq(n0,X8)
| ~ leq(n0,X9)
| ~ leq(X8,n5)
| ~ leq(X9,n5) )
& ! [X10,X11] :
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ gt(pv57,X10)
| ~ leq(n0,X10)
| ~ leq(n0,X11)
| ~ leq(X10,n5)
| ~ leq(X11,n5) )
& ! [X12] :
( ! [X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5) )
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32]),skolemize(X0,sK31),skolemize(X1,sK32)],[f197]) ).
fof(f289,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f309,plain,
! [X12,X13] :
( a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(n0,X13)
| ~ leq(X13,n5)
| ~ leq(n0,X12)
| ~ leq(X12,pred(pv57)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f321,plain,
leq(sK31,pred(pv57)),
inference(cnf_transformation,[],[f198]) ).
fof(f322,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f323,plain,
leq(sK32,n5),
inference(cnf_transformation,[],[f198]) ).
fof(f324,plain,
leq(n0,sK32),
inference(cnf_transformation,[],[f198]) ).
fof(f327,plain,
a_select3(id_ds1_filter,sK31,sK32) != a_select3(id_ds1_filter,sK32,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f388,plain,
leq(sK31,minus(pv57,n1)),
inference(definition_unfolding,[],[f321,f289]) ).
fof(f389,plain,
! [X12,X13] :
( ~ leq(n0,X13)
| a_select3(id_ds1_filter,X12,X13) = a_select3(id_ds1_filter,X13,X12)
| ~ leq(X13,n5)
| ~ leq(n0,X12)
| ~ leq(X12,minus(pv57,n1)) ),
inference(definition_unfolding,[],[f309,f289]) ).
fof(f566,plain,
! [X0] :
( a_select3(id_ds1_filter,X0,sK32) = a_select3(id_ds1_filter,sK32,X0)
| ~ leq(sK32,n5)
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv57,n1)) ),
inference(resolution,[],[f389,f324]) ).
fof(f567,plain,
! [X0] :
( ~ leq(n0,X0)
| a_select3(id_ds1_filter,X0,sK32) = a_select3(id_ds1_filter,sK32,X0)
| ~ leq(X0,minus(pv57,n1)) ),
inference(forward_subsumption_resolution,[],[f566,f323]) ).
fof(f573,plain,
( a_select3(id_ds1_filter,sK31,sK32) = a_select3(id_ds1_filter,sK32,sK31)
| ~ leq(sK31,minus(pv57,n1)) ),
inference(resolution,[],[f567,f322]) ).
fof(f575,plain,
~ leq(sK31,minus(pv57,n1)),
inference(forward_subsumption_resolution,[],[f573,f327]) ).
fof(f594,plain,
$false,
inference(forward_subsumption_resolution,[],[f575,f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 10:14:34 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.20/0.29 % (74117)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (74127)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=659082060:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (74123)% WARNING: option uhcvi not known.
% 0.20/0.29 % (74126)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1783118377:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (74122)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2770929486_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (74128)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4147962041:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (74127) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-74117-74127"...
% 0.20/0.29 % (74123)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3696336950:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (74124)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3288427203:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (74125)dis+10_1_sil=32000:sp=arity:random_seed=1160552519:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (74127)...printing done.
% 0.20/0.29 % (74127)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (74127)------------------------------
% 0.20/0.29 % (74127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (74127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (74127)CaDiCaL version: 2.1.3
% 0.20/0.29 % (74127)Termination reason: Refutation
% 0.20/0.29 % (74127)Time elapsed: 0.007 s
% 0.20/0.29 % (74127)Peak memory usage: 12 MB
% 0.20/0.29 % (74127)Instructions burned: 22 (million)
% 0.20/0.29 % (74117)Success in time 0.039 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------