%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 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 01:09:10 PM UTC 2026
% Result : Theorem 2.80s 1.16s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 77 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 40 ~; 29 |; 14 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 41 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( ( contains_pq(X0,X1)
& issmallestelement_pq(X0,X1) )
=> findmin_pq_res(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f58,axiom,
! [X0,X1] :
( pi_sharp_find_min(X0,X1)
<=> ( contains_pq(X0,X1)
& issmallestelement_pq(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f63,axiom,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main4_l7) ).
fof(f64,conjecture,
! [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
=> ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> ? [X3] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),X3)
& findmin_cpq_res(triple(X0,X1,X2)) = findmin_pq_res(i(triple(X0,X1,X2)),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co4) ).
fof(f65,negated_conjecture,
~ ! [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
=> ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> ? [X3] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),X3)
& findmin_cpq_res(triple(X0,X1,X2)) = findmin_pq_res(i(triple(X0,X1,X2)),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f72,plain,
! [X0,X1,X2] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ pi_sharp_find_min(i(triple(X0,X1,X2)),X3)
| findmin_cpq_res(triple(X0,X1,X2)) != findmin_pq_res(i(triple(X0,X1,X2)),X3) )
& phi(findmin_cpq_eff(triple(X0,X1,X2)))
& pi_find_min(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ! [X3] :
( ~ pi_sharp_find_min(i(triple(X0,X1,X2)),X3)
| findmin_cpq_res(triple(X0,X1,X2)) != findmin_pq_res(i(triple(X0,X1,X2)),X3) )
& phi(findmin_cpq_eff(triple(X0,X1,X2)))
& pi_find_min(triple(X0,X1,X2)) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f76,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) ),
inference(flattening,[],[f75]) ).
fof(f89,plain,
( ! [X3] :
( ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),X3)
| findmin_cpq_res(triple(sK0,sK1,sK2)) != findmin_pq_res(i(triple(sK0,sK1,sK2)),X3) )
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
& pi_find_min(triple(sK0,sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f74]) ).
fof(f90,plain,
! [X0,X1] :
( ( pi_sharp_find_min(X0,X1)
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) )
& ( ( contains_pq(X0,X1)
& issmallestelement_pq(X0,X1) )
| ~ pi_sharp_find_min(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f91,plain,
! [X0,X1] :
( ( pi_sharp_find_min(X0,X1)
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) )
& ( ( contains_pq(X0,X1)
& issmallestelement_pq(X0,X1) )
| ~ pi_sharp_find_min(X0,X1) ) ),
inference(flattening,[],[f90]) ).
fof(f100,plain,
! [X2,X0,X1] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f89]) ).
fof(f103,plain,
! [X3] :
( findmin_cpq_res(triple(sK0,sK1,sK2)) != findmin_pq_res(i(triple(sK0,sK1,sK2)),X3)
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),X3) ),
inference(cnf_transformation,[],[f89]) ).
fof(f104,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f105,plain,
! [X0,X1] :
( contains_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f106,plain,
! [X0,X1] :
( pi_sharp_find_min(X0,X1)
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f111,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ contains_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f141,plain,
! [X0] :
( findmin_cpq_res(triple(sK0,sK1,sK2)) != X0
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),X0)
| ~ contains_pq(i(triple(sK0,sK1,sK2)),X0)
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),X0) ),
inference(superposition,[],[f103,f111]) ).
fof(f142,plain,
! [X0] :
( findmin_cpq_res(triple(sK0,sK1,sK2)) != X0
| ~ contains_pq(i(triple(sK0,sK1,sK2)),X0)
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),X0) ),
inference(forward_subsumption_resolution,[],[f141,f106]) ).
fof(f143,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
| ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(equality_resolution,[],[f142]) ).
fof(f144,plain,
( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(resolution,[],[f143,f104]) ).
fof(f145,plain,
~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(forward_subsumption_resolution,[],[f144,f105]) ).
fof(f147,plain,
~ phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(resolution,[],[f100,f145]) ).
fof(f148,plain,
$false,
inference(forward_subsumption_resolution,[],[f147,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 10:51:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.80/1.16 % (281491)Detected formulas, will run a generic FOF schedule.
% 2.80/1.16 % (281500)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1025639246:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.16 % (281500)First to succeed.
% 2.80/1.16 % (281500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-281491"
% 2.80/1.16 % (281499)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1195448811:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.16 % (281498)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=1493124149:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.16 % (281496)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=4185227847:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.16 % (281501)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=868141121:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.16 % (281497)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=4182446237:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.16 % (281502)dis-21_1_sil=8000:lcm=predicate:random_seed=377178819: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)
% 2.80/1.16 % (281499)Also succeeded, but the first one will report.
% 2.80/1.16 % (281501)Also succeeded, but the first one will report.
% 2.80/1.16 % (281502)Instruction limit reached!
% 2.80/1.16 % (281502)------------------------------
% 2.80/1.16 % (281502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (281502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (281502)CaDiCaL version: 2.1.3
% 2.80/1.16 % (281502)Termination reason: Instruction limit
% 2.80/1.16 % (281502)Termination phase: Saturation
% 2.80/1.16 % (281502)Time elapsed: 0.055 s
% 2.80/1.16 % (281502)Peak memory usage: 88 MB
% 2.80/1.16 % (281502)Instructions burned: 129 (million)
% 2.80/1.16 % (281500)Refutation found. Thanks to Tanya!
% 2.80/1.16 % SZS status Theorem for theBenchmark
% 2.80/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.16 % (281500)------------------------------
% 2.80/1.16 % (281500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (281500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (281500)CaDiCaL version: 2.1.3
% 2.80/1.16 % (281500)Termination reason: Refutation
% 2.80/1.16 % (281500)Time elapsed: 0.002 s
% 2.80/1.16 % (281500)Peak memory usage: 88 MB
% 2.80/1.16 % (281500)Instructions burned: 3 (million)
% 2.80/1.16 % (281500)------------------------------
% 2.80/1.16 % (281500)------------------------------
% 2.80/1.16 % (281491)Success in time 0.309 s
% 2.80/1.16 % Vampire exiting
%------------------------------------------------------------------------------